High-resolution measurements of swordfish skin surface roughness

The three-dimensional morphology of swordfish skin roughness remains poorly understood. Subsequently, its importance to the overall physiology and hydrodynamic performance of the swordfish is yet to be determined. This is at least partly attributable to the inherent difficulty in making the required measurements of these complex biological surfaces. To address this, here two sets of novel high-resolution measurements of swordfish skin, obtained using a modular optical coherence tomography system and a gel-based stereo-profilometer, are reported and compared. Both techniques are shown to provide three-dimensional morphological data at micron-scale resolution. The results indicate that the skin surface is populated with spiny roughness elements, typically elongated in the streamwise direction, in groups of up to six, and in good agreement with previously reported information based on coarser measurements. In addition, our data also provide new information on the spatial distribution and variability of these roughness features. Two approaches, one continuous and another discrete, are used to derive various topographical metrics that characterize the surface texture of the skin. The information provided here can be used to develop statistically representative synthetic models of swordfish skin roughness.


Introduction
Many practical engineering problems involve the interaction between a fluid and a solid boundary.Nevertheless, our ability to accurately predict the extent to which the topography of a given surface will influence the properties of the flow remains an open challenge, which comes with related economic consequences (Chung et al 2021).Part of the issue relates to the broad variety of surfaces that can be encountered and this is coupled with the uncertainty surrounding which roughness characteristics to focus on, making an exhaustive investigation of the parameter space prohibitively expensive.
One potential approach to circumvent this problem, and thus improve understanding, is to turn to the natural world, and fish skin in particular (e.g.Bechert et al 2000, Sudo et al 2002, Choi et al 2012, Bixler and Bhushan 2013, Drelich et al 2018).For fishes, the outer surface of the skin represents the interface between their body and the external fluid environment, allowing for homeostasis as well as influencing locomotion (Lauder et al 2016, Wainwright 2019).The primary benefit of studying fish skin is that it gives an example of a realistic roughness structure which we can hypothesize, has evolved to optimize the hydrodynamic performance.Hence it may have greater potential to guide the development of synthetic surfaces where, for example, it is desirable to minimize the drag penalty, control heat transfer or achieve antifouling or antimicrobial conditions.A precedent has already been established in this regard through extensive investigations into the properties of the dermal denticles of sharks for drag reduction (e.g.Dean and Bhushan 2010, Domel et al 2018, García-Mayoral et al 2019, Lloyd et al 2021) and antifouling (e.g.Sullivan and Regan 2011, Pu et al 2016, Chien et al 2020).However, despite the success with cartilaginous fish, little work has been conducted on bony fish (Lauder et al 2016).This is perhaps somewhat surprising given the number of species exhibiting similar hydrodynamic performance to sharks (e.g.tuna, billfish), albeit with distinctive surface morphology (see e.g.Nakamura 1983, Wainwright et al 2018).In this respect, swordfish represent one of several potentially fruitful examples to study.Swordfish (Xiphias gladius) are members of the billfish family (Collette et al 2006) and are recognized as being amongst the fastest swimming fish in the ocean (Aleyev 1977).Many hypotheses have been proposed to explain their exceptional hydrodynamic capabilities.However, the functional significance of their skin roughness remains virtually unexplored.Despite their familial association, and the similarity in their reported hydrodynamic characteristics, the scale morphology of the swordfish is quite distinct from the other species of billfishes.Early sketches of scale morphology (e.g.Arata 1954, Potthoff andKelley 1982) show a particular form consisting of a basal plate from which a single conical spine protrudes.As swordfish approach a length of 200 mm, these scales first appear at specific dorsal, ventral, and lateral locations ('row scales') and then at intermediate locations between ('scatter scales'), developing posteriorly and anteriorly, until the majority of the body is populated, including the rostrum (bill).The scatter scales are initially smaller but eventually grow to become equal in size to the row scales.As the fish matures the scales develop multiple recurved conical spines along the basal plate.Beyond the larval stages, the rostral and cranial scales disappear while the tips of the spines elsewhere tend to become blunt and the row and scatter scales become indistinguishable from one another.Potthoff and Kelley (1982: figure 32) indicate that a typical scale on a 668 mm long specimen has a triangular basal plate, approximately 1 mm long, with up to 6 blunt spines which are all curved towards the posterior and range between 20 to 100 µm in height.Nakamura et al (1951) describe changes in scale development in swordfish across a range of specimen sizes from 21 mm to 2280 mm, noting their gradual disappearance with age.They noted that the spines on the scales are easily detached upon contact and since they do not degenerate they must be 'deciduous' during some stage of growth.Many other early studies describe the adult swordfish as being scaleless (e.g.La Monte 1958, Walters 1962, Ovchinnikov 1970, Beckett 1974, Palko et al 1981, Nakamura 1983).Arata (1954) mentions certain conflicting reports of scale development from previous studies and concludes that scales must be lost at some stage beyond the fish reaching four feet (1.22 m) in length.As noted, Potthoff and Kelley's (1982) measurements demonstrate the presence of scales on a specimen 668 mm in length, and more recently, Govoni et al (2004) show photomicrographic evidence of scales in an adult specimen, 3300 mm in length.Govoni et al (2004) state that some of the confusion surrounding the presence of scales stems from the fact that the dermis above the scales thickens as the swordfish ages, which buries all but the tips of the spines on the scales.The spine tips themselves are often easily abraded and fractured when caught and processed, further masking their existence.
From a hydrodynamic perspective, to properly uncover the functional significance of the scales, it is imperative to understand them as the flow would see them.Therefore, measurements of the outer surface of the skin that reveal the surface manifestation of these subcutaneous features are required.As of yet, however, these features remain to be mapped and carefully quantified.At least one important factor that has limited the accumulation of data on skin roughness is the inherent difficulty in measuring these complex biological surfaces.It is worthwhile to note that this point applies more broadly to most bony fish (Lauder et al 2016).
One of the earliest attempts to capture the highresolution morphology of bony fish scales was made by Sudo et al (2002) who carried out surface profilometry measurements on the scales of a type of surfperch and rockfish using an automatic focus microscope attached to a motorized x-y stage.The authors were able to produce a representative threedimensional digital model of each of the scales, capturing details on the order of tens of microns.More recently, Muthuramalingam et al (2019) used a digital microscope to map and reconstruct the surface scales of European bass and common carp.Alongside this, a new line of research into fish scale morphology has been established by Wainwright and Lauder (2016) who used gel-based surface profilometry to resolve micron-scaled features on the skin of a bluegill sunfish over an area of approximately 7.5 by 5 mm.The technique has further been demonstrated to work in vivo and on fish skin coated in mucus (Wainwright andLauder 2017, Wainwright et al 2017).
Profilometry measurements are limited to capturing details on the outer layer of the skin and therefore, techniques that are capable of imaging through solid objects, such as micro-computed tomography (µCT), have also been employed to capture threedimensional information on fish scales throughout the dermal layer (see e.g.Yang et al 2015, Wainwright and Lauder 2016, Wainwright et al 2017).A drawback of µCT is its inherent inability to image and distinguish soft tissues, which is an important component of the skin of many fishes.Optical coherence tomography (OCT), on the other hand, is an alternative volumetric technique offering a noninvasive and non-destructive approach for capturing volume measurements through partly transparent media (Huang et al 1991).As such, OCT is well suited to the imaging of fish skin however, the adequacy of this technique for the assessment of roughness properties of billfish skin remains to be determined.
The aim of this study is therefore to advance understanding of some of these issues by reporting novel high-resolution measurements of skin samples from the body of a swordfish using both a modular OCT system and a gel-based stereo-profilometer.Following this introduction, the measurement of the swordfish skin samples is described in §2.Results are provided in §3, looking firstly at bulk statistical properties of the measured skin surface, and secondly, at the geometrical characteristics of the discrete roughness elements identified on the skin surface.The paper closes in §4 with a discussion of the hydrodynamic implications of the findings and conclusions in §5.

