EDGE WAVES OVER A SLOPING BEACH IN A ROTATING TWO-LAYERED SYSTEM

1963 ◽  
Author(s):  
Hayato Iida ◽  
Takashi Ichiye
Keyword(s):  
Layered System ◽  
Edge Waves ◽  
Sloping Beach

Edge waves on a gently sloping beach: uniform asymptotics

1991 ◽  
Vol 233 ◽  
pp. 483-493 ◽  
Author(s):  
Peter Zhevandrov
Keyword(s):  
Finite Number ◽  
Shallow Water Equation ◽  
Uniform Asymptotics ◽  
Trapped Modes ◽  
Edge Waves ◽  
Trapped Mode ◽  
Complete Set ◽  
Constant Slope ◽  
Sloping Beach ◽  
Uniform Asymptotic Expansions

Edge waves on a beach of gentle slope ε [Lt ] 1 are considered. For constant slope, Ursell (1952) has obtained a complete set of trapped modes and shown that there exists only a finite number n of such modes, (2n + 1)β < ½π, β = tan−1ε. For non-uniform slope the formulae for the trapped-mode frequencies were heuristically derived by Shen, Meyer & Keller (1968). For small n ∼ O(1) Miles (1989) has obtained formulae which coincide with Shen et al.'s (1968) with accuracy to O(ε) and differ from them by O(ε2). However, Miles’ formulae fail at n ∼ 1/ε. In this paper it is proved that Shen et al.'s (1968) formulae are valid for all n (including n ∼ 1/ε) with accuracy to O(ε) and corrections of any order in ε are given. Uniform asymptotic expansions are obtained for the corresponding eigenfunctions. These expansions give Miles’ (1989) result for small n. The formulae for the frequencies and the eigenfunctions have the same structure for both the full dispersion system and the shallow-water equation. For small n the frequencies for both models coincide with accuracy to O(ε2), but for n ∼ 1/ε they differ by O(1). In the last section the effect of rotation following Evans (1989) is taken into account. All the asymptotics have formal character, i.e. they satisfy the corresponding equations with accuracy to O(εN), N being arbitrarily large. The rigorous justification of these asymptotics is under way.

The generation of surface waves over a sloping beach by an oscillating line source

1976 ◽  
Vol 79 (3) ◽  
pp. 573-585 ◽  
Author(s):  
Clare A. N. Morris
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Line Source ◽  
Short Wave ◽  
Long Waves ◽  
Edge Waves ◽  
Wave Regime ◽  
Wave Solutions ◽  
Sloping Beach

AbstractA line source whose strength varies sinusoidally with time and also with the co-ordinate measured along its length is situated parallel to the shoreline of a beach of angle ¼π0. Both long-and short-wave solutions are found. It is shown that for certain positions of the source, long waves are not radiated to infinity, while in the short-wave regime, the solutions take the form of edge-waves, with resonances occurring at certain wavenumbers. Computations of the free-surface contours are presented for a range of wavenumbers.

scholarly journals OBSERVATION OF NEARSHORE CURRENT AND EDGE WAVES

1978 ◽  
Vol 1 (16) ◽  
pp. 45 ◽  
Author(s):  
Tamio O. Sasaki ◽  
Kiyoshi Horikawa
Keyword(s):  
Energy Spectrum ◽  
Velocity Field ◽  
Conceptual Models ◽  
Edge Waves ◽  
Nearshore Zone ◽  
Nodal Lines ◽  
Spatial Velocity ◽  
Sloping Beach

Nodal lines normal to the shoreline of infragravity low mode edge waves in the nearshore zone were observed with eleven wave staffs simultaneously with the nearshore current spatial velocity field on a gently sloping beach. About five peaks were found in the energy spectrum and their frequencies agreed well with cut-off mode edge waves [Huntley(1976)]. Based on the above observation, conceptual models of nearshore current patterns for the infragravity domain are proposed and general current patterns for the three domains are discussed by combining the horizontal patterns of Harris(1969) and the vertical patterns of Sasaki et al.(1976).

scholarly journals Edge waves along a sloping beach

2001 ◽  
Vol 34 (45) ◽  
pp. 9723-9731 ◽  
Author(s):  
Adrian Constantin
Keyword(s):  
Edge Waves ◽  
Sloping Beach

Mechanisms for the generation of edge waves over a sloping beach

1988 ◽  
Vol 186 ◽  
pp. 379-391 ◽  
Author(s):  
D. V. Evans
Keyword(s):  
Water Wave ◽  
Wave Theory ◽  
Dominant Mode ◽  
Mode Shapes ◽  
Edge Waves ◽  
Longshore Current ◽  
Linear Water Wave Theory ◽  
Pressure Distributions ◽  
Sloping Beach ◽  
Standing Edge Waves

Two mechanisms for the generation of standing edge waves over a sloping beach are described using classical linear water-wave theory. The first is an extension of the result of Yih (1984) to a class of localized bottom protrusions on a sloping beach in the presence of a longshore current. The second is a class of longshore surface-pressure distributions over a beach. In both cases it is shown that Ursell-type standing edge-wave modes can be generated in an appropriate frame of reference. Typical curves of the mode shapes are presented and it is shown how in certain circumstances the dominant mode is not the lowest.

scholarly journals Instability of edge waves along a sloping beach

2014 ◽  
Vol 256 (12) ◽  
pp. 3999-4012 ◽  
Author(s):  
Delia Ionescu-Kruse
Keyword(s):  
Edge Waves ◽  
Sloping Beach

Edge waves over a shelf: full linear theory

1984 ◽  
Vol 142 ◽  
pp. 79-95 ◽  
Author(s):  
D. V. Evans ◽  
P. Mciver
Keyword(s):  
Shallow Water ◽  
Wide Class ◽  
Shallow Water Equations ◽  
Water Waves ◽  
Explicit Solution ◽  
Mode Shapes ◽  
Edge Waves ◽  
Wave Solutions ◽  
Linearized Theory ◽  
Sloping Beach

Edge-wave solutions to the linearized shallow-water equations for water waves are well known for a variety of bottom topographies. The only explicit solution using the full linearized theory describes edge waves over a uniformly sloping beach, although the existence of such waves has been established for a wide class of bottom geometries. In this paper the full linearized theory is used to derive the properties of edge waves over a shelf. In particular, curves are presented showing the variation of frequency with wavenumber along the shelf, together with some mode shapes for a particular shelf geometry.

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.

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