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.

Trapping modes in the theory of surface waves

1951 ◽  
Vol 47 (2) ◽  
pp. 347-358 ◽  
Author(s):  
F. Ursell
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Total Energy ◽  
Surface Waves ◽  
Radiation Condition ◽  
Finite Width ◽  
Energy Trapping ◽  
Sloping Beach ◽  
The Waves

ABSTRACTIt is shown that a mass of fluid bounded by fixed surfaces and by a free surface of infinite extent may be capable of vibrating under gravity in a mode (called a trapping mode) containing finite total energy. Trapping modes appear to be peculiar to the theory of surface waves; it is known that there are no trapping modes in the theory of sound. Two trapping modes are constructed: (1) a mode on a sloping beach in a semi-infinite canal of finite width, (2) a mode near a submerged circular cylinder in an infinite canal of finite width. The existence of trapping modes shows that in general a radiation condition for the waves at infinity is insufficient for uniqueness.

The generation of surface waves over a sloping beach by an oscillating line-source. I. The general solution

1974 ◽  
Vol 76 (3) ◽  
pp. 545-554 ◽  
Author(s):  
Clare A. N. Morris
Keyword(s):  
General Solution ◽  
Integral Representation ◽  
Surface Waves ◽  
Line Source ◽  
Wave Train ◽  
Wave Generation ◽  
Outgoing Wave ◽  
Arbitrary Angle ◽  
Laplace Integral Representation ◽  
Sloping Beach

AbstractThe problem of wave generation by a line source of sinusoidally varying strength situated in water above a beach of arbitrary angle α(0 < α ≤ π) is solved by the use of a Laplace-integral representation of the solution. It is shown that a solution can be constructed which is regular at the shoreline and gives an outgoing wave-train at infinity.

The generation of surface waves over a sloping beach by an oscillating line-source. II. The existence of wave-free source positions

1974 ◽  
Vol 76 (3) ◽  
pp. 555-562 ◽  
Author(s):  
Clare A. N. Morris
Keyword(s):  
Surface Waves ◽  
Line Source ◽  
Sloping Beach ◽  
The Waves

AbstractAn expression is obtained for the amplitude of the waves radiated to infinity by a line source of sinusoidally-varying strength situated in water over a beach of angle α (0 < α ≤ π). It is shown that, for certain positions of the source, this amplitude is zero. Equations for the loci of these positions, and approximations to their solutions in particular cases, are derived.

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.

Edge waves on a gently sloping beach

1989 ◽  
Vol 199 ◽  
pp. 125-131 ◽  
Author(s):  
John Miles
Keyword(s):  
Free Surface ◽  
Turning Point ◽  
Surface Displacement ◽  
Dominant Mode ◽  
Variational Approximation ◽  
Edge Waves ◽  
Flat Bottom ◽  
Free Surface Displacement ◽  
Complete Set ◽  
Sloping Beach

Edge waves of frequency ω and longshore wavenumber k in water of depth h(y) = h1H(σy/h1), 0 [les ] y < ∞, are calculated through an asymptotic expansion in σ/kh1 on the assumptions that σ [Lt ] 1 and kh1 = O(1). Approximations to the free-surface displacement in an inner domain that includes the singular point at h = 0 and the turning point near gh ≈ ω2/K2 and to the eigenvalue λ ≡ ω2/σgh are obtained for the complete set of modes on the assumption that h(y) is analytic. A uniformly valid approximation for the free-surface displacement and a variational approximation to Λ are obtained for the dominant mode. The results are compared with the shallow-water approximations of Ball (1967) for a slope that decays exponentially from σ to 0 as h increases from 0 to h1 and of Minzoni (1976) for a uniform slope that joins h = 0 to a flat bottom at h = h1 and with the geometrical-optics approximation of Shen, Meyer & Keller (1968).

