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The tank wall effect on internal waves due to a transient vertical force moving at fixed depth in a density-stratified fluid

Published online by Cambridge University Press:  19 April 2006

E. W. Graham  and
B. B. Graham
E. W. Graham
Affiliation:
Graham Associates, Shaw Island, WA. 98286
B. B. Graham
Affiliation:
Graham Associates, Shaw Island, WA. 98286
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Abstract

The fluid is incompressible, inviscid and non-diffusive. It has a uniform Brunt–Väisälä frequency, N, and is of constant depth, D. A body or wing moves horizontally through the fluid at velocity U in a straight line, exerting a vertical force during a given time interval. The force is constant, or oscillatory with frequency σ. The vertical average of the strain rate in a thin surface layer is calculated for a network of points behind the body.

The linearized analysis is first applied with tank walls, then modified for remote walls and a vertical force of long duration.

For moderately high velocity and forcing frequency (U/ND = 5, σ/N≅ 4−16) the recurring internal wave pattern just behind the body is well established in one cycle of the oscillatory force. A tank width one or two times the depth gives good agreement between tank and no-wall calculations for the chosen examples.

For a stationary wing (U/ND = 0) in a cubic tank with forcing frequency one-half the natural frequency (σ/N = ½) the strain rates after one cycle are 103 times greater than for the moving wing case. After five cycles the magnitudes are twenty times larger than after one cycle. Presumably these large increases are due to the continuous and efficient feeding of energy into a small fluid volume which occurs for the stationary wing. No-wall calculations for many cycles give amplitudes roughly one-half those for five cycles in the tank, showing the effect of escaping energy.

The relation of these developments to stationary phase analysis and preferred directions is discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 97 , Issue 1 , 11 March 1980 , pp. 91 - 114
Copyright
© 1980 Cambridge University Press

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References

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