Stability of linear shear flows in shallow water

1995 ◽  
Vol 303 ◽  
pp. 203-214 ◽  
Author(s):  
Charles Knessl ◽  
Joseph B. Keller
Keyword(s):  
Shallow Water ◽  
Shear Flows ◽  
Special Functions ◽  
Rigid Wall ◽  
Eigenvalue Equation ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Linear Shear ◽  
The Stability ◽  
Rigid Walls

The stability or instability of various linear shear flows in shallow water is considered. The linearized equations for waves on the surface of each flow are solved exactly in terms of known special functions. For unbounded shear flows, the exact reflection and transmission coefficients R and T for waves incident on the flow, are found. They are shown to satisfy the relation |R|2= 1+ |T|2, which proves that over reflection occurs at all wavenumbers. For flow bounded by a rigid wall, R is found. The poles of R yield the eigenvalue equation from which the unstable mides can be found. For flow in a channel, with two rigid walls, the eigenvalue equation for the modes is obtained. The results are compared with previous numerical results.

Travelling waves on a membrane: reflection and transmission at a corner of arbitrary angle. I

1995 ◽  
Vol 451 (1943) ◽  
pp. 657-683 ◽  
Keyword(s):  
Special Functions ◽  
Numerical Study ◽  
Travelling Waves ◽  
Wedge Angle ◽  
Complete Agreement ◽  
Arbitrary Angle ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Edge Conditions ◽  
Impedance Conditions

This article is the first part of a study into the reflection, transmission and scattering of waves on the semi-infinite faces of a compressible fluid wedge of arbitrary angle. This class of problems, in which the wedge surfaces are described by high order impedance conditions (that is, containing derivatives with respect to variables both normal and tangential to the boundary), is of great interest in structural acoustics and electromagnetism. Here, for mathematical convenience, the canonical problem of a fluid wedge with two plane membrane surfaces is examined. Forcing is taken as an unattenuated fluid coupled surface wave incident from infinity on one of the wedge faces. Explicit application of the edge-constraints allows the boundary value problem to be formulated as an inhomogeneous difference equation which is then solved in terms of Maliuzhinets special functions. An analytical solution is thus obtained for arbitrary wedge angle and the membrane wave reflection and transmission coefficients are deduced. The solution method is straightforward to apply and can easily be generalized to any boundary or edge conditions. Also in Part I, the solution obtained for the case of a wedge of angle 2π is compared with that determined by the Wiener-Hopf technique. The two methods are in complete agreement. In the second half of this work the reflection coefficients calculated here will be shown to confirm those given previously in the literature for certain specific wedge angles. A full numerical study, for a range of fluid-membrane parameter values, will also be presented in Part II.

scholarly journals Effect of Mooring Lines on the Hydroelastic Response of a Floating Flexible Plate Using the BIEM Approach

2021 ◽  
Vol 9 (9) ◽  
pp. 941
Author(s):  
Sarat Chandra Mohapatra ◽  
C. Guedes Soares
Keyword(s):  
Shallow Water ◽  
Reflection And Transmission Coefficients ◽  
Physical Parameters ◽  
Flexible Plate ◽  
Approximation Model ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Deflection Amplitude ◽  
Shallow Water Approximation ◽  
Hydroelastic Response

A boundary integral equation method (BIEM) model for the problem of surface wave interaction with a moored finite floating flexible plate is presented. The BIEM solution is obtained by employing the free surface Greens function and Green’s theorem, and the expressions for the plate deflection, reflection, and transmission coefficients are derived from the integro-differential equation. Furthermore, the shallow water approximation model and its solution is obtained based on the matching technique in a direct manner. The accuracy of the present BIEM code is checked by comparing the results of deflection amplitude, reflection, and transmission coefficients with existing published results and experimental datasets as well as the shallow water approximation model. The hydroelastic response of the moored floating flexible plate is studied by analyzing the effects of the mooring stiffness, incidence angle, and flexural rigidity on the deflection amplitude, plate deformations, reflection, and transmission coefficients. The present analysis may be helpful in understanding the different physical parameters to model a wave energy conversion device with mooring systems over BIEM formulations.