scholarly journals Asymptotics of sloshing eigenvalues for a triangular prism

2021 ◽  
pp. 1-33
Author(s):  
JULIEN MAYRAND ◽  
CHARLES SENÉCAL ◽  
SIMON ST–AMANT
Keyword(s):  
Asymptotic Expansion ◽  
Surface Waves ◽  
Counting Function ◽  
Three Dimensional ◽  
Triangular Prism ◽  
Edge Waves ◽  
Counting Problem ◽  
Sloping Beach

Abstract We consider the three-dimensional sloshing problem on a triangular prism whose angles with the sloshing surface are of the form ${\pi}/{2q}$ , where q is an integer. We are interested in finding a two-term asymptotic expansion of the eigenvalue counting function. When both angles are ${\pi}/{4}$ , we compute the exact value of the second term. As for the general case, we conjecture an asymptotic expansion by constructing quasimodes for the problem and computing the counting function of the related quasi-eigenvalues. These quasimodes come from solutions of the sloping beach problem and correspond to two kinds of waves, edge waves and surface waves. We show that the quasi-eigenvalues are exponentially close to real eigenvalues of the sloshing problem. The asymptotic expansion of their counting function is closely related to a lattice counting problem inside a perturbed ellipse where the perturbation is in a sense random. The contribution of the angles can then be detected through that perturbation.

scholarly journals Free surface waves over a depression

2002 ◽  
Vol 65 (2) ◽  
pp. 329-335 ◽  
Author(s):  
J. W. Choi
Keyword(s):  
Free Surface ◽  
Solitary Wave ◽  
Incompressible Fluid ◽  
Surface Waves ◽  
Froude Number ◽  
Kdv Equation ◽  
Forcing Term ◽  
Free Surface Waves ◽  
Wave Solutions

Steady waves at the free surface of an incompressible fluid passing over a depression are considered. By studying a KdV equation with negative forcing term, new types of solutions are discovered numerically and a new cut-off value of the Froude number, above which unsymmetric solitary-wave-like wave solutions exist, is also found.

scholarly journals Fundamental solutions for the long–short-wave interaction system

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1093-1099
Author(s):  
Mustafa Inc ◽  
Samia Zaki Hassan ◽  
Mahmoud Abdelrahman ◽  
Reem Abdalaziz Alomair ◽  
Yu-Ming Chu
Keyword(s):  
Fluid Mechanics ◽  
Traveling Wave ◽  
Inverse Method ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Wave Interaction ◽  
Fundamental Solutions ◽  
Short Wave ◽  
Wave Solutions ◽  
Physical Environments

Abstract In this article, the system for the long–short-wave interaction (LS) system is considered. In order to construct some new traveling wave solutions, He’s semi-inverse method is implemented. These solutions may be applicable for some physical environments, such as physics and fluid mechanics. These new solutions show that the proposed method is easy to apply and the proposed technique is a very powerful tool to solve many other nonlinear partial differential equations in applied science.

scholarly journals Experiments on generation of surface waves by an underwater moving bottom

2015 ◽  
Vol 471 (2178) ◽  
pp. 20150069 ◽  
Author(s):  
Timothée Jamin ◽  
Leonardo Gordillo ◽  
Gerardo Ruiz-Chavarría ◽  
Michael Berhanu ◽  
Eric Falcon
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Surface Deformation ◽  
Fluid Layer ◽  
Fluid Velocity ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass ◽  
Spatio Temporal ◽  
Experimental Findings

We report laboratory experiments on surface waves generated in a uniform fluid layer whose bottom undergoes an upward motion. Simultaneous measurements of the free-surface deformation and the fluid velocity field are focused on the role of the bottom kinematics (i.e. its spatio-temporal features) in wave generation. We observe that the fluid layer transfers bottom motion to the free surface as a temporal high-pass filter coupled with a spatial low-pass filter. Both filter effects are often neglected in tsunami warning systems, particularly in real-time forecast. Our results display good agreement with a prevailing linear theory without any parameter fitting. Based on our experimental findings, we provide a simple theoretical approach for modelling the rapid kinematics limit that is applicable even for initially non-flat bottoms: this may be a key step for more realistic varying bathymetry in tsunami scenarios.

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