Effect of underwater vehicle wake on sound propagation characteristics in stratified medium

Due to the uneven distribution of seawater temperature and salinity, the density distribution at different depths is different, thus forming a density step layer with a certain gradient. Acquiring the wake internal wave field generated by underwater vehicles passing through this layered structure and mastering its modulation characteristics for the sound field can provide new technical support for the tracking and identification of underwater vehicles. In this paper, the real size model of a certain type of underwater vehicle is taken as the research object to explore the characteristics of its wake internal wave field, and the influence of navigation parameters on the wake field and the change of winning characteristics under the influence of internal waves are simulated and analyzed. The results show that the navigation parameters of underwater vehicles have obvious influence on the wake field, and then have specific influence on the sound field structure in a certain range, especially on the sound signal of the sound field.


Introduction
The sea area under our jurisdiction is more than 3 million square kilometers, so how to effectively safeguard our maritime rights and interests has become an important topic.Underwater warfare is a key part of the battle for sea power, and underwater vehicles such as submarines with good concealment have always been an important combat weapon in underwater warfare, and anti-submarine warfare has become one of the important tasks in modern Marine warfare [1] .With the continuous improvement of science and technology, the self-noise level of underwater vehicles is gradually reduced and close to the Marine environment noise level, so it is urgent to develop the detection technology of underwater vehicles, and the combination of acoustic and non-acoustic detection methods will become the main means of underwater vehicle detection in the future.
Due to the uneven distribution of seawater temperature and salinity, there are differences in density distribution at different depths, and a certain gradient density step layer is formed.When the underwater vehicle travels, it compresses and disturbs the sea water, which breaks the original equilibrium state and forms internal waves.The non-uniform distribution of density will cause gravity and buoyancy to change in the depth direction, and the restoring force of internal waves is lower in frequency, wider in diffusion and longer in duration than that of ordinary water waves such as surface gravity waves.The internal wave generated by the motion of underwater vehicles can be used as an important means of detection and tracking.
According to the different excitation sources, internal waves can be divided into two categories: volume effect internal waves and wake effect internal waves.Experimental studies show that in a fluid with density stratification, when the motion speed and depth of the object are fixed, the near field will produce multi-mode nonlinear internal waves [2,3] , and the nonlinearity will gradually increase during the propagation process, and finally the internal wave mode tends to be uniformed [4,5] .Keller and Munk [6] for the first time use ray theory to study the volume effect internal waves in stratified fluids and derive the waveform governing equation.The research on the propagation characteristics of internal waves to sound was elaborated in depth in the 1980s.Apel [7,8] et al. conducted experiments in the New Jersey continental Shelf, and the research showed that the generation of internal waves would cause the energy fluctuation of 1~7dB in the propagation process of sound waves, and analyzed the formation reasons through the normal wave coupling theory.
Most of the Marine environmental models established in the experiment are dominated by ideal strong density layered models and continuous density layered models, which are different from the actual complex ocean conditions.In this paper, COMSOL Multiphysics simulation software was selected to solve the special hydrodynamic problem of underwater vehicles moving in dense layered fluids.A dense-mixed layered environmental model that is closer to the actual Marine environment is constructed, and a slender rotating body model of a certain type of underwater vehicle is established to explore the characteristics of its wake internal wave field during navigation and analyze the impact of changes in navigation parameters.Bellhop is used to analyze the change of sound field characteristics under the influence of internal waves, compare the influence of wake on sound propagation loss, arrival structure and sound signal waveform, give the correlation between the target parameters of underwater vehicles and sound field, and explain some phenomena in the process of sound propagation.

Environmental parameters
Combined with the data of the ocean density step layer measured by the Center of Ocean Meteorology and Hydrology in the South China Sea [9] , a density stratified fluid model of mixed stratified form based on the temperature density flow theory is established.The model is divided into three layers, the upper layer thickness of the step layer is 20m, the thickness of the step layer is 20m, its strength is 0.25kg/m 4 , and the maximum depth of the sea water is 200m.The temperature in the calculation domain is set as a vertical distribution, and the relationship between temperature T and depth h satisfies the function of equation ( 2

Vehicle model
The underwater moving object studied in this paper is a full-size model of slender rotary body based on a foreign submarine.The total length of the model is 115m, the diameter of the front end is 10m, and the minimum diameter of the back end is 5m.Comsol multi-physical field software is used to build the model, which does not consider the noise produced by the shell vibration and the propeller.The threedimensional structure of the model is show in fig 3

