Study on the Load Characteristics of Submerged Body Under Internal Solitary Waves on the Continental Shelf and Slope

Based on the high-quality observation data and the numerical simulation,the evolution characteristics of internal solitary waves(ISWs)and the load on the suspend submerged body are studied on the continental shelf and slope separately.The observed ISWs exhibit the first mode depression ISWs.The amplitudes of ISWs on the shelf and slope areas reach 50 m and 80 m,respectively.The upper layer velocity in the westward direction is about 0.8 m/s on the continental shelf and 0.9 m/s on the continental slope during the passing through of ISWs.The lower layer is dominated by the eastward compensating flow.In the vertical direction,the water in front of the wave flows downward,while the water behind the wave flows upward,and the maximum vertical velocity exceeds 0.2 m/s.Numerical simulation results show that the larger the amplitude of ISWs,the larger the load on the submerged body.The force on the submerged body by ISWs is dominated by the vertical force,and the corresponding maximum vertical forces on the continental shelf and slope are−25 kN and −27 kN.The submerged body is subjected to a large counterclockwise moment and the sudden change of the moment will also cause the submerged body to capsize.This paper not only gives a deeper understanding of the characteristics of ISWs from the deep continental slope to the shallow continental shelf,but also has a certain guiding value for the prediction of ISWs and for marine military activities.

Simulation model of SAR remote sensing of turbulent wake of semi-elliptical submerged body

In terms of the 2-dimensional hydrodynamic simplified model of a semi-elliptical submerged body moving horizontally at high speed, by using the full-spectrum model of SAR（synthetic aperture radar） remote sensing and taking the effect of oceanic interior turbulence on surface gravity capillary waves into account, applying the k-ε model of turbulence with internal wave mixing, and adopthag the Nasmyth spectrum of oceanic turbulence, the 2-dimensional simulation model of SAR remote sensing of this semi-elliptical submerged body is built up. Simulation by using this model at X band and C band is made in the northeastern South China Sea （21°00＇ N, 119°00＇ E）. Satisfactory results of the delay time and delay distance of turbulent surface wake of this semi-elliptical submerged body, as well as the minimum submerged depth at which this submerged body which cannot be discovered by SAR, are obtained through simulation.

Multi-Parameter Influence Analysis of Interaction Between Internal Solitary Wave and Fixed Submerged Body

To obtain the interaction characteristics between Internal solitary waves(ISWs)and submerged bodies,a three-dimensional numerical model for simulating ISWs was established in the present study based on the RANS equation.The velocity entrance method was adopted to generate the ISWs.First,the reliability of this numerical model was validated by comparing it with theoretical and literature results.Then,the influence of environmental and navigation parameters on interactions between ISWs and a fixed SUBOFF-submerged body was studied.According to research,the hydrodynamic performance of the submerged body has been significantly impacted by the ISWs when the body is nearing the central region of the wave.Besides,the pitching moment(y')will predominate when the body encounters the ISWs at a certain angle between 0°and 180°,and the lateral force is larger than the horizontal force.Additionally,the magnitude of the force acting on the body is mostly affected by the wave amplitude.The variation of the vertical force is the main way that ISWs affect the hydrodynamic performance of the bodies.The investigations and findings discussed above can serve as a guide to forecast how ISWs will interact with submerged bodies.

Time-frequency analysis of internal waves generated by a towed and self-propelled submerged body model

The spectrogram,based on a short-time Fourier transform,can visualize the time-dependent frequency spectrum of waves and is easy to compute.This time-frequency analysis method provides crucial information about waves generated by moving vessels and has been utilized to analyze Kelvin ship waves and internal waves.To further study the internal waves induced by a submerged body,an experiment is conducted for the towed and self-propelled SUBOFF model in a stratified fluid.The internal wave elevation signals are captured using electronic conductivity probes.Comparing with the calculation results of theoretical model,the high-frequency component of internal waves is identified.The high-frequency component has the exact same characteristics in both the towed and self-propelled model experiment and is consistent with the theoretical results for all Froude numbers.Therefore,this component is composed mainly of lee waves.Through spectral characteristics identification,a low-frequency component is discovered in the spectrogram in addition to the lee wave component.The intensity of the low-frequency component is tightly related to the vortex structure behind the submerged body.The vortex structure depends on the net momentum imparted by the submerged body.Therefore,this component is composed mainly of wake waves induced by the vortex structure.

SECOND-ORDER DRIFT FORCES AND MOMENTS BETWEEN TWO SUBMERGED BODIES IN WAVES ON 3D METHOD

Two near field methods, namely the integral method and differential method, were presented for giving second order mean drift forces and moments between two fixed submerged bodies in regular waves. For the integral method, with a series of mathematical manipulations, second order drift forces and moments could be easily expressed by distributed sources which could be calculated by source distribution techniques with the assumption that the amplitude of ship motions are small on the basis of the linear 3D frequency theory. For the differential method, drift forces and moments could be expressed by the derivative of velocity potential with respect to space coordinate. Because two bodies would behave as a single body while the clearance is very large, the numerical results of one sphere in such case were given and compared with analytical results of a single sphere which does not involve the effect of free surface. When submerged depth becomes enough large, a good agreement can be reached. Then the integral method was used to predict the second order drift forces and moments of two submerged spheres and spheroids with a small lateral separation distance in waves compared with the numerical results obtained by the differential method and they agree well. By comparison, it indicates the interaction effects between two submerged bodies have a profound influence on the drift forces and moments. In this paper, the forward speed effect on submerged spheres was also considered.

TWO-DIMENSIONAL FINITE ELEMENT METHOD FOR DETERMINING NONLINEAR WAVE FORCES ON LARGE SUBMERGED BODIES

In this paper, we first develop the far field asymptotic solutions of the second-order scattering waves for the vertical plane problem taking the second-order Stokes waves as the incident waves. The asymptotic solutions satisfy the Laplace equation, the sea bed and free surface boundary conditions and are the out-going waves. Then the radiation conditions of the second-order mattering waves are derived by using the asymptotic solutions. By using the two-dimensinal finite clement method with the radiation conditions imposed on the ar- tificial boundaries, the computer program, known as 'NWF2', for determining nonlinear wave forces on large submerged bodies has been written. As a numerical example, nonlinear wave forces on a semi-circu- lar cylinder lying on the sea bed arc presented.