OCT
A sample of fresh swordfish was obtained from a local fishmonger in Aberdeen, UK.OCT was then used to conduct a volumetric measurement through a portion of the dermal layer.The measurement was carried out at Thorlabs facility in Lübeck, Germany, using a modular system comprising a Ganymede base unit (GAN620) and OCT-LK4-BB scan lens kit.This system was chosen for its high spatial resolution, fast scanning rates, and large depth of field.The field of view of the lens kit was 16.0 × 16.0 × 2.0 mm in the longitudinal (x-axis), transverse (y-axis), and vertical (z-axis) directions, respectively, and a total of 800 × 800 × 1024 data points were measured within this sample volume.An extract from a characteristic image slice in the x-z plane at y = 8 mm is shown in figure 1, highlighting the presence of multiple spines at non-equidistant spacings.
The OCT system had a penetration depth of approximately 500 µm, revealing information about the epidermal layer, in particular, scale pockets that lie just beneath the spiny protrusions.The shape and occurrence of these features are in good agreement with the photomicrograph results reported by Govoni et al (2004).

Gel-based stereo profilometry 2.2.1. Initial measurement using the GelSight sensor
A GelSight Mobile 0.5x sensor (GelSight Inc., Waltham, MA, USA), a type of gel-based stereoprofilometer, was also used to measure the surface roughness of the skin, taken from the body of the same swordfish, at two independent locations, adjacent to where the OCT measurement was made.The GelSight (GS) sensor provided surface elevation measurements at 13.6 µm spacing within a field of view of 16.8 mm by 14.0 mm.The sensor was calibrated before the measurements, using a standardized set of targets with predefined geometrical properties, and the measured results were found to be within  1.0% of the known values.Further, the sensor was clamped to a motorized three-axis stage to improve vertical control while pressing the gel cartridge onto the skin surface.
Since the appropriate pressing force cannot be known a priori, the vertical height of the sensor, z sens , for the first measurement location was established by manually inspecting a real-time scan of the surface.Initially, the sensor was carefully lowered until the point at which it made contact with the sample.It was then lowered by an additional 1.25 mm, in 250 µm increments, to the final measurement height, z sens0 , by which point the visual appearance of the scan was no longer changing with increasing pressing force.The sensor was then retracted and translated (∆x = 10 mm, ∆y = 15 mm) to the second measurement location before again being lowered to z sens0 .The corresponding images of the skin surface from the GS scans are shown in figure 2.
Figure 2 shows that both scans are populated with the same spine-like protrusions that were observed in figure 1 and that they are grouped in varying numbers.For example, in some places, single spines are observed, whereas in other places distinct clusters with up to six spines are visible.This picture is in good agreement with the sketches published by Potthoff and Kelley (1982) and Nakamura (1983).However, the GS scans also reveal ring-like structures, examples of which are highlighted in the inset of figure 2(a).These features do not appear to have been reported previously and are not as readily identifiable from the OCT data set, owing to its lower spatial resolution.There is also an apparent difference in the skin morphology between locations 1 and 2, with the roughness features at location 1 appearing longer and more sparsely distributed relative to location 2. As to whether this reflects a physical change in the roughness characteristics between the sample locations or whether it is a result of the measurement technique will be assessed in the next section.

Sensitivity of the GelSight sensor to the applied pressing force
To check the sensitivity of the GS sensor to changes in the pressing force (i.e.vertical position of the sensor), six additional measurements were made at a third location on the skin, offset by ∆x = ∆y = 5 mm, from location 2, with the sensor height retracted vertically in increments of 250 µm between each measurement from an initial height of z sens0 .The standard deviation of the sample, σ z , was then calculated at each of the six sensor heights and the results are plotted in figure 3.There is an approximately linear decrease in σ z between z sens = z sens0 and z sens = z sens0 + 0.75 mm, after which the value of σ z falls rapidly as the gel cartridge no longer fully conforms to the skin.More specifically, the measured standard deviation of the surface is seen to decrease by 2.7 µm, a 25% change, for a 0.75 mm change in sensor height.
Returning to the apparent differences in the visual appearance of the GS scans from locations 1 and 2, it could be that an element of the observed difference is due to inherent location-dependent variation in the roughness.However, current knowledge of swordfish scale morphology is insufficient to verify if such differences are physically plausible.Rather, it is deemed more probable, given the relatively small spatial separation (compared to body length) between locations 1 and 2 and based on the sensitivity analysis, that the GS sensor was applying a lower pressing force at location 1.This was likely due to a small difference in the thickness of the swordfish sample between locations 1 and 2. This is further supported by a comparison of the standard deviation of the measured surfaces at location 1 (σ z = 6.58 µm) and location 2 (σ z = 11.9 µm), a 45% difference, corresponding to an equivalent difference in sensor height of ∼1 mm, according to figure 3. Further, as will be shown later (see e.g.table 2), the value of σ z at location 2 closely matches the results from the nonintrusive OCT approach and the published results of Wainwright et al (2019).For this reason, only the data from the scan at location 2 is taken forward for comparison with the OCT data.
Lastly, it is worthwhile noting that these discrepancies could only be properly checked after the GS measurements had been completed and the data had been pre-processed, following the steps outlined in §2.3, by which time it was no longer possible to repeat the measurements.This was first due to the degradation of the swordfish skin itself and second due to damage to the paint on the gel cartridge of the GS sensor, which itself was only available for a limited time.The cartridge problem is already a noted issue of performing gel-based surface profilometry on biological surfaces (see e.g.Wainwright et al 2017) but it is hoped that the findings here can offer additional instruction to others when planning and executing similar kinds of measurements.

Summary of the final data set
A number of pre-processing steps were applied to the raw data before performing the remaining analysis.First, the location of the outer surface of the skin sample was extracted from the OCT volume data.The elevation of the outer surface, z s , was identified at every (x,y) point in the volume as the z coordinate having the maximum image intensity.Second, to keep the sample dimensions consistent and free from large-scale heterogeneities, both the OCT and GS scans were cropped to a uniform size of 12 mm by 8 mm.Third, low-wavelength curvature ('form') inherent in the raw data was removed through a process of detrending by fitting and then subtracting a cubic spline smoothing function to the cropped data.This process set the mean value of z s equal to zero.Fourth, all OCT data points with a value greater than 40 µm below the mean were deleted (∼3% of all measured points).This threshold was chosen to match the minimum surface elevation measured by the GS sensor, which, unlike the OCT system, cannot measure below the surface.Deleted data was replaced through interpolation using an inpainting algorithm (D'Errico 2023).Finally, to further reduce high-frequency noise, an edge-preserving bilateral filter was applied to the filtered OCT data.The resultant surfaces are shown in figure 4, wherein good general agreement in the visual appearance of the measurements from both systems can be observed.A more robust assessment of their similarities is carried out next.