16.—Waves over Obstacles on a Shallow Seabed

1973 ◽  
Vol 71 (3) ◽  
pp. 181-192 ◽  
Author(s):  
Alan Jeffrey ◽  
Saw Tin
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Recurrence Relations ◽  
Reflection And Transmission Coefficients ◽  
Shallow Water Waves ◽  
Reflection And Transmission ◽  
Transmission Coefficients

SynopsisIn this paper we consider the effect of the passage of shallow water waves over vertical walled objects on a flat seabed. The effect of reflections at the successive walls is taken into account when determining the place of breaking of the wave. The results are obtained by the introduction of special reflection and transmission coefficients at each wall and recurrence relations are formulated connecting their values at successive walls. The effect of this is to reduce the calculation of the place of breaking of the wave over a stepped seabed to an equivalent one for a wave over a flat seabed, the result of which is well known.

scholarly journals Shallow water dynamics on linear shear flows and plane beaches

2017 ◽  
Vol 29 (7) ◽  
pp. 073602 ◽  
Author(s):  
Maria Bjørnestad ◽  
Henrik Kalisch
Keyword(s):  
Shallow Water ◽  
Shear Flows ◽  
Water Dynamics ◽  
Linear Shear ◽  
Shallow Water Dynamics

Extension of forward modeling phase-screen code in isotropic and anisotropic media up to critical angle

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. SM107-SM114 ◽  
Author(s):  
James C. White ◽  
Richard W. Hobbs
Keyword(s):  
Critical Angle ◽  
Model Space ◽  
Anisotropic Media ◽  
Forward Modeling ◽  
Phase Screen ◽  
Computationally Efficient ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Phase Corrections ◽  
Converted Phases

The computationally efficient phase-screen forward modeling technique is extended to allow investigation of nonnormal raypaths. The code is developed to accommodate all diffracted and converted phases up to critical angle, building on a geometric construction method. The new approach relies upon prescanning the model space to assess the complexity of each screen. The propagating wavefields are then divided as a function of horizontal wavenumber, and each subset is transformed to the spatial domain separately, carrying with it angular information. This allows both locally accurate 3D phase corrections and Zoeppritz reflection and transmission coefficients to be applied. The phase-screen code is further developed to handle simple anisotropic media. During phase-screen modeling, propagation is undertaken in the wavenumber domain where exact expressions for anisotropic phase velocities are available. Traveltimes and amplitude effects from a range of anisotropic shales are computed and compared with previous published results.

Reflection and Transmission Coefficients of Plane Waves in Magnetoelectroelastic Layered Structures

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
J. Y. Chen ◽  
H. L. Chen ◽  
E. Pan
Keyword(s):  
Piezoelectric Materials ◽  
Plane Waves ◽  
Layered Structures ◽  
Organic Glass ◽  
Reflection And Transmission Coefficients ◽  
Material Structure ◽  
Layered System ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Novel Material

Reflection and transmission coefficients of plane waves with oblique incidence to a multilayered system of piezomagnetic and/or piezoelectric materials are investigated in this paper. The general Christoffel equation is derived from the coupled constitutive and balance equations, which is further employed to solve the elastic displacements and electric and magnetic potentials. Based on these solutions, the reflection and transmission coefficients in the corresponding layered structures are subsequently obtained by virtue of the propagator matrix method. Two layered examples are selected to verify and illustrate our solutions. One is the purely elastic layered system composed of aluminum and organic glass materials. The other layered system is composed of the novel magnetoelectroelastic material and the organic glass. Numerical results are presented to demonstrate the variation of the reflection and transmission coefficients with different incident angles, frequencies, and boundary conditions, which could be useful to nondestructive evaluation of this novel material structure based on wave propagations.

scholarly journals Propagation Characteristics of Oblique Incident Terahertz Wave in Nonuniform Dusty Plasma

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Yunhua Cao ◽  
Haiying Li ◽  
Zhe Wang ◽  
Zhensen Wu
Keyword(s):  
Dusty Plasma ◽  
Terahertz Wave ◽  
Dust Particles ◽  
Number Density ◽  
Propagation Characteristics ◽  
Absorption Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Propagation Matrix ◽  
Transmission And Absorption

Propagation characteristics of oblique incident terahertz wave from the nonuniform dusty plasma are studied using the propagation matrix method. Assuming that the electron density distribution of dusty plasma is parabolic model, variations of power reflection, transmission, and absorption coefficients with frequencies of the incident wave are calculated as the wave illuminates the nonuniform dusty plasma from different angles. The effects of incident angles, number density, and radius of the dust particles on propagation characteristics are discussed in detail. Numerical results show that the number density and radius of the dust particles have very little influences on reflection and transmission coefficients and have obvious effects on absorption coefficients. The terahertz wave has good penetrability in dusty plasma.

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