Current Velocity Impacts from Interaction of Semidiurnal and Diurnal Tidal Constituents for Tidal Stream Energy in East Flores

The combination of the Semidiurnal and Diurnal Tidal Constituents results in a variability of tidal range and current speed through the months of the year. Tidal stream predicted from astronomical harmonic constituents and also tidal stream is a current that its speed can be optimized as renewable energy. Constituent Semidiurnal components have huge impact on the forming of tidal stream phase. Larantuka Strait is one of the highest current velocities in indonesia waters. This study uses the method of calculating the mean least squares analysis, with the approach of the vector of the current component to the tidal harmonic constituent. Tidal velocities exceeds 3 m/s in this area, this value is very potential. The results of current and tide analysis at this area showedstrong interaction. 0.73 at Formzhal value shows mixed tide type, prevailing semidiurnal. Constituent values which dominate in the forming of strong current are M2 with value of 2.22 m/s, and another semi diurnal contituent, S2 value at current vector is 1.11 m/s. The linkages between current velocity with tide shows advantage in the production of available maximum power in a day will varies on each tide type. An asymmetric pattern of both tidal elevation and tidal velocity can be observed during each day.


Introduction
East Flores Waters is an area with the dominance of narrow strait morphology.This location is very suitable to be developed as renewable energy sources [1], such as tidal range [2] and tidal stream [3]. Larantuka Strait is one of optimal strait can be optimized to conversed potential tidal stream. Recent study result this area is very potential area with current velocity exceeding 3 m/s [4], another study result Larantuka Strait have tidal range almost 3 meters on spring phase [2]. There are two forms that are carried out in utilizing tidal energy, tidal range and tidal stream [5].Tidal current energy is the most favorable renewable energy source according to the physical oceanography characteristics in East Flores Waters especially.
Tidal power was one of form of renewble energy to be used by human life [6]. Hydrokinetic resources from tide involves extracting power from moving tidal stream by fast to generate electricity. Fluid driven by tidal has a great advantage in hydrokinetic energy sources, considering that sea water has a density of 800x greater than that of wind [7]. As we know, tidals are driven by the gravitational interaction of the moon (lunar) and sun (solar), and the tide causes a gradient to the water level, then the mass of waters are move, hereinafter referred to as tidal currents. Basically tidal currents can be predicted, because they have periodic harmonic constituents. The combination of the semidiurnal and diurnal tidal constituents result in a variability of tidal range and current speed through months of the year. There are dozens of other harmonic forcing constituents (components) of tide, each with a different period and amplitude [7].In most areas in the strait morphology the semidiurnal constituents play dominan role. Previous studies describe from one of strait at East Flores Waters, Molo strait result this area has rapid change of M2 amplitude and phase difference from java-banda sea to Indian Ocean [4]. Others similiar dominant, Mansuar strait result the strong current is produced by amplitude and phase differece of the M2 constituents, meanwhile diurnal constituent only has phase lag with small amplitude change [8]. A significant diurnal component results in different type of tidal cycles. Sites with dominant S2 and M2 tides show a simple pattern of two tidal cycles in a day. Areas dominated by K1 and O1 components have one cycle a day. [4] As previously studies Godin, 1991 [9] [10], asymmetry in current velocity may derive from three sources; density-driven circulation, the local influence of bathymetry and topography, and nonlinear interactions between tidal constituents. In harmonic analyses, this asymmetry aliases energy in the primary tidal constituents to higher frequencies (e.g., M2 aliased to shallow water constituents M4, M6, etc.). In term of power production these harmonic analyses needed to develop how interaction harmonic constiutuents with strong current appearance. Adventages from this analyses is tidal current can be predicted, in some case it can be modified by wind stress acting for extended periods.

Scope
The scope of this study was to analyse harmonic components from interaction of semidiurnal and diurnal tidal constituents (M2, S2, K1, O1) that possibly worked and have an impact on current velocity in East Flores waters. Data collection was carried out at the sample area, Larantuka Strait as a representation of the waters in the East Flores region. Depth averaged layers are used to analyze, tidal currents velocity that are reduced to a single dimension by neglecting vertical velocities.