Results
In the following section, we use two complementary statistical approaches to characterize the surface roughness of the swordfish skin samples.The first considers the surface as a random field of surface elevations and is referred to as a 'continuous' approach, whereas the second approach considers the surface roughness to be comprised of distinct elements and is hence termed a 'discrete' approach (Grinvald andNikora 1988, Nikora et al 1998).According to the discrete approach the surface can be characterized by properties such as the geometrical dimensions of the elements (e.g.size, height, width, steepness, etc.) and their spatial distribution (e.g.spacing, orientation, etc.).However, it is not always possible to unambiguously define such distinct roughness features, particularly on complex biological surfaces like the swordfish skin considered in this study.Additional tools are therefore required to enable a fuller classification of the surface roughness characteristics for such cases.In this respect, the continuous approach has been successfully applied in the study of many complex, natural surfaces, particularly gravel bed rivers (e.g.Nikora et al 1998, Marion et al 2003, Smart et al 2004, Aberle and Nikora 2006).Within the framework of the continuous approach, each surface can generally be written as z s = f (x,y,t) where t is time.Such a random field can be completely characterized by its m-dimensional probability density as m→∞ (Bendat and Piersol 2011).In practice, it is not possible to measure the higher-dimensional properties and instead, it becomes necessary to simplify the problem.For example, if the surface is assumed to be stationary, homogeneous, and Gaussian, then moment functions (e.g.correlation functions, structure functions, and power spectral density functions) of the second order will provide full information about the surface (Nikora et al 1998).This method is advantageous as it provides an additional set of objective metrics to quantify surface roughness features that can then be more easily compared with available information on other types of realistic surface roughness.The surfaces measured by OCT and GS, and analysed in this section, are openly available in an online repository (Stewart et al 2023).

