基于非静压模型的波浪空间聚焦研究

Research on Spatial Wave Focusing Based on Non-Hydrostatic Wave Model

为研究波浪聚焦特性,分析极端波浪的产生机理,采用非静压模型通过数值模拟的方法对波浪聚焦的影响因素进行了详细研究。本文采用SWASH非静压波浪模型,模型垂向均匀分三层以保证足够的色散精度以及非线性精度来高效准确的模拟波浪在变化地形上的传播。研究发现在最大波浪未发生破碎时,波浪在半圆形凸起斜坡浅滩上传播,波浪聚焦是波高增大的最主要原因。初始kR(波数与浅滩半径乘积)值对波浪在该地形上的聚焦特性有着重要影响。初始kR越大,最大波高位置距聚焦地形坡脚的距离越远。当kR在1.4π~4.05π之间时,随着kR的减小,最大相对波高先增大后减小,当kR=2.45π时,最大相对波高达到极大值,可达2.48倍初始波高。

To study the characteristics of spatial wave focusing and analysis of the generation mechanism of extreme waves,the focusing and influence factors of spatial wave focusing by a semicircular convex slope are studied in detail by means of numerical simulation based on non-hydrostatic pressure model,SWASH.Based on the vertical pressure decomposition,the SWASH model was applied with three equal vertical layers to ensure efficiency and enough accuracy of frequency dispersion and nonlinearity.The focusing bathymetry is a combination of semi-cylinder over a plane slope.To mitigate the side effects,the numerical simulation domain was extended to triple the radius R of the cylinder.By comparing the wave height and the energy composition of the same incident waves propagating on the focusing bathymetry against the reference plane slope,it is found that there is a significant nonlinear process for the waves propagating on the variable depth topography and the super harmonics grow dramatically.Over the plane slope,the extrema of fundamental frequency and super harmonic frequency appear almost at the same positions.But on the focusing slope,the positions of extrema are different.Before the breaking of the maximum waves,the spatial wave focusing is the main reason for the agitation of wave height when the waves propagating over the shoals of a semicircular convex slope.Through comparing the focusing characteristics of seven groups waves propagating on the specify three-dimensional slope with the same wave steepness,it is obvious that the dimensionless parameters kR(where k is the wave number)plays an important role in the spatial focusing characteristics of waves on the present bathymetry.The larger the initial kR,the greater the distance between the position of the maximum wave height and the toe of bathymetry.The maximum waves height generated by wave focusing is not only related to the size of the focusing region,but also related to the intensity of the wave nonlinearity.When kR is between 1.4πand 4.05π,with the decrease of the dimensionless parameters kR,the maximum relative waves height tends to increase to an extreme value and then declines.The maximum relative waves height reaches the maximum value as large as 2.48 H 0(where H 0 is the initial wave height)when kR is equal to 2.45π.