Data Collection
The ADCP measurement used in this study have been obtained from instrument sea-bed mounted at Larantuka Strait, East Flores Waters. The accoustic instrument has been ran a 75kHz ADCP between October 30 th , 2017 until November 13 th , 2017 during 15 days (neap-spring cycle). The ADCP locations on UTM projections are 51, E 502571 N 9080955 are shown figure 1.
The ADCP-Instruments transmit sounds, commonly referred to as pings, of known frequecy along three beams into water collumn. The ocean velocity in three dimentions are relative to the instruments [11]. The ADCP dataset use here consist 10 minutes and some 60 minutes essembles, vertically the ADCP data are separated into 2 meters bins at 10 layers, but in this study we used depth averaged layer to determine current velocity impacts from interaction of semidiurnal and diurnal tidal constituents for tidal stream energy at site study, Configurations shown in table 1. . Thetidal current harmonic analysis is based on a least-squares fit of the current velocity observations that is specified at a set of m/s points. The analysis is strengthened by utilising known relationship tidal constituents found at a neighbouring reference site [13]. The least squares has similarities of analyze to Fourier analysis with linear regression, but is preferable because tidal frequencies are not integer multiples of a fundamental frequency (as is required for Fourier analysis) [10]. Measured currents are ensemble averaged over a 10 minute interval prior to harmonic analysis to smooth turbulent fluctuations. The least square method is a tidal calculation method by ignoring meteorological factors, this method essentially allowfor determination of harmonic constituent factors dominant driven tidal current at site of study.As previously on section 2, tidal current streams direction in favor of speed (ebb signed negative, flood signed positive). The equations used in this method are as follows: cos ( ) and = sin ( ) at set of meter poin; ℎ is elevation of current velocityi ; are amplitude component; is the frequency of a given constituent; 1 are periode component, is phase of component; and 0 is still water level at set meter point. The tidal constituents that have been extracted, three category of principal constituents, are listed in Table 2 along with their respective period and frequency.Constituents are included in order of influence, as determined by equilibrium tide theory [14], a least-squares equation of the form given in equation (1)  Current harmonic hodograph is the ellipse parameters [11] are applied for semi-major and semi-minor axes of current harmonic, ellipse inclination, and greenwich phase lag. A simple illustration of the ellipse parameters is shown in Figure 2.The major and minor axes represent maximum and minimum current speeds of the given tidal harmonics, the inclination is the counterclockwise angle between the east direction and the major axis.
(1)  Figure 2. Illustration of a rotating tidal current ellipse and parameters. Maj is the Major axis and Min is the Minor axis. The counter clockwise angle between East and the northern major axis, is the inclination of the ellipse. The star marks where in the ellipse cycle the current is at the time of the maximum equilibrium tide at the Greenwich Meridian. [11] A the Formzhal number is used to analyze the tidal type. The amplitude of the principal diurnal and semidiurnal constituents (lunar and solar) are compared by this number. It is expressed as [4]: where, AK1 and AO1 are the amplitudes of lunar diurnal tides and AM2 and AS2 are the amplitudes of principal lunar and solar semidiurnal. A Formzhal number F ≤ 0.25 indicates two tidal cycles per day, and F > 3 indicates a single cycle per day. Formzhal number in between create mixed tides. For 0.25 < F ≤ 1 the mix is principally semidiurnal, partly diurnal, whilst for 1 < F ≤ 3 the mix is principally diurnal, partly semidiurnal. However, complex interactions between the components can occur [4].

Power Density Analysis
The instaneous power density of a flowing fluid incident on a tidal current turbine is given by equations following as [6]: WherePis kinetic power energy of tidal stream,A are the efficiency and the area in direction of stream of the turbine, respectively, and is the density of salt-water (1025 kg/m 3 ), and V is the current speed (m/s), by convention, kinetic power density is expressed in units of kW/m 2 , mean kinetic power density and ebb/flood asimmetry are calculated similiarly to currents.

Tidal curent analysis of velocity components
Tidal current velocity analysis on the 15-days measurements deployed at averaged dept are presented in Fig 3 and 6 with 0.8 m/s at the spring phase, it shows that current pattern is not cappeble, at the previously section has been explained non-harmonic fetures emerge caused density, local influence (bathymetri/ morfologi), and non-linear interactions [9] [10].  Tidal current have linkage to tide level change, tidal current are produced by the large quantities of water moving toward or away from site as the tide change. Figure 4 shows the elevation of tidal range and currents velocity are compared at time series function each velocity component (v and u velocity). The figure 4 shows elevation of tide have the mixed pricipally semidiurnal by typed, is characterized by two tidal cycle a day with two high tides and two low tides are unequal in height. V-velocity from figure 4 (top panel) explained during flood tide, when the water level is rising between peak low and high tides, the tidal current flows toward shore. During an ebb tide, when that water level is falling between high and low tides, the tidal current moves from north to east of Larantuka Strait.The greatest tidal currents occur midway between high and low tide.
Analyzed results are a slack tide is when there is no current. slack tides occur near peak high and peak low tide when the flow of water is changing direction. Figure 4 v-velocity at the top panels shows that slack time occur at the peak level of ebb -1.40 m the v-velocity level shows no current with 0.096 m/s. Similiar condition shows at u-velocity slack time occur at peak level of tide ebb show current with 0.056 m/s. as theoriticaly this condition occur cause tidal generator force, in this condition equilibrium occurs so that no momentum transfer occurs, which results in the absence of a period of moving water. Other analyzed shows that current emerge when tidal level at near 0, as example from site measurement shown at v-velocity graphs (figure 4) maximum value -3.41 m/s and water level -0.013 m, from u-velocity maximum value of current is 0.845 m/s at water level -0.013 m. Moving waters toward and away through strait are ussually the strongest current, in addition strait morphology and bathimetri have influenced occour moving current by strong.