Statistical properties of skin surface roughness: continuous approach
When considering the highly dynamic behavior of a swimming fish, one might expect temporal effects to be non-negligible, however, in the present case, the surfaces are assumed to be static, with no dependence on time i.e. z s = f (x,y).We deem this to be a reasonable approximation, to build an initial understanding before addressing the more complex dynamic case.In the following analysis, we use the probability density function (PDF) and corresponding moments (i.e.variance, skewness, and kurtosis) as well as moment functions (i.e.correlation functions, structure functions, and power spectra) to characterize each surface.
Looking first at the normalized two-dimensional autocorrelation function, R(∆x,∆y), figure 5 compares the results computed from the GS and OCT data sets, respectively.To ensure the orientation of the samples are comparable, the measured surfaces have been rotated such that the major axis of R(∆x,∆y) is aligned with the horizontal axis.All subsequent results are derived from the rotated data.The agreement between the OCT and GS data sets is reasonable, with both plots in figure 5(a) exhibiting contours with an elliptical shape.The elliptical shape of the contours provides a visual measure of the anisotropy of the surface roughness.Both the shape and spatial extent of the contour patterns in figure 5 reflect, in a statistical sense, the geometrical properties of the predominant roughness features that were seen in figures 2 and 4.
One-dimensional sections of the twodimensional autocorrelation functions, extracted along the horizontal (∆y = 0) and transversal (∆x = 0) axes, are compared in figures 5(b) and (c), respectively, where differences between the OCT and GS data sets can be more readily visualized.Therein we comment on the observation that the correlation appears minimal at spatial lags beyond 0.3 mm.
A complementary measure to the correlation function is the so-called structure function which is the second moment (i.e.variance) of the surface elevation differences between two spatially separated points.An expression for the two-dimensional structure function can also be formulated according to equation ( 1) (e.g.Nikora et al 1998): where ∆x = n•δx, ∆y = m•δy, δx and δy are the sampling intervals and N and M are the total number of surface elevation points in the x-and y-directions, respectively.For homogenous random fields the second-order structure function D 2,hom (∆x,∆y) is related to the correlation function through equation ( 2) (Monin and Yaglom 1975): The results from computing equations (1) and (2) are plotted in figure 6.In this case, we are only showing the one-dimensional profiles, normalized on 2σ z 2 , extracted from the full two-dimensional array.The similarity in the profiles of D 2,hom and D 2 across all spatial lags confirms the spatial homogeneity of the skin samples.At large spatial lags the profiles tend to a constant value (D 2 →2σ z 2 ), as expected.Studies of other types of roughness have reported the presence of a scaling region at the smallest spatial lags, where D 2 varies as a power function (i.e.D 2 ∝ ∆x α x and D 2 ∝ ∆y α y ), before leveling off in the transition zone (see e.g.Nikora et al 1998).However, in  the present case, D 2 appears only to approach such a region, without exhibiting any definite power law scaling.For reference, a power function with an exponent of 1.8 is shown in figures 6(a) and (b), and although it does capture the behavior of D 2 at the very smallest spatial lags, it only incorporates a couple of data points.
Figure 7 shows power spectra for the GS and OCT measurements.These one-dimensional profiles have been integrated out of the corresponding twodimensional power spectra.There is a close agreement in the behavior of the plots in figure 7(a), with both exhibiting a saturation region at large wavelengths (low wavenumbers), where the spectra are essentially flat, and a region at small wavelengths (high wavenumbers) where the spectra decay rapidly To the authors' knowledge, this is the first report of the spectral structure of fish skin roughness and so it is not yet possible to comment on the generality of the findings.However, the three-range spectral shape and quasi-self-similar properties of the scaling region are in good agreement with many other natural surfaces, from gravel and fluvial riverbeds (Hino 1968, Nikora et al 1997, Butler et al 2001), to glaciated landscapes (Hubbard et al 2000, Mankoff et al 2017) and the ocean floor (Bell 1975), to name a few.The roughness structure in these examples results from a complex interplay of physical processes, and the reason behind the common emergence of fractality is still open to debate (e.g.Hinkle et al 2020).For the swordfish, on the other hand, it is predominantly a combination of biological growth mechanisms and long-term evolutionary processes that have led to the development of the observed surface roughness properties.In this respect, Stewart et al (2019) have demonstrated the importance of the spectral exponent to the overall hydraulic resistance of a surface.For all else equal, they observed a 50% reduction in the friction factor of a surface with a spectral exponent of 3.0 relative to a corresponding surface with an exponent of 1.0.We may then speculate that the observed roughness patterns have developed to offer certain hydrodynamic advantages, set within the restrictions imposed by any preferred (e.g.self-similar) growth mechanisms.
