scholarly journals Geophysical Equatorial Edge Wave with Underlying Currents in the f-Plane Approximation

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 118
Author(s):  
Hsu
Keyword(s):  
Edge Wave ◽  
Edge Waves ◽  
Governing Equations ◽  
Wave Dynamics ◽  
Transport Velocity ◽  
Mass Transport Velocity ◽  
Uniform Currents ◽  
Exact And Explicit Solution ◽  
Sloping Beach ◽  
Analytical Expressions

I present an exact and explicit solution to the nonlinear governing equations in the equatorial f-plane, describing geophysical edge waves propagating over a plane-sloping beach, in the presence of underlying uniform currents. I also derive the analytical expressions of geophysical edge wave dynamics and the mass transport velocity.

scholarly journals EDGE WAVE INDUCED BY AN ATMOSPHERIC PRESSURE DISTURBANCE MOVING ALONG A SLOPING BEACH

2018 ◽  
pp. 82
Author(s):  
Yixiang Chen ◽  
Xiaojing Niu
Keyword(s):  
Shallow Water Equations ◽  
Atmospheric Pressure ◽  
Edge Wave ◽  
Edge Waves ◽  
Translation Speed ◽  
Pressure Disturbance ◽  
Significant Edge ◽  
Spatial Size ◽  
Sloping Beach ◽  
Wave Induced

Edge wave can be generated by an atmospheric pressure disturbance moving along the shoreline on a sloping beach. A two-dimensional numerical model based on non-linear shallow water equations is established and a set of numerical experiments are conducted to study the edge wave packets evolution in coastal ocean. In light of the analytical solutions by Greenspan, some dominant factors are discussed, such as disturbance spatial size, translation speed, its location and the slope inclination, that influence the generation conditions and evolution process of edge waves. The results indicate on what circumstances significant edge waves will be excited and how long it takes for the wave growth.

Edge waves on a sloping beach

1952 ◽  
Vol 214 (1116) ◽  
pp. 79-97 ◽  
Keyword(s):  
Mechanical System ◽  
Continuous Spectrum ◽  
Cutoff Frequency ◽  
Edge Wave ◽  
Finite Width ◽  
Edge Waves ◽  
Frequency Range ◽  
Discrete Frequency ◽  
Mixed Spectrum ◽  
Sloping Beach

The set of eigenfrequencies of a mechanical system forms its spectrum. A discussion is given of systems with discrete, continuous and mixed spectra. It is shown that resonance occurs at discrete points of the spectrum, and at cut-off frequencies (end-points of the continuous spectrum). The motion in a semi-infinite canal of finite width closed by a sloping beach has a mixed spectrum. The inviscid theory predicts that at a discrete frequency the resonance is confined to the neighbourhood of the beach (inviscid edge wave), while at a cutoff frequency the resonance extends a long way down the canal. The latter resonance is confined to the neighbourhood of the beach (viscous edge wave) by viscosity which is important near a cut-off frequency. Especially large resonances are predicted for a series of critical angles, of which the largest is 30°. The theory is verified experimentally in the frequency range 100 to 17c/min for the angles 37⋅6 and 29⋅5°.

Wave-induced vorticity in free-surface boundary layers: application to mass transport in edge waves

1975 ◽  
Vol 70 (2) ◽  
pp. 257-266 ◽  
Author(s):  
B. D. Dore
Keyword(s):  
Free Surface ◽  
Mass Transport ◽  
Gravity Waves ◽  
Surface Boundary ◽  
Edge Waves ◽  
Vorticity Field ◽  
Surface Boundary Layer ◽  
Transport Velocity ◽  
Mass Transport Velocity ◽  
Wave Induced

The time-averaged vorticity field within the free-surface boundary layer associated with a general class of propagating gravity waves is considered. The principal results are applied in a calculation of the mass transport velocity field for edge waves.

scholarly journals MECHANISM OF BEACH PROFILE DEFORMATION DUE TO ON-OFFSHORE SAND DRIFT