Simulation Analysis
According to the actual combat situation of the submarine, the speed of the underwater vehicle is set to 10 knots and 20 knots respectively, and the sailing depth is 30m.The simulation shows that the flow field results tend to be stable after 60s.Therefore, the results of 60s are taken as the research object to analyze the change rules of speed, temperature and sound speed under different sailing speeds.According to the experimental results of excited internal wave properties of towed submersible in densestratified fluid with different aspect ratios conducted by Wang Jin et al. [10] , it can be seen that the dominant type of internal waves is related to two critical transition Froude numbers   and   , which have an approximate linear relationship with the aspect ratio.When   <   , the volume effect internal wave, namely Lee wave, is the main control internal wave.When   <   <   , the Lee wave is still the main internal wave, but the influence of wake internal wave is increasing gradually.When   >   , the wake effect internal wave turns into the main control internal wave.The linear relationship between   and   and length-diameter ratio is shown in the following equation   = 0.0957 + 0.7254 (3-1)   = 0.2391 + 1.7579 (3-2) According to the Froude number   = / (where U is the characteristic velocity of the object, D is the characteristic diameter of the object, N is the maximum floating frequency, N(z)=[g(∂ρ/∂z)/ρ]^(1/2)).It is calculated that the Froude number Fr=10.101>  =4.50755 when the speed is 10 knots, so the internal wave of wake effect is the main control internal wave at the two speeds.
In the simulation calculation, the underwater vehicle made steady motion, the sailing depth was 30m, and it was in the density step layer with a gradient of 0.25kg/m 4 .The following figure shows the velocity field results under the sailing speed of 10 knots and 20 knots respectively.When the flow velocity field tends to be stable, an area similar to a semicircle will appear at the front end of the underwater vehicle, and the flow velocity in this area is small, while the flow velocity behind this area becomes larger than the initial flow velocity due to the mutual extrusion of fluids.There will be a confluence zone behind the underwater vehicle, the flow rate in this area gradually increases from inside to outside, and the greater the speed, the longer the length of this area.It can be seen that when the depth is less than 30m, the sound velocity decreases compared with the original sound velocity, and the shallower the depth, the more obvious the change of sound velocity, with the maximum change of sound velocity about 0.9m/s.When the depth is greater than or equal to 30m, the sound speed increases compared with the original sound speed, and the deeper the depth, the more obvious the change, the maximum change of sound speed is about 2.5m/s.It can be seen from the figure that the sound velocity of the tail with a depth of less than 30m significantly increases and appears a peak value with a amplitude of 4m/s, while the sound velocity of the tail with a depth of 30-60m significantly decreases and appears a peak value with a amplitude of 4m/s.Moreover, the change of speed has a more obvious impact on the distance from the rear 200m of the vehicle.Under the simulated speed of 10 knots and 20 knots, the disturbance difference between the two wakes on the sound velocity is about 0.5m/s.A sound source is set at a depth of 60m, the amplitude of the sound source is 1N/m, and the depth of the calculation area is 200m and the horizontal distance is 1km.In order to study the influence of wake internal waves on acoustic signal propagation, a sound source is set at a depth of 20m and a sinusoidal signal with a frequency of 20kHz is transmitted, and the receiver is set at a depth of 40m and a distance of 1km.be seen that the influence of signal arrival time is not obvious when wake internal waves exist.However, due to the energy loss of acoustic signal when it passes through wake internal wave field during propagation, the received signal amplitude decreases at different depths.

Conclusions
In this paper, a mixed stratified fluid was constructed with the shallow sea step bed as the research background, and the real size slender rotary body model was taken as the research object.The influences of different speeds on flow field velocity distribution, sound velocity field distribution, propagation loss and sound signal propagation were simulated and analyzed, and the following conclusions were drawn: 1.The velocity field at different speeds is characterized by a lower velocity at the front end of the vehicle, a larger velocity at both sides and greater than the initial velocity, and a confluence zone at the rear of the vehicle, whose length increases with the increase of speed.
2. The wake internal wave generated breaks the original sound velocity distribution of the environmental field, and the sound velocity at different depths is affected to different degrees.The difference between the speed of 10 knots and 20 knots on the sound velocity is about 0.5m/s.
3. The wake internal wave field formed by underwater vehicles will have an impact on sound propagation loss, and the change of speed will lead to obvious fluctuation of propagation loss within a certain distance of underwater vehicles.
4. The impact of wake internal waves on signal arrival time is not obvious, and its impact is mainly reflected in the impact on the amplitude of signal arrival structure.With the increase of speed and receiving depth, the amplitude of arrival signal decreases more and more obviously.

1 )Figure 1 .
Figure 1.Vertical distribution of temperature Figure 2. Vertical distribution of density

Figure 3 .
Figure 3. Three-dimensional model of underwater vehicle

Figure 6 .Figure 7 .
Figure 6.Sound velocity field distribution at 10 knots Figure 7. Sound velocity field distribution at 20 knots The change results of the sound velocity field when the speed is 10 knots and 20 knots show in fig 6 and fig 7. The results show that the sound velocity distribution near the tail of the vehicle is broken, and the stratified narrates suddenly, and gradually widens with the increase of distance, which is approximately the same as the initial sound velocity field.

Figure 8 .Figure 9 .
Figure 8. Sound speed comparison between initial and speed 10 knots at different depths Figure 9. Sound speed comparison between initial and speed 20 knots at different depths The comparison between the initial sound velocity and the disturbed sound velocity under different speeds show in fig 8 and fig 9.It can be seen that when the depth is less than 30m, the sound velocity decreases compared with the original sound velocity, and the shallower the depth, the more obvious the change of sound velocity, with the maximum change of sound velocity about 0.9m/s.When the depth is greater than or equal to 30m, the sound speed increases compared with the original sound speed, and the deeper the depth, the more obvious the change, the maximum change of sound speed is about 2.5m/s.

Figure 15 .
Comparison of propagation loss curves at 100m depth under different conditions The comparison of propagation loss curves at a depth of 100m under different conditions show in fig 15.It can be seen from fig 15(a) that the scattering of the craft itself has a great influence on the sound propagation loss.It can be seen from fig 15(b)(c) that there are differences in the amplitude of propagation loss at 0-320m behind the vehicle, in which the maximum difference is 22dB at 230m at 10 knots and 14dB at 150.5m at 20 knots.The propagation loss amplitude at the distance of 320-1000m from the rear of the vehicle is delayed.It can be seen from fig 15(d) that there is a significant difference in propagation loss at different flow rates starting from 540m later, while the peak occurs earlier at 20 knots.