Figure 7(b) shows spectra as a function of the transverse wavelength λ y .The extent of the scaling region is reduced compared to the profiles in figure 7(a), with λ y,c1 and λ y,c2 ranging between 330 and 90 µm, respectively.Further, both the OCT and GS results show a steeper drop-off within the scaling region, with β y between 3.4 and 3.6 (see table 1), which can be taken as another measure of anisotropy of the surface roughness.Although, we can observe from the confidence intervals of these estimates that additional measurements would be required to clarify the significance of the discrepancies between β x and β y , for the GS data at least.
Figures 7(c) and (d) show the spectra in premultiplied form, which is useful for indicating the wavelengths that make a dominant contribution to the variance of the surface.In this case, the locations of the peak in each premultiplied spectrum are identified in figures 7(c) and (d) and are listed in table 1.These values correspond to roughness wavelengths of λ x,peak between 430 and 570 µm, and λ y,peak between 290 and 360 µm, and thus are similar to the geometrical dimensions derived from the analysis of the discrete roughness elements later in §3.2.3.The ratios of these peak wavelengths are given in table 1 and may provide a metric for quantifying the anisotropy of the roughness features, wherein for the present case a value of approximately 1.5 is observed.
Based on the results from the correlation and structure function plots in figures 5 and 6, each measured skin sample was subdivided into 1 mm by 1 mm non-overlapping blocks, to provide 96 statistically independent sub-samples, from which further statistical properties could be computed.The resulting PDFs, averaged over the 96 sub-samples, are shown in figure 8.The PDFs are closely aligned in the region z s ⩾ 15 µm, where the prevalence of the spiny roughness elements on the surface of the skin is  [Kuz,n], are the mean values of standard deviation, skewness and kurtosis, respectively, estimated across the Ns = 96 sub-samples.Confidence intervals for ⟨σz⟩ and standard errors for ⟨Skz⟩ and ⟨Kuz⟩ are approximated following the procedure described in Stewart et al (2019).
seen to positively skew the distributions.The PDF for the GS data is steeper around the mean and shows a sharper drop-off in measured values below the mean, relative to the OCT data, which is representative of the greater scatter in the results obtained through OCT.
The corresponding standard deviation, skewness and kurtosis of the nth sub-sample was estimated according to equations ( 3)-( 5), respectively, where N x and N y are the number of grid points in the x-and y-directions of each sub-sample, respectively.Table 2 lists the mean values for these moments, calculated from the 96 individual estimates.Similar values, as reported by Wainwright et al (2019), are also listed for comparison.In general, there is close agreement between the magnitudes of the three parameters, ⟨σ z ⟩, ⟨Sk z ⟩ and ⟨Ku z ⟩, across all three data sets.
The values for standard deviation, ⟨σ z ⟩, range from 11.6 to 12.8 µm and can be used in formulating a measure of the overall characteristic roughness height (see §4).Non-zero values for skewness, ⟨Sk z ⟩, and kurtosis, ⟨Ku z ⟩, confirm that the distribution of surface elevations of the skin is non-Gaussian, as already indicated by the shape of the PDFs in figure 8 but now the magnitude of these parameters is confirmed.
As mentioned, the positive values for ⟨Sk z ⟩, varying between 0.7 and 1.3, are attributable to the prevalence of the spiny roughness elements which populate the skin surface.The positive values for ⟨Ku z ⟩, varying between 1.4 and 1.7, suggest an increased intermittency of surface elevations, relative to a Gaussian distribution, due to the occasional presence of large roughness features.Wainwright et al (2019) reported similar non-Gaussian properties for the skin of odontocetes whereas, for a selection of other species, including trout (Salmo trutta), near-Gaussian distributions were found (Wainwright et al 2017), thus indicating that the results are not general but instead are species specific.

