Hostname: page-component-7c8c6479df-995ml Total loading time: 0 Render date: 2024-03-28T17:02:28.767Z Has data issue: false hasContentIssue false

Internal waves generated by a translating oscillating body

Published online by Cambridge University Press:  29 March 2006

R. G. Rehm
Affiliation:
Calspan Corporation, Buffalo, New York
H. S. Radt
Affiliation:
Calspan Corporation, Buffalo, New York

Abstract

The internal-wave system is calculated for a body oscillating transversely, and translating uniformly, through an infinite stratified fluid of constant Brunt-Väisälä frequency. A linearized, time-dependent analysis is used, in which the vertical displacement of a fluid element is the basic dependent variable. Axisym-metric slender-body theory for a homogeneous fluid is used to determine the time-dependent source and dipole distributions required to represent the motion of the body for excitation of the internal waves. The equations are solved by Fourier-transform techniques; and the internal-wave amplitude is evaluated in the far field by the method of stationary phase. The surfaces of constant phase are found to change character as the ratio of the oscillation frequency ω of the body to the Brunt-Väisälä frequency N varies through unity. Along preferred directions, the amplitude of the internal waves is found to decay inversely with distance to the $\frac{5}{6}$ power, whereas, for uniform translation, the amplitude of the internal waves falls off inversely with distance from the body. An asymptotic expression for the amplitude in preferred directions is calculated for several values of the ratio ω/N.

Type
Research Article
Copyright
© 1975 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Erdélyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F. G. 1954 Tables of Integral Transforms. McGraw-Hill.
Frankl, F. I. & Karpovich, E. A. 1953 Gas Dynamics of Thin Bodies. Interscience.
Hendersrott, M. C. 1969 J. Fluid Mech. 36, 513.
Hurley, D. G. 1969 J. Fluid Mech. 36, 657.
Keller, J. B. & Munk, W. H. 1970 Phys. Fluids, 13, 1425.
Liepmann, H. W. & Rosrko, A. 1957 Elements of Gasdynamics. Wiley.
Lighthill, M. J. 1959 Phil. Trans. A 252, 397.
Lighthill, M. J. 1967 J. Fluid Mech. 27, 725.
Magnus, W. & Oberhettinger, F. 1949 Formulas and Theorems for the Functions of Mathematical Physics. Chelsea.
Mclaren, T. I., Pierce, A. D., Fohl, T. & Murphy, B. L. 1973 J. Fluid Mech. 57, 229.
Miles, J. W. 1971 Geophys. Fluid Dyn. 2, 63.
Mowbray, D. E. & Rarity, B. S. H. 1967 J. Fluid Mech. 28, 1.
Olver, F. W. J. 1964 Handbook of Mathematical Functions (ed. I. Abramowitz & I. A. Stegun), p. 355. Washington: U.S. Government Printing Office.
RAO, G. V. P. 1973 J. Fluid Mech. 61, 129.
Stevenson, T. N. & Thomas, N. H. 1969 J. Fluid Mech. 36, 505.
Stevenson, T. N. 1973 J. Fluid Mech. 60, 759.