Wave attractors and the asymptotic dissipation rate of tidal disturbances

Journal of Fluid Mechanics

Volumn 543, Issue , 2005, Pages 19-44

  Ogilvie, Gordon I ^a,b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; DAMPING; EIGENVALUES AND EIGENFUNCTIONS; GRAVITY WAVES; LINEAR EQUATIONS; NATURAL FREQUENCIES; NAVIER STOKES EQUATIONS; VISCOSITY; VORTEX FLOW;

INERTIAL WAVES; WAVE FREQUENCIES;

ROTATIONAL FLOW;

INTERNAL WAVE; INVISCID FLUID; ROTATING FLOW;

EID: 28244482840     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112005006580     Document Type: Article

References (28)

1. Aldridge, K. D. & Lumb, L. I. 1987 Inertial waves identified in the Earth's fluid outer core. Nature 325, 421-423.
2. Bretherton, F. P. 1964 Low-frequency oscillations trapped near the equator. Tellus 16, 181-185.
3. Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
4. Christensen-Dalsgaard, J. 2002 Helioseismology. Rev. Mod. Phys. 74, 1073-1129.
5. Goldreich, P. & Tremaine, S. 1980 Disk-satellite interactions. Astrophys. J. 241, 425-441.
6. Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
7. Hollerbach, R. & Kerswell, R. R. 1995 Oscillatory internal shear layers in rotating and precessing flows. J. Fluid Mech. 298, 327-339.
8. Ioannou, P. J. & Lindzen, R. S. 1993 Gravitational tides in the outer planets. I. Implications of classical tidal theory. Astrophys. J. 406, 252-265.
9. Kato, S. 2001 Basic properties of thin-disk oscillations. Proc. Astr. Soc. Japan 53, 1-24.
10. Maas, L. R. M. 2001 Wave focusing and ensuing mean flow due to symmetry breaking in rotating fluids. J. Fluid Mech. 437, 13-28.
11. Maas, L. R. M., Benielli, D., Sommeria, J. & Lam, F.-P. A. 1997 Observation of an internal wave attractor in a confined, stably stratified fluid. Nature 388, 557-561.
12. Maas, L. R. M. & Lam, F.-P. A. 1995 Geometric focusing of internal waves. J. Fluid Mech. 300, 1-41.
13. Manders, A. M. M. & Maas, L. R. M. 2003 Observations of inertial waves in a rectangular basin with one sloping boundary. J. Fluid Mech. 493, 59-88.
14. Moore, D. W. & Saffman, P. G. 1969 The structure of free vertical shear layers in a rotating fluid and the motion produced by a slowly rising body. Phil. Trans. R. Soc. Lond. A 264, 597-634.
15. Ogilvie, G. I. & Lin, D. N. C. 2004 Tidal dissipation in rotating giant planets. Astrophys. J. 610, 477-509.
16. Rieutord, M., Georgeot, B. & Valdettaro, L. 2001 Inertial waves in a rotating spherical shell: Attractors and asymptotic spectrum. J. Fluid Mech. 435, 103-144.
17. Rieutord, M. & Valdettaro, L. 1997 Inertial waves in a rotating spherical shell. J. Fluid Mech. 341, 77-99.
18. Rieutord, M., Valdettaro, L. & Georgeot, B. 2002 Analysis of singular inertial modes in a spherical shell: The slender toroidal shell model. J. Fluid Mech. 463, 345-360.
19. Savonije, G. J. & Papalaoizu, J. C. B. 1997 Non-adiabatic tidal forcing of a massive, uniformly rotating star - II. The low-frequency, inertial regime. Mon. Not. R. Astr. Soc. 291, 633-650.
20. Savonije, G. J., Papaloizou, J. C. B. & Alberts, F. 1995 Non-adiabatic tidal forcing of a massive, uniformly rotating star. Mon. Not. R. Astr. Soc. 277, 471-496.
21. ○ star with a binary companion. Astr. Astrophys. 386, 211-221.
22. Stern, M. E. 1963 Trapping of low-frequency oscillations in an equatorial 'boundary layer'. Tellus 15, 246-250.
23. Stewartson, K. 1972 On trapped oscillations in a slightly viscous rotating fluid. J. Fluid Mech. 54, 749-761.
24. Stewartson, K. & Rickard, J. A. 1969 Pathological oscillations of a rotating fluid. J. Fluid Mech. 35, 759-773.
25. Tassoul, J.-L. 1978 Theory of Rotating Stars. Princeton University Press.
26. Tilgner, A. 1999 Driven inertial oscillations in spherical shells. Phys. Rev. E 59, 1789-1794.
27. Zahn, J.-P. 1970 Forced oscillations in close binaries. The adiabatic approximation. Astr. Astrophys. 4, 452-461.
28. Zhang, K., Liao, X. & Earnshaw, P. 2004 On inertial waves and oscillations in a rapidly rotating spheroid. J. Fluid Mech. 504, 1-40.