Statistical properties of skin surface roughness: discrete approach
Having summarized the bulk statistical properties of the skin surface roughness, next we consider the characteristics of the individual spines and scales.For the purposes of this study, what we refer to as spines and scales are in fact the surface manifestation of the underlying roughness features that exist within the epidermal layer.However, given that this same surface 'footprint' is what the flow encounters as the fish swims, the characteristics of these surface features are deemed to be appropriate for developing representative synthetic models of swordfish skin roughness.The approach in this section may be considered as 'discrete' , focusing predominantly on aspects of the discrete roughness elements, and should be viewed as complementary to the 'continuous' approach of §3.1 (e.g.Nikora and Goring 2004).

Locating the scales and spines
The first step in this part of the analysis was to isolate the individual scales on each measured sample.This was done through a process of manual image segmentation of the surfaces.The result was the creation of a binary mask, consisting of individual segments demarcated by boundary lines.Each segment contained a single scale and was individually numbered for ease of reference during subsequent analysis.Any segment touching the boundary of the sample was labelled and ignored in any proceeding analysis.There was a degree of subjectivity in determining what constituted a scale however, the result of the manual segmentation was deemed to be more reliable than an alternative automated attempt which was made using a watershed algorithm.Further, to improve consistency across the samples, whenever there was a doubt as to the extent of a given scale, it was subdivided into smaller components.This means that the results on properties such as scale length are likely conservative.Within each segment (i.e.scale), individual peaks (spines) were identified separately in the xand y-directions.Only those locations where the peak coincided in both directions were counted.Additional filters were applied to minimize the likelihood of counting erroneous peaks, including a minimum peak height threshold of 1.0 × σ z and maximum peak width of 200 µm.

Spine properties
Counts of spines per scale were made for each of the samples and the results are shown in figure 9.The scale counts have been normalized by the total number of scales observed on the sample.Between 35% to 52% of the observed spines are from scales with just a single spine.
There is an approximately logarithmic drop-off in the number of observations of spines per scale, reaching a maximum in all cases of six spines per scale.The tendency for this drop-off in spine count per scale could be influenced by the fragility of the spines themselves, with prior studies suggesting that the spines can be easily damaged through handling (e.g.Govoni et al 2004).It could also be the case that less prominent spine tips have no surface footprint such that only the most prominent spines are detectable, however, this latter assertion is not supported by the OCT measurements.Given there is no published information on spine counts to date, the generality of the results here remain to be verified.In addition, the total body length or age of the swordfish was unknown in this case but in future it would be interesting to check whether there is any dependency of the results seen in figure 9 with the body length (age) of the fish.
In addition to spine count, the peak height of each spine, z p , was measured and is shown in figure 10.The bulk statistics corresponding to the distributions of the peak heights of the spines are given in table 3, where close agreement across all measured properties can be observed.
The measured peak heights range between 8 µm and 70 µm, with a median height of approximately 30 µm.The average distance between the spine peaks within an individual scale, δ peak , was also calculated.Note, this calculation was only performed for scales with two or more spines.In turn, the reported values of ⟨δ peak ⟩ in table 3, represent the ensemble-averaged values of δ peak , calculated over all scales where two or more spines were identified.

Scale properties
Scale length, width, and aspect ratio are now investigated, along with scale spacing.Scale length L and width w are defined as the length of the major and minor axes, respectively, of an ellipse fitted to the region where a scale has been identified.A spacing parameter, s, is defined for each scale as the distance between the centroid of that scale and the centroid of its nearest neighbor.PDFs for L, w, w/L, and s are shown in figure 11 while corresponding median values for these parameters are listed in table 4. The measured parameters are again in close agreement between the OCT and GS data sets.The reported values for L and w of approximately 370 and 240 µm, respectively, match the extent of the correlation contours shown in figure 5 and lends further support to the earlier assertion that the contour patterns reflect the presence of those roughness features.With respect to the spacing, it is interesting to note that the ratio, s/w, is close to unity, indicating some degree of regularity in the spatial distribution of the scales.This point will be explored in more detail in §4.
The dependence of the spine and scale properties on their spatial (x and y) location within the sample was also assessed and the corresponding plots are available as supplementary material.The plots show no discernible effect on the spine height or the size   and spacing of the scales with their longitudinal or transverse location.This is most likely a consequence of the limited size of the measured samples and such variations may only become appreciable when considering samples from across the entire body of the fish.