1984 ◽  
Vol 1 (19) ◽  
pp. 142
Author(s):  
Wi-Gwang Pae ◽  
Yuichi Iwagaki
Keyword(s):  
Sediment Transport ◽  
Mass Transport ◽  
Deformation Model ◽  
Two Dimensional ◽  
Sand Drift ◽  
Transport Velocity ◽  
Equilibrium Profile ◽  
Mass Transport Velocity ◽  
Load Movement ◽  
Sloping Beach

In the present study, two-dimensional laboratory experiments were performed to investigate the sediment transport due to waves on a fixed sloping beach. Polystyrene particles and glass balls were used as tracers to determine the mass transport velocity near the bottom and the net transport velocity of sediment moving on an impermeable slope. Relationships between the mass transport velocity of water and the net sediment transport velocity are investigated experimentally. The mechanism of two-dimensional beach deformation from an initial uniform slope toward an equilibrium profile due to bed-load movement is discussed on the basis of spatial distributions of the net sediment transport velocity. In addition, some results of experiments using a movable bed are presented to confirm the validity of a beach deformation model derived from the discussion of the tracer experiments.

scholarly journals A Review on Analytical Modeling for Collapse Mode Capacitive Micromachined Ultrasonic Transducer of the Collapse Voltage and the Static Membrane Deflections

Micromachines ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 714
Author(s):  
Jiujiang Wang ◽  
Xin Liu ◽  
Yuanyu Yu ◽  
Yao Li ◽  
Ching-Hsiang Cheng ◽  
...  
Keyword(s):  
Analytical Modeling ◽  
Ultrasonic Transducer ◽  
Governing Equations ◽  
Von Karman ◽  
Von Kármán Equations ◽  
Collapse Mode ◽  
Capacitive Micromachined Ultrasonic Transducer ◽  
Gap Height ◽  
Von Kármán ◽  
Analytical Expressions

Analytical modeling of capacitive micromachined ultrasonic transducer (CMUT) is one of the commonly used modeling methods and has the advantages of intuitive understanding of the physics of CMUTs and convergent when modeling of collapse mode CMUT. This review article summarizes analytical modeling of the collapse voltage and shows that the collapse voltage of a CMUT correlates with the effective gap height and the electrode area. There are analytical expressions for the collapse voltage. Modeling of the membrane deflections are characterized by governing equations from Timoshenko, von Kármán equations and the 2D plate equation, and solved by various methods such as Galerkin’s method and perturbation method. Analytical expressions from Timoshenko’s equation can be used for small deflections, while analytical expression from von Kármán equations can be used for both small and large deflections.

Mass transport under partially reflected waves in a rectangular channel

1994 ◽  
Vol 266 ◽  
pp. 121-145 ◽  
Author(s):  
Jiangang Wen ◽  
Philip L.-F. Liu
Keyword(s):  
Mass Transport ◽  
Vector Potential ◽  
Numerical Solutions ◽  
Rectangular Channel ◽  
Scalar Potential ◽  
Second Order ◽  
Nonlinear Transport ◽  
Reflected Waves ◽  
Transport Velocity ◽  
Mass Transport Velocity

Mass transport under partially reflected waves in a rectangular channel is studied. The effects of sidewalls on the mass transport velocity pattern are the focus of this paper. The mass transport velocity is governed by a nonlinear transport equation for the second-order mean vorticity and the continuity equation of the Eulerian mean velocity. The wave slope, ka, and the Stokes boundary-layer thickness, k (ν/σ)½, are assumed to be of the same order of magnitude. Therefore convection and diffusion are equally important. For the three-dimensional problem, the generation of second-order vorticity due to stretching and rotation of a vorticity line is also included. With appropriate boundary conditions derived from the Stokes boundary layers adjacent to the free surface, the sidewalls and the bottom, the boundary value problem is solved by a vorticity-vector potential formulation; the mass transport is, in gneral, represented by the sum of the gradient of a scalar potential and the curl of a vector potential. In the present case, however, the scalar potential is trivial and is set equal to zero. Because the physical problem is periodic in the streamwise direction (the direction of wave propagation), a Fourier spectral method is used to solve for the vorticity, the scalar potential and the vector potential. Numerical solutions are obtained for different reflection coefficients, wave slopes, and channel cross-sectional geometry.

