Critical layer instability as a resonance between a non-singular mode and continuous modes

Fluid Dynamics Research

Volumn 25, Issue 2, 1999, Pages 63-86

  Iga, Keita ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

Continuous modes; Critical layer instability; Critical level; Potential vorticity gradient; Pseudomomentum; Resonance of waves

Indexed keywords

RESONANCE; VORTEX FLOW;

CRITICAL LAYER INSTABILITY; POTENTIAL VORTICITY GRADIENT; PSEUDOMOMENTUM;

WATER WAVES;

INSTABILITY; POTENTIAL VORTICITY; RESONANCE; WAVE;

EID: 0033180559     PISSN: 01695983     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0169-5983(98)00031-8     Document Type: Article

References (24)

1. Blumen W. Shear layer instability of an inviscid compressible flow. J. Fluid Mech. 40:1970;769-781.
2. Bretherton F.P. Critical layer instability in baroclinic flows. Quart. J. Roy. Meteor. Soc. 92:1966;325-334.
3. Cairns R.A. The role of negative energy waves in some instabilities of parallel flows. J. Fluid Mech. 92:1979;1-14.
4. Case K.M. Stability of inviscid plane Couette flow. Phys. Fluids. 3:1960;143-148.
5. Eady E.T. Long waves and cyclone waves. Tellus. 1:1949;33-52.
6. Hayashi Y.-Y., Young W.R. Stable and unstable shear modes on rotating parallel flows in shallow water. J. Fluid Mech. 184:1987;477-504.
7. Held I.M. Pseudomomentum and the orthogonality of modes in shear flows. J. Atmos. Sci. 42:1985;2280-2288.
8. Howard L.N. Note on a paper of John W. Miles. J. Fluid Mech. 10:1961;509-512.
9. Iga K. Reconsideration of Orlanski's instability theory of frontal waves. J. Fluid Mech. 255:1993;213-236.
10. Iga K. Instability of a front with a layer of uniform potential vorticity. J. Meteor. Soc. Japan. 75:1997;1-11.
11. Killworth P.D., Paldor N., Stern M.E. Wave propagation and growth on a surface front in a two-layer geostrophic current. J. Mar. Res. 42:1984;761-785.
12. Kubokawa A. Instability of a geostrophic front and its energetics. Geophys. Astrophys. Fluid Dyn. 33:1985;223-257.
13. Kubokawa A. Instability caused by the coalescence of two modes of a one-layer frontal model. J. Oceanogr. Soc. Japan. 42:1986;373-380.
14. Lin C.C. On the stability of two-dimensional parallel flows Part. II. Quart. Appl. Math. 3:1945;218-234.
15. Lin C.C. Some mathematical problems in the theory of the stability of parallel flows. J. Fluid Mech. 10:1961;430-438.
16. Paldor N. Linear stability and stable modes of geostrophic modes. Geophys. Astrophys. Fluid Dyn. 24:1983;299-326.
17. Paldor N. Stability and stable modes of coastal fronts. Geophys. Astrophys. Fluid Dyn. 27:1983;217-228.
18. Pedlosky J. The stability of currents in the atmosphere and the ocean: Part I. J. Atmos. Sci. 21:1964;201-219.
19. Ripa P. General stability conditions for zonal flows in a one-layer model on the. β -plane or the sphere J. Fluid Mech. 126:1983;463-489.
20. Sakai S. Rossby-Kelvin instability: a new type of ageostrophic instability caused by a resonance between Rossby waves and gravity waves. J. Fluid Mech. 202:1989;149-176.
21. Satomura T. An investigation of shear instability in a shallow water. J. Meteor. Soc. Japan. 59:1981;148-167.
22. Takayabu I. Wave-momentum diagnosis on various development mechanisms of baroclinic waves in the Eady problem. J. Meteor. Soc. Japan. 71:1993;503-515.
23. Thorncroft C.D., Hoskins B.J. Frontal cyclogenesis. J. Atmos. Sci. 47:1990;2317-2336.
24. Vanneste J. Rossby wave interaction in a shear flow with critical levels. J. Fluid Mech. 323:1996;317-338.