Discussion on hydrodynamic implications
The values reported thus far help to characterize the absolute size of the roughness elements on the skin.However, the effect of this roughness on the hydrodynamics of the swordfish is contingent on the overlying flow conditions.We can make preliminary estimations of these effects by forming non-dimensional ratios between the dominant roughness length scales and the relevant length scales of the flow.The first of these, the roughness Reynolds number, is given in equation ( 6), where, ∆ is the roughness height, which can be reasonably approximated as 4σ z (see e.g.Nikora et al 2019), u * is the shear velocity, and ν is the kinematic viscosity.The combination ν/u * is known as the viscous length scale, δ ν .Here, parameters normalized on δ ν are denoted with a '+' .
To estimate the value of ∆ + we can first infer the value of u * from equation ( 7), where τ is the shear stress acting on the boundary (skin) of the fish, ρ is fluid density, F is the total drag force acting on the boundary (skin) of the fish, A is the wetted area of the fish, C D is the drag coefficient and U is the swimming speed.Equation ( 7) has been derived assuming that the total drag force is due to skin friction alone, following Sagong et al (2013)  BL of the swordfish to be 1.28 m, again in line with the value reported in their study.An alternative formulation of the roughness Reynolds number, z p + , based on the average peak height of the spines, is also shown in figure 12. Which of the parameters, z p + or ∆ + , is most relevant to characterizing the hydrodynamics of the swordfish remains to be determined.At the slowest speeds, between 0.6 and 2.4 BL s −1 , figure 12 suggests that the flow will be at the threshold between what is traditionally assigned as hydraulically-smooth and transitionally-rough flow (i.e.around ∆ + ∼ 5, Schlichting and Gersten 2017).Following Nikora et al (2019), we may also observe what is posited as marginally rough-bed turbulent flow, which will depend on the relative importance of dispersive stresses to the overall bed shear stress.
Another ratio of interest is the non-dimensional spacing between the roughness elements, given by equation ( 8), This non-dimensional spacing parameter is also shown in figure 12 as a function of the swimming speed.The potential significance of s + for drag reduction has been demonstrated in numerous studies on shark denticles and riblets (see e.g.Dean and Bhushan 2010, García-Mayoral and Jiménez 2011, Lloyd et al 2021).Optimum results have been achieved when the streamwise aligned riblets have spacings of s + between 10 and 20.An alternative parameter, l g + = (A g + ) 0.5 , which is based on the cross-sectional area A g + of the spacing between riblets, and hence accounts for the height as well as the spacing between riblets, was found by García-Mayoral and Jiménez (2011) to collapse available experimental data better than simply using s + .According to García-Mayoral and Jiménez (2011), riblet geometries with an l g + value of 10.7 ± 1.0 provided optimum drag reduction.For reference, we also plot l g + in figure 12.We should note however that in our case we deal with 'discontinuous riblets' made of spines rather than with continuous riblets traditionally studied.Indeed, it is not possible to draw a direct comparison between those previous studies and the present swordfish skin samples, owing to the difference between the idealized geometrical arrangement of the riblets and the natural irregularity in the spatial distribution of the roughness features on the swordfish skin.However, based on the average values of the swordfish skin roughness metrics, as reported here, we can identify a particular range of flow conditions where further investigation of the flow field might be warranted.This region covers typical cruising swimming speeds, between 0.4 and 2.3 BL s −1 , where s + ranges between 8 and 41, l g + ranges between 2.5 and 12.8 and ∆ + (z p + ) ranges between 1.7 (1.1) and 8.4 (5.2).Thus, in this region, we capture the expected optimum values for s + (≈ 10) and l g + (≈9.7-11.7)as well as the expected transition from hydraulicallysmooth to transitionally-rough flow (∆ + ≈ 4-8).
From an evolutionary perspective, it is appealing to suppose that the skin would be optimized to minimize viscous and pressure drag, and hence energy expenditure, especially at cruising speeds, where the swordfish will spend the majority of its time (see e.g.Block et al 1992).Of course, we can note that Sagong et al (2013) reported no apparent dragreducing properties of the skin roughness at cruising swim speeds.They chose to match the bulk Reynolds number, based on the total length of the fish, in their investigation.However, they give no indication as to the values of other important similarity numbers, in particular ∆ + or s + .Without this information, the results cannot be definitively contextualized and as such, while their study was an important step in improving understanding of billfish hydrodynamics, the potential significance of the skin roughness remains unclear.
Uncovering new examples of riblet-like drag reduction is desirable owing to the practical applications that could follow.However, it is only one aspect of a wider study that needs to be undertaken to fully understand the function of the skin roughness and its role in the fundamental hydrodynamics and overall physiology of the swordfish.From this perspective, attention should also be paid to sprinting conditions, which, based on available published information on swimming speeds of swordfish (e.g.Walters 1962, Ovchinnikov 1970), would be on the order of 10-12 BL s −1 .Extrapolating the results from figure 12 to an assumed maximum speed of 12 BL s −1 suggests that the flow will remain in the transitionally-rough regime throughout.However, these projections are to be interpreted with caution, given that we are ignoring effects such as body curvature, pressure gradients, and flow three-dimensionality, etc. when deriving u * , and so it may prove problematic to extrapolate the behavior to higher swimming speeds, where these effects will become increasingly important.

