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Shallow Water Turbulent Surface Wave Striking an Adverse Slope

Bose S. K.

Acta Geophysica

2015

Vol. 63, no. 4

1090--1102

The problem of a sinusoidal wave crest striking an adverse slope due to gradual elevation of the bed is relevant for coastal sea waves. Turbulence based RANS equations are used here under turbulence closure assumptions. Depth-averaging the equations of continuity and momentum, yield two differential equations for the surface elevation and the average forward velocity. After nondimensionalization, the two equations are converted in terms of elevation over the inclined bed and the discharge, where the latter is a function of the former satisfying a first order differential equation, while the elevation is given by a first order evolution equation which is treated by Lax-Wendroff discretization. Starting initially with a single sinusoidal crest, it is shown that as time progresses, the crest leans forwards, causing a jump in the crest upfront resulting in its roll over as a jet. Three cases show that jump becomes more prominent with increasing bed inclination.

Nonlinear ship wake waves as a model of rogue waves and a source of danger to the coastal environment: a review

Soomere T.

Oceanologia

2006

No. 48 (S)

185-202

A substantial part of the energy of wake waves from high-speed ships sailing in shallow water is concentrated in nonlinear components which at times have a solitonic nature. Recent results of investigations into solitonic wave interactions within the framework of the Kadomtsev-Petviashvili equation and their implications for rogue wave theory are reviewed. A surface elevation four times as high as the counterparts occurs if the properties of the interacting waves are specifically balanced. The slope of the water surface may increase eightfold. The resulting structure may persist for a long time. Nonlinear wake components may exert a considerable influence on the marine ecosystem in coastal areas .

Non-linear water waves - experiments and theory

Wilde P., Sobierajski E., Sobczak Ł.

Archives of Hydro-Engineering and Environmental Mechanics

2001

Vol. 48, nr 2

107-128

The paper concems laboratory experiments on shallow water waves. The waves in our flume were generated as programmed groups, with gentle fading-in and fading-out of amplitudes of the wavemaker's piston's motions. The higher harmonic components have been considered in the motion. Their influence on characteristics of generated waves has also been studied. The measurements were carried out at 6 cross sections along the propagation path; both wave profiles and velocities were recorded. As a description of phenomena, the wave profiles were approximated by harmonic com-ponents according to the Stokes solution. It was noted, that parameters of harmonic components change along the propagation path; there are energy transfers between them. The higher harmonic components are more significant for the description of wave profiles, than for the velocities. The results of the experiments were used in verifications in a research program on the theoretical description and numerical al-gorithm for shallow water waves generated and propagated in a flume.