Baroclinic Instability Variations. F. Javier Beron-Vera J. Fluid Mech., 352: 245 (1997) M. Josefina Olascoaga J. Geophys. Res., 104: 23,357 (1999) Pedro Miguel Ripa J. Fluid Mech . , 403: 1 (2000) J. Fluid Mech . , 428: 387 (2001) Rev. Mex. Fís. , in press. Outline. Background
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J. Fluid Mech., 352: 245(1997)
J. Geophys. Res., 104: 23,357(1999)
J. Fluid Mech., 403: 1(2000)
J. Fluid Mech., 428: 387(2001)
Rev. Mex. Fís., in press
Eady (1949): β = 0, rigid horizontal boundaries
Blumsack & Gierasch (1972): β = 0, sloping bottom
Fukamachi et al. (1995):β = 0, free bottom, βT = 0 (topographic)
Beron-Vera (1997):β = 0, free bottom, βT 0
Lindzen (1994): β 0, but q uniform.
Phillips (1951): β 0, rigid horizontal boundaries
Bretherton (1966): β = 0, rigid sloping boundaries
Olascoaga (1999) : β 0, free bottom , βT 0
Basic Flow: Two Charney # (beta/shear)
Outside the wedge, a hamiltonian (“energy”) is H > 0: nonlinear stability (Arnold’s First Theorem)
All hamiltonians are sign independent for
κL(b,bT) < κ < κS(b,bT)
Notice the finite region for κL(b,bT) = 0
Normal Mode instability, for κL(b,bT) < κ < κS(b,bT)
Growth Rate along different directions in the (b,bT) plane (see color coded regions in slide 5)
The conditionb + bT 0 corresponds to the cancellation of both beta effects+ T 0: near resonance of true waves.This “explains” the maximum growth rate.
Bounding the wavy part of the perturbation qj,à la Shepherd, or the whole perturbation qj