scholarly journals Non-linear analysis of laminated composite doubly curved shallow shells

2006 ◽  
Vol 28 (1) ◽  
pp. 43-55
Author(s):  
Dao Huy Bich
Keyword(s):  
Laminated Composite ◽  
Governing Equations ◽  
Shallow Shells ◽  
Approximate Analytical Solutions ◽  
Linear Buckling ◽  
Non Linear ◽  
Vibration Problems ◽  
Doubly Curved ◽  
Analytical Expressions ◽  
Load Deflection Curve

This paper deals with governing equations and approximate analytical solutions based on some wellknown assumptions to the non-linear buckling and vibration problems of laminated composite doubly curved shallow shells. Obtained results will be presented by analytical expressions of the lower critical load, the postbuckling load-deflection curve and the fundamental frequency of non-linear free vibration of the shell.

Effect of Coriolis force on edge waves (I) Investigation of the normal modes

2020 ◽  
Vol 78 (4) ◽  
pp. 229-261
Author(s):  
Robert O. Reid
Keyword(s):  
Coriolis Force ◽  
Wind Stress ◽  
Formal Solution ◽  
Wave Length ◽  
Normal Modes ◽  
Low Frequency ◽  
Phase Speed ◽  
Free Edge ◽  
Edge Wave ◽  
Edge Waves

Essentially two classes of free edge waves can exist on a sloping continental shelf in the presence of Coriolis force. For small longshore wave length, fundamental waves of the first class behave like Stokes edge waves. However, for great wave lengths (of several hundred kilometers or more) the characteristics of the first class are significantly altered. In the northern hemisphere the phase speed for waves moving to the right (facing shore from the sea) exceeds the speed for waves which move to the left. Also, the group velocity for a given edge wave mode has a finite upper limit. Waves of the second class are essentially quasigeostrophic boundary waves with very low frequency and, like Kelvin waves, move only to the left (again facing shore from the sea). Unlike Stokes edge waves, those of the quasigeostrophic class are associated with large vorticity. Examination of the formal solution for forced edge waves indicates that those of the second class may be excited significantly by a wind stress vortex. Also, in contrast to the conclusion of Greenspan (1956), it is proposed that a hurricane can effectively excite the higher order edge wave modes in addition to the fundamental if wind stress is considered.

Mass transport in water waves over an elastic bed

1995 ◽  
Vol 450 (1939) ◽  
pp. 371-390 ◽  
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Mass Transport ◽  
Water Waves ◽  
Viscous Boundary Layer ◽  
Curvilinear Coordinate ◽  
Transport Velocity ◽  
Mass Transport Velocity ◽  
Orthogonal Curvilinear Coordinate System ◽  
Viscous Boundary

The mass transport velocity in water waves propagating over an elastic bed is investigated. Water is assumed to be incompressible and slightly viscous. The elastic bed is also incompressible and satisfies the Hooke’s law. For a small amplitude progressive wave perturbation solutions via a boundary-layer approach are obtained. Because the wave amplitude is usually larger than the viscous boundary layer thickness and because the free surface and the interface between water and the elastic bed are moving, an orthogonal curvilinear coordinate system (Longuet-Higgins 1953) is used in the analysis of free surface and interfacial boundary layers so that boundary conditions can be applied on the actual moving surfaces. Analytical solutions for the mass transport velocity inside the boundary layer adjacent to the elastic seabed and in the core region of the water column are obtained. The mass transport velocity above a soft elastic bed could be twice of that over a rigid bed in the shallow water.

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