Study On Evolution Mechanism Of Ocean Internal Waves Based On High Order KdV Equation

The ocean forms a stable density stratification structure in the vertical direction because of the uneven distribution of light and marine life,and when disturbed from inside or outside,it generates oceanic internal waves at the stratification interface.The oceanic internal waves in the natural environment have larger amplitude,longer wavelength and carry higher energy,and therefore have a great impact on marine ecology and human marine activities.Internal solitary waves are the main form of ocean internal waves,thus the nonlinear Kd V equation with solitary wave solution is commonly used in the study of ocean internal waves.This article explores the evolution mechanism of ocean internal waves based on the weakly nonlinear Kd V equation,the m Kd V equation and the e Kd V equation which have high-order nonlinear terms under the twolayer fluid model.In addition,numerical wave generation experiments are conducted to analyze the applicability conditions of these three equations in the study of ocean internal waves,and the effects of vortex and trailing waves on the waveform of ocean internal waves are also studied.Based on the theory of the KdV equation for shallow water long waves,the Kd V equation is derived from the Laplace equation and the model boundary conditions for two fluid layers,and its isolated wave solutions are obtained.By studying the derivation process and the isolated wave solutions,it is found that the weak nonlinearity assumption is the main reason for the poor performance of the Kd V equation in modeling large amplitude oceanic internal waves,based on which the e Kd V equation with higher-order nonlinear terms is introduced;and for the shortcoming that the Kd V equation loses its significance when the depth ratio of the two fluid layers reaches the limit condition,the m Kd V equation is introduced in the limit condition.By analyzing the isolated wave solutions of the three equations,it is concluded that the Kd V and e Kd V equations have better simulatability for weak nonlinear waves,but m Kd V is more applicable in stronger nonlinear wave simulations.It is also found that there is an upper limit to the isolated wave amplitude that can be simulated by e Kd V and m Kd V.In the numerical experimental part,this paper improves the velocity inlet wave generation method by adding monitoring data to the velocity inlet wave generation method.In this paper,a rationalization test is conducted in the established real-scale numerical sink and a suitable grid division and iteration step are selected.Based on this,the controllability of the internal isolated wave generation is investigated and several optimization methods for wave generation experiments are proposed.The improved wave generation methods are used to conduct wave generation experiments with different amplitudes from Kd V,e Kd V and m Kd V theories,and the applicability of the three equations to different nonlinear intensities of internal isolated waves is verified.By analyzing the transmission characteristics of the oceanic internal waves in numerical simulations,it is found that excessive energy input is the main cause of vortex and wake generation,and the interference of both on the velocity field of the traveling internal isolated waves will destroy the symmetric distribution of the waveform;finally,the interference of vortex and wake on the test results is successfully reduced by limiting the input energy intensity of the numerical sink by controlling the duration of the initial velocity potential of the velocity inlet.