Hostname: page-component-7c8c6479df-27gpq Total loading time: 0 Render date: 2024-03-28T15:32:31.741Z Has data issue: false hasContentIssue false

Radiation of acoustic and gravity waves and propagation of boundary waves in the stratified fluid from a time-varying bottom boundary

Published online by Cambridge University Press:  25 May 2009

SHINGO WATADA*
Affiliation:
Earthquake Research Institute, University of Tokyo, Bunkyo-ku Yayoi 1-1-1, Tokyo 113-0032, Japan
*
Email address for correspondence: watada@eri.u-tokyo.ac.jp

Abstract

Energy flow and radiation of linearized acoustic–gravity waves and propagation of boundary waves in a gravitationally stratified isothermal compressible inviscid semi-infinite fluid from a time-varying bottom boundary are investigated in the frequency–wavenumber domain. Impedance Z, the ratio of the bottom vertical displacement to the fluid pressure above it, is a function of the frequency and horizontal wavenumber (ω, k) of the bottom boundary undulation. The amplitude and phase of Z at the bottom boundary divide the (ω, k) coordinates into wave-type regimes. In contrast to the pure acoustic or gravity wave case, the phase of Z is continuous but changes quickly across the regime boundaries between the propagating waves and trapped waves at the bottom, except for the Lamb wave branch along which the amplitude is infinite and across which the phase jumps by π. The phase of Z determines the efficiency of the work against the fluid by the deforming bottom boundary, showing reduced upward wave-energy flow from the bottom near the regime boundaries in which the phase of Z approaches ±π/2. For precise modelling of pressure waves and the energy flow of acoustic and gravity waves in the fluid originating from a time-dependent bottom-surface deformation with an apparent phase velocity comparable to the speed of sound in the fluid, it is necessary to include the dependency on (ω, k) of impedance Z.

Type
Papers
Copyright
Copyright © Cambridge University Press 2009

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

REFERENCES

Arendt, S. & Fritts, D. C. 2000 Acoustic radiation by ocean surface waves. J. Fluid Mech. 415, 121.CrossRefGoogle Scholar
Baines, P. G. 1995 Topographic Effects in Stratified Flows. Cambridge University Press.Google Scholar
Beer, T. 1974 Atmospheric Waves. Adam Hilger.Google Scholar
Blackstock, D. T. 2000 Fundamentals of Physical Acoustics. John Wiley.Google Scholar
Booker, J. R. & Bretherton, F. P. 1967 The critical layer for internal gravity waves in a shear flow. J. Fluid Mech. 27, 513539.CrossRefGoogle Scholar
Cushman-Roisin, B. 1994 Introduction to Geophysical Fluid Dynamics. Prentice HallGoogle Scholar
Gill, A. E. 1982 Atmosphere–Ocean Dynamics. Elsevier.Google Scholar
Golitsyn, G. S. & Klyatskin, V. I. 1967 Atmospheric oscillations caused by movements of Earth's surface. Izv. Atmos. Ocean. Phys. 3, 613617.Google Scholar
Gossard, E. E. & Hooke, W. H. 1975 Waves in the Atmosphere. ElsevierGoogle Scholar
Guo, Y. P. 1987 Waves induced by source near the ocean surface. J. Fluid Mech. 181, 293310.Google Scholar
Houghton, J. T. 1986 The Physics of Atmosphere, 2nd ed. Cambridge University Press.Google Scholar
Lighthill, J. 1978 Waves in Fluids. Cambridge University Press.Google Scholar
Mikumo, T., Shibutani, T., Pichon, A. L., Garces, M., Fee, D., Tsuyuki, T., Watada, S. & Morii, W. 2008 Low-frequency acoustic–gravity waves from coseismic vertical deformation associated with the 2004 Sumatra–Andaman earthquake (Mw = 9.2) J. Geophys. Res. 113, B12402. Doi: 10.1029/2008JB005710.CrossRefGoogle Scholar
Watada, S., Kunugi, T., Hirata, K., Sugioka, H., Nishida, K., Sekiguchi, S., Oikawa, J., Tsuji, Y. & Kanamori, H. 2006 Atmospheric pressure change associated with the 2003 Tokachi-Oki earthquake. Geophys. Res. Lett. 33, L24306. Doi: 10.1029/2006GL027967.Google Scholar
Waxler, R. & Gilbert, K. E. 2006 The radiation of atmospheric microbaroms by ocean waves. J. Acoust. Soc. Am. 119, 26512664.CrossRefGoogle Scholar
Whitham, G. B. 1999 Linear and Nonlinear Waves. John Wiley.Google Scholar
Williams, W. G. 1999 Fourier Acoustics. Academic.Google Scholar
Yih, C.-S. 1980 Stratified Flows. AcademicGoogle Scholar