Generation of long waves in a basin of variable depth in the process of formation of a region of perturbations of atmospheric pressure

2000 ◽  
Vol 11 (1) ◽  
pp. 1-10
Author(s):  
A. A. Bukatov ◽  
S. F. Dotsenko
Keyword(s):  
Atmospheric Pressure ◽  
Long Waves ◽  
Variable Depth

Long waves induced by short-wave groups over an uneven bottom

1984 ◽  
Vol 139 ◽  
pp. 219-235 ◽  
Author(s):  
Chiang C. Mei ◽  
Chakib Benmoussa
Keyword(s):  
Group Velocity ◽  
Short Wave ◽  
Long Waves ◽  
Finite Region ◽  
Variable Depth ◽  
Wave Groups ◽  
One Dimensional ◽  
Uneven Bottom ◽  
Short Waves ◽  
Horizontal Bottom

Unidirectional and periodically modulated short waves on a horizontal or very nearly horizontal bottom are known to be accompanied by long waves which propagate together with the envelope of the short waves at their group velocity. However, for variable depth with a horizontal lengthscale which is not too great compared with the group length, long waves of another kind are further induced. If the variation of depth is only one-dimensional and localized in a finite region, then the additional long waves can radiate away from this region, in directions which differ from those of the short waves and their envelopes. There are also critical depths which define caustics for these new long waves but not for the short waves. Thus, while obliquely incident short waves can pass over a topography, these second-order long waves may be trapped on a ridge or away from a canyon.

scholarly journals The tidal oscillation in an elliptic basin of variable depth-II

1936 ◽  
Vol 155 (884) ◽  
pp. 12-32 ◽  
Author(s):  
George Ridsdale Goldsbrough
Keyword(s):  
Infinite Series ◽  
Elliptic Cylinder ◽  
Long Waves ◽  
Analogous Problem ◽  
Algebraic Polynomials ◽  
Variable Depth ◽  
Finite Sets ◽  
Tidal Oscillation ◽  
The Subject ◽  
Arithmetical Calculation

The problem of the long waves in an elliptic lake with a paraboloidal law of depth was solved in a previous paper.* It appeared that the solutions could be expressed in terms of certain algebraic polynomials, from whose general properties the character of the motions could be readily derived. The subject of the present paper is the more important problem of the same basin subjected to rotation. The analogous problem of a rotating elliptic lake of uniform depth has been solved by Goldstein who used infinite series of elliptic cylinder functions. The law of depth used in the present paper, however, enables the solutions to be expressed in terms of finite sets of polynomials. The earlier modes can be completely determined without recourse to long arithmetical calculation and the interpretation of the analysis is easier. In the course of the work many properties of the polynomial are investigated.

scholarly journals The tidal oscillations in an elliptic basin of variable depth

1930 ◽  
Vol 130 (812) ◽  
pp. 157-167 ◽  
Keyword(s):  
Bessel Function ◽  
Simple Formula ◽  
Elliptic Cylinder ◽  
Long Waves ◽  
The Other ◽  
Transcendental Function ◽  
Algebraic Polynomials ◽  
Variable Depth ◽  
Numerical Approximations

The problem of the "long" waves in a circular basin of uniform depth involves in its solution a transcendental function–the Bessel function, and the determination of the free periods requires a knowledge of the zeros of this function or an allied function. On the other hand, when the basin, still circular, has a certain variable depth, it was shown by Lamb that the solution is expressed in terms of simple algebraic polynomials and the free periods of oscillation are expressed by an extremely simple formula. In similar fashion, the solution of the problem of the "long" waves in an elliptic basin of uniform depth involves the use of elliptic cylinder functions, and the free periods are only obtained as the result of lengthy numerical approximations.

The response of a continental shelf to travelling pressure disturbances

1973 ◽  
Vol 24 (2) ◽  
pp. 143 ◽  
Author(s):  
VT Buchwald ◽  
RA de Szoeke
Keyword(s):  
Continental Shelf ◽  
Closed Form ◽  
Atmospheric Pressure ◽  
Step Function ◽  
Long Waves ◽  
Wave Number ◽  
Long Wave ◽  
Sinusoidal Disturbance ◽  
Speed Of Propagation ◽  
Rectangular Model

Assuming a rectangular model of a continental shelf, this paper sets out to calculate the response of the shelf and ocean regions to plane atmospheric pressure disturbances travelling with constant speed in a longshore direction. It is shown that, for a sinusoidal disturbance, there is resonance at a given speed of propagation c only if c lies between the speeds of long waves on the shelf and ocean regions, and then only if the wave number of the disturbance matches one of the possible modes of long waves trapped on the shelf. In addition, the passage of a pressure front along the shelf is modelled by a step function, and the response to such a disturbance is calculated in closed form. If the speed of the disturbance is between the speed of long waves in the shelf and ocean regions, then there is a wake of trapped long-wave modes, the amplitudes of which may be quite large compared with the change in the atmospheric pressure.

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