Conclusions
This study reports high-resolution measurements of the three-dimensional morphology of swordfish skin for the first time.As part of this, two techniques, OCT and gel-based stereo profilometry, have been applied and compared.While the adequacy of gelbased stereo-profilometry for capturing skin surface roughness of bony fish in general is already well established, here its use is further extended to provide a detailed account of swordfish skin roughness for the first time.Similarly, OCT has been shown here to provide an effective surface representation of the swordfish skin.OCT also offers additional information throughout the epidermal layer, in particular indicating the presence of scale pockets, in a nonintrusive manner.
Initial visualization of the surfaces revealed the appearance of spine-like protrusions across the entirety of the measured samples, in good agreement with available information on swordfish scale morphology.However, an additional suite of topographical metrics, calculated from 'continuous' and 'discrete' approaches, have also been reported.This includes, for the first time, information on the spectral structure of the skin roughness, which in this case was observed to have self-similar properties within a certain range of wavelengths.The measured skin thus shares similarities with many other natural and engineered surfaces.Furthermore, the PDF of the surface elevations was found to be non-Gaussian, owing primarily to the effect of the spiny roughness features populating the skin.
The results, of course, are not without limitation, and future work in this area should seek to address the lack of samples that are currently available.Targeted sampling strategies, in the spirit of Loose et al (2017), are preferred to properly identify intra-specific variations across the body of the fish as well as ontogenetic variations for fish of varying ages.Regardless, the information provided here should be sufficient in the first instance for developing representative synthetic surfaces which share the same statistical characteristics as the swordfish skin.In turn, such idealized models can then be implemented in both numerical simulations and physical experiments, with a view to uncovering the possible functional significance of the skin not only to the hydrodynamics of the swordfish itself but also possibly to additional application areas.

Figure 1 .
Figure 1.Extract of a typical image slice in the x-z plane at y = 8 mm from the OCT measurements.

Figure 2 .
Figure 2. Extracts of scans of swordfish skin made using the GS sensor at location 1 (a) and location 2 (b).The inset in (a) shows an example of ring-like features found on the surface.Note, each extract is approximately 11.3 × 6.4 mm in size.

Figure 3 .
Figure 3. Standard deviation of the swordfish skin surface as a function of the GelSight sensor height (pressing force).Note, zsens = zsens0 = 0 mm was the sensor height used to record the measurements at locations 1 and 2.

Figure 4 .
Figure 4. Plan (x-y) view of the processed swordfish skin samples measured by the GelSight sensor (left) and by OCT (right).Note, the y-coordinate of the OCT measurement has been offset by +8.5 mm for visualization purposes only.

Figure 5 .
Figure 5. (a) Two-dimensional correlation patterns for the GS and OCT datasets, respectively and corresponding one-dimensional line extracts along the (b) ∆y = 0 and (c) ∆x = 0 axes.

Figure 6 .
Figure 6.One-dimensional extracts of D2(∆x,∆y) along the ∆y = 0 (a) and ∆x = 0 axes (b), respectively.The lines represent the estimation of D2(∆x,∆y) computed from equation (1) while the symbols represent the estimation of D 2,hom (∆x,∆y) from equation (2).The dash-dot line in (a) and (b) shows a reference power function with an exponent of 1.8 and the solid horizontal line corresponds to the saturation value of 2σz 2 .

Figure 7 .
Figure 7. Wavenumber spectra as a function of λx (a) and λy (b).The dash-dot line in (a) and (b) shows a reference curve with a spectral exponent of β = 3.The same spectra are also shown in premultiplied form in (c) and (d), respectively.The '+' (GS) and '•' (OCT) symbols in figures (c) and (d) indicate the location of the peak magnitude in the premultiplied spectra.Note, the premultiplied spectra in (c) and (d) were low-pass filtered (thick lines) to permit easier identification of the peak location.

Figure 8 .
Figure 8. Probability density functions of surface elevations from the GS and OCT measurements.Note, zs = 0 is the mean bed level.

Figure 9 .
Figure 9. Spine counts per scale for GS and OCT samples, where ζ is the scale count normalized on the total number of scales on the sample.

Figure 10 .
Figure 10.Histograms of individual spine peak heights for OCT and GS data sets.

Figure 11 .
Figure 11.Histograms of scale properties including scale length L (a), scale width w (b), scale aspect ratio w/L (c) and scale spacing s (d).

Table 1 .
Spectral exponents, βx and βy, and wavenumbers, λx ,peak and λy ,peak , corresponding to the location of the peak magnitude in the premultiplied spectra.Note: the '±' values denote the 95% confidence intervals for βx and βy. a

Table 4 .
Median values of the key geometrical properties of the scales shown in figure11.The standard deviation of each parameter is also listed.
Sagong et al (2013)gure12as a function of swimming speed, which is given in terms of Body Length's per second (BL/s).As part of our assumptions, we use the drag coefficients reported bySagong et al (2013)and we take the Figure 12.