scholarly journals Models for the formation of a critical layer in water wave propagation

2012 ◽  
Vol 370 (1964) ◽  
pp. 1638-1660 ◽  
Author(s):  
R. S. Johnson
Keyword(s):  
Boundary Condition ◽  
Wave Propagation ◽  
Surface Wave ◽  
Water Wave ◽  
Vries Equation ◽  
Critical Layer ◽  
Constant Depth ◽  
Pressure Boundary Condition ◽  
Pressure Region ◽  
Critical Layers

A theory is presented which provides a model for the appearance of critical layers within the flow below a water wave. The wave propagates over constant depth, with constant (non-zero) vorticity. The mechanism described here involves adjusting the surface-pressure boundary condition; two models are discussed. In the first, the pressure at the surface is controlled (mimicking the movement of a low-pressure region associated with a storm) so that the speed and development of the pressure region ensure the appearance of a critical layer. In the second, the pressure boundary condition is allowed to accommodate the reduction of pressure with altitude, although the effects have to be greatly enhanced for this mechanism to produce a critical layer. These two problems are analysed using formal parameter asymptotics. In the second problem, this leads to a Korteweg–de Vries equation for the surface wave, and then the evolution of appropriate solutions of this equation gives rise to the appearance of a critical layer near the bottom; the corresponding problem at the surface can be formulated but not completely resolved. The appearance of a stagnation point and then a critical layer, either at the surface or the bottom, are discussed; the nature of the flow, and the corresponding streamlines are obtained and some typical flow fields are depicted.

scholarly journals Nonlinear tsunami generation mechanism

2001 ◽  
Vol 1 (4) ◽  
pp. 251-253 ◽  
Author(s):  
M. A. Nosov ◽  
S. N. Skachko
Keyword(s):  
Surface Wave ◽  
Surface Water ◽  
High Frequency ◽  
Water Wave ◽  
Wave Amplitude ◽  
Water Layer ◽  
Generation Mechanism ◽  
Tsunami Generation ◽  
Constant Depth ◽  
Nonlinear Mechanism

Abstract. The nonlinear mechanism of long gravitational surface water wave generation by high-frequency bottom oscillations in a water layer of constant depth is investigated analytically. The connection between the surface wave amplitude and the parameters of bottom oscillations and source length is investigated.

Guided Surface Waves on an Elastic Half Space

1971 ◽  
Vol 38 (4) ◽  
pp. 899-905 ◽  
Author(s):  
L. B. Freund
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Body Wave ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Normal Displacement ◽  
Rigid Barrier ◽  
Wave Disturbances

Three-dimensional wave propagation in an elastic half space is considered. The half space is traction free on half its boundary, while the remaining part of the boundary is free of shear traction and is constrained against normal displacement by a smooth, rigid barrier. A time-harmonic surface wave, traveling on the traction free part of the surface, is obliquely incident on the edge of the barrier. The amplitude and the phase of the resulting reflected surface wave are determined by means of Laplace transform methods and the Wiener-Hopf technique. Wave propagation in an elastic half space in contact with two rigid, smooth barriers is then considered. The barriers are arranged so that a strip on the surface of uniform width is traction free, which forms a wave guide for surface waves. Results of the surface wave reflection problem are then used to geometrically construct dispersion relations for the propagation of unattenuated guided surface waves in the guiding structure. The rate of decay of body wave disturbances, localized near the edges of the guide, is discussed.

scholarly journals A Solution to Pressure Equation with Its Boundary Condition of Combining Tangential and Normal Pressure Relations

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1507
Author(s):  
Hui Xiao ◽  
Wei Liu
Keyword(s):  
Boundary Condition ◽  
Numerical Algorithm ◽  
Iteration Process ◽  
Normal Pressure ◽  
Constitutive Law ◽  
Navier Stokes ◽  
Numerical Verification ◽  
Pressure Equation ◽  
Navier Stokes Equation ◽  
Pressure Boundary Condition

Pressure is a physical quantity that is indispensable in the study of transport phenomena. Previous studies put forward a pressure constitutive law and constructed a partial differential equation on pressure to study the convection with or without heat and mass transfer. In this paper, a numerical algorithm was proposed to solve this pressure equation by coupling with the Navier-Stokes equation. To match the pressure equation, a method of dealing with pressure boundary condition was presented by combining the tangential and normal direction pressure relations, which should be updated dynamically in the iteration process. Then, a solution to this pressure equation was obtained to bridge the gap between the mathematical model and a practical numerical algorithm. Through numerical verification in a circular tube, it is found that the proposed boundary conditions are applicable. The results demonstrate that the present pressure equation well describes the transport characteristics of the fluid.

scholarly journals A coupled finite and boundary spectral element method for linear water-wave propagation problems

2017 ◽  
Vol 48 ◽  
pp. 1-20 ◽  
Author(s):  
Antonio Cerrato ◽  
Luis Rodríguez-Tembleque ◽  
José A. González ◽  
M.H. Ferri Aliabadi
Keyword(s):  
Wave Propagation ◽  
Water Wave ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Element Method
Sign in / Sign up

Export Citation Format

Share Document