Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-23T18:55:03.138Z Has data issue: false hasContentIssue false
  • English
  • Français

Energy intensity of inertial waves in a sphere

Published online by Cambridge University Press:  17 February 2009

W. W. Wood
W. W. Wood
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria 3052.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The decay at large wavenumbers of the energy density in an inertial wave generated in a sphere by an arbitrary initial disturbance is determined as a first step to a comparison with the general theory of Phillips [17] for a statistically steady field of random inertial waves in an arbitrary cavity.

Type
Research Article
Information
The ANZIAM Journal , Volume 25 , Issue 2 , October 1983 , pp. 145 - 160
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Bjerknes, V. and Solberg, H., “Zelluläre Trägheitswellen und Turbulenz”, Avhandl. Norsk Vid. Akad. Mat. Nat. Kl. 7 (1929), 1–16.Google Scholar
[2]Bretherton, F. P., “Low frequency oscillations trapped near the equator”, Tellus 16 (1964), 181–185.Google Scholar
[3]Chandler, S. C., “On the variation in latitude”, Astronom. J. 12 (1892), 17–24.CrossRefGoogle Scholar
[4]Erdélyi, A., Higher transcendental functions, Vol. 1 (McGraw-Hill, New York, 1953).Google Scholar
[5]Frederiksen, J. S. and Sawford, B. L., “Statistical dynamics of two-dimensional inviscid flow on a sphere”, J. Atmos. Sci. 37 (1980), 717–732.2.0.CO;2>CrossRefGoogle Scholar
[6]Greenspan, H. P., The theory of rotating fluids (Cambridge University Press, 1968).Google Scholar
[7]Haurwitz, B., “The motion of atmospheric disturbances on the spherical earth”, J. Mar. Res. 3 (1940), 254–267.Google Scholar
[8]Hide, R., “Free hydromagnetic oscillations of the earth's core and the theory of the geomagnetic secular variation”, Phil. Trans. Roy. Soc. London Ser. A 259 (1966), 615–647.Google Scholar
[9]Hough, S. S., “The oscillations of a rotating ellipsoidal shell containing fluid”, Phil. Trans. Roy. Soc. London Ser. A 186 (1895), 469–506.Google Scholar
[10]Israeli, M., Time-dependent motions of confined rotating fluids, Ph.D. Thesis, Massachusetts Institute of Technology, 1971.Google Scholar
[11]Lord, Kelvin, “Vibrations of a columnar vortex”, Philos. Mag. 10 (1880), 155–168.Google Scholar
[12]Kraichnan, R. H., “Statistical dynamics of two-dimensional flow”, J. Fluid Mech. 67 (1975), 155–175.CrossRefGoogle Scholar
[13]Liapounoff, A., “Sur la stabilité des figures ellipsoidales d'équilibre d'un liquide animé d'un mouvement de rotation”, Annales de la Faculté des Sciences de l' Université de Toulouse 2e serie 6 (1904) and 9 (1908).CrossRefGoogle Scholar
[14]Lyttleton, R. A., The stability of rotating liquid masses (Cambridge University Press, 1953).Google Scholar
[15]Malkus, W. V. R., “Hydromagnetic planetary waves”, J. Fluid Mech. 28 (1967), 793–802.CrossRefGoogle Scholar
[16]McEwan, A. D., “Inertial oscillations in a rotating fluid cylinder”, J. Fluid Mech. 40 (1970), 603–640.CrossRefGoogle Scholar
[17]Phillips, O. M., “Energy transfer in rotating fluids by reflection of inertial waves”, Phys. Fluids 6 (1963), 513–520.CrossRefGoogle Scholar
[18]Poincaré, H., “Sur l'équilibre d'une masse fluide animée d'un mouvement de rotation”, Acta Math. 7 (1885), 259–380.CrossRefGoogle Scholar
[19]Poincaré, H., “Sur la précession des corps déformables”, Bull. Astronom. 27 (1910), 321–356.CrossRefGoogle Scholar
[20]Rumyantsev, V. V., “Stability of motion of solid bodies with liquid-filled cavities by Lyapunov's methods”, Adv. Appl. Mech. 8 (1964), 183–232.CrossRefGoogle Scholar
[21]Smith, M. L., “Wobble and nutation of the earth”, Geophys. J. Roy. Astronom. Soc. 50 (1977),103–140.CrossRefGoogle Scholar
[22]Stewartson, K., “On trapped oscillations of a rotating fluid in a thin spherical shell”, Tellus 24 (1972), 283–287.CrossRefGoogle Scholar
[23]Stewartson, K. and Rickard, J. A., “Pathological oscillations of a rotating fluid”, J. Fluid Mech. 35 (1969), 759–773.CrossRefGoogle Scholar
[24]Thorne, R. C., “The asymptotic expansion of Legendre functions of large degree and order”, Phil. Trans. Roy. Soc. London Ser. A 249 (1957), 597–620.Google Scholar
[25]Wood, W. W., “An oscillatory disturbance of rigidly rotating fluid”, Proc. Roy. Soc. London Ser. A 293 (1966), 181–212.Google Scholar
[26]Wood, W. W., “A note on the westward drift of the earth's magnetic field”, J. Fluid Mech. 82 (1977), 389–400.CrossRefGoogle Scholar
[27]Wood, W. W., “Inertial oscillations in a rigid axisymmetric container”, Proc. Roy. Soc. London Ser. A 358 (1977), 17–30.Google Scholar
[28]Wood, W. W., “Inertial modes with large azimuthal wavenumbers in an axisymmetric container”, J. Fluid Mech. 105 (1981), 427–449.CrossRefGoogle Scholar