16:00
Linear and non-linear waves II
Chair: Yifei Zhang
16:00
30 mins
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SOLITONS CAUSED BY A TWO-DIMENSIONAL FOIL AT SUPER-CRITICAL AND HYPER-CRITICAL SPEEDS IN SHALLOW WATER
G.D. Xu, Q. Meng
Abstract: When a hydrofoil craft cruises in shallow water, such as a river or marginal sea, the hydrodynamic performance of the hydrofoil travelling at super-critical and hyper-critical speed should be considered. The nonlinear free surface effects of shallow water would become important, especially when the submergence h is small with respect to the chord length of the foil . It has been observed that a rigid body or pressure distribution moving in finite water zone may cause upstream solitary waves when the advancing velocity Fh= U/sqrt(gH) is around ([1][2][3][4]), where U is the speed of the body or pressure distribution, g is the gravitational acceleration and H is the depth of undisturbed water. In present study the nonlinear hydrodynamics and the wave patterns caused by a 2D foil advancing in water zone of finite depth are concerned with. It has been found that there would be a strong circulation when there is an attack angle. The cross effects of circulation, bottom and free surface, and the resulting resistance, lifting force and the moment at various speeds will be investigated.
A NACA0012 foil moving at constant speed U in quiescent shallow water will be simulated using Boundary Element Method (BEM) through time stepping scheme. The nonlinear free surface boundary conditions and the unsteady Kutta condition[5] are imposed. Numerical simulations have been carried out to study the wave patterns caused by the hydrofoil in shallow water. When the supercritical speed is concerned, the upstream wave is above the initial calm surface and run forward; the trailing wavetrain propagates aftward and a depressed region behind the hydrofoil forms. When ‘hyper-critical’ speed is considered, a single soliton forms above the foil as the trailing waves propagate aftward. The effects of the speed, submergence and angle of attack on the hyper-critical soliton will be further investigated.
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16:30
30 mins
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APPLICABLITY OF FULLY-DISPERSIVE NONLINEAR MILD SLOPE EQUATIONS FOR BROAD-BAND WAVES
Zhili Zou
Abstract: The fully-dispersive nonlinear mild slope equations for broad-band waves are a newly-developed wave model with full dispersion and nonlinearity to any desired order. It is superior to the higher order Boussinesq equations by its accurate dispersion property, and also superior to the classic mild slope equation by its broad-band spectral feature. Although the mild slope assumption is adopted by this model, the application of the model to a considerable steep topography (the steepness being up to 1:5) is still possible.
The present paper presents a comprehensive numerical results to demonstrate the applicablity of fully-dispersive nonlinear mild slope equations mentioned above. Comparison to the numerical results of higher order Boussinesq equations are made in order to show the advantage of the model. Numerical examples include:
(1) nonlinear evolution of wave groups.
(2) crescent wave generation and evolution.
(3) wave propagation over submarine breakwater with different slopes.
(4) wave propagation over bottom with a patch of sand bars.
(5) wave propagation over a shoal.
The first two examples are for the demonstration of the advantage of accurate dispersion and high order nonlinearity of the model. The third is for the illustration of applicability of mild slope assumption. The fourth is for the demonstration of applicability of simulating Bragg-reflection over topography with rapidly-varying depth. The fifth is for the illustration of applicability of wave refraction property of the model.
The study's numerical results verify the abilities of the fully-dispersive nonlinear mild slope equations to model the effects of dispersion, nonlinearity and complex bottom topography on wave motions.
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