Tidal curent analysis of harmonic components
Least-square analyzed for tidal level measured by ADCP result show at figure 5. Figure 5 show type of tidal is mix is principally semidiurnal, with formzhal value is 0.73. In a mixed tidal cyclethe tides also occur twice daily, but the two high tides and two low tides are unequal in height (figure 5.) It mean tidal velocity with strong current emerge twice at ebb current, and twice at flood current, and slack water condition emerge each peak condition, ebb or flood condition.   Figure 6 describe the two major semidiurnal an two major diurnal tidal constituents from our leastsquare analyzed of the measurement data recorded. M2 as principal lunar semi-diurnal tidal constituents, as the dominant constituent. Maximum M2 value tidal curent speedsare 2.22 m/s show at figure 7 top panels its about 63.3% from total speed probability, and has overal average 1.1 m/s. The ellipses are generally elongated with the major axes oriented approximately meridionally of our measurement site. The second most dominant harmonic component is S2, the principal Solar semi-diurnal tide. Overall, the maximum S2 tidal current speeds at the positions of the ellipses in Figure 6 are approximately half speed of the maximum M2 current speeds.These condition also describe at figure 7 all panels showed by blu line curve. Accordingly, the greatest S2 tidal current speeds are 1.11 m/s or 31.6% from total current measurement. The major axis of the S2 ellipses are oriented more or less meridionally,The phase of the S2 tidal current is quite variable, revealing no clear propagating pattern compared to that we see in the phase of the M2 tidal current [9], with phase 335.9 o , semi-major axis from S2 components is given 1 The two main diurnal tidal constituents K1 and O1 on average, both have their respective maximum speeds (see figure 7, top panels) that are 0.124 m/s (2.85% from total current measurement) and 0.07 m/s (1.99% from total current measurement). The orientation / inclination of degree of the ellipses of the diurnal constituents is quite similiar with semi-diurnal constituents, that are 75 o for K1 and 76.    Figure 8 shows kinetic power density from conversion measurements result by equation 7 (smoothed to remove the effect of residual or non-harmonic constituents), the harmonic generate from 4 tidal constituents are dominant, and residual between harmonic constituent and measurements for kinetic power density.The reason for use of a reduced number of tidal consituents (on this case we provide from 4 constituentsM2. S2. K1, O1) use principally to simplify interpretation of data, also this constituents are semi-diurnal and diurnal predominant generate velocity with strongest current. Harmonic from 4 tidal constituents predominant are describes the major features of kinetic power density, there are no residuals of up to 1 kW/m 2 , maximum kinetic power density from residual appearence is 0.876 kW/m 2 throughout the tidal cycle. This condition occour caused these residuals have little effect on operational metrics, as shown in the first column of Table 3. Figure 8 is describe peak flood and ebb currents have maximum average kinetic power density are also well-described. Spring condition have maximum kinetic power density with 21.7 kW/m 2 from measurement conversion, 21.2 kW/m 2 generated from 4 tidal constiuents semi-diurnal and diurnal predominant (M2. S2. K1, O1), also 0.876 kW/m 2 for residual current conversion of kinetic power density. We analyzed these condition caused metrics for speed and power density are comparable, even with the cubic dependence of power density on speed. Also see equation 7 describe velocity of currents are directly proportional with kinetic power density [6], these condition applied for whole tidal cycle. From these results, we conclude that harmonic analysis providesa robust fit to measured currents in the context of tidal energy potential.   11 The analyzed with which the tidal stream show current velocity is impact from interactional semidiurnal and diurnal tidal constituent, although other variable components also influence the emergence of current velocity strongly.

Conclusion
From these result we conclude Larantuka Strait, East Flores Waters have 0.73 of formzhal value, means type of tide is mix is principally semidiurnal. Semi-diurnal constituents are dominant caused current velocity; M2 2.22 m/s show (63.3%), S2 is 1.11 m/s (31.6%), K1 is 0.124 m/s (2.9%) and O1 is 0.07 m/s (1.9%). From the fourth constituents estimation of kinetic power density obtained 21.2 kW/m 2. Harmonic analysis provides a robust fit to measure currents in the context of tidal energy potential. Harmonic constituents from interaction of semidiurnal and diurnal tides have impacts on faster current velocity.