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Understanding Barotropic and Baroclinic Rossby Waves: Observations and Theory

Explore the physics behind Rossby waves, including their dispersion relations, phase and group speeds, and phase propagation. Discover the differences between barotropic and baroclinic modes, and learn about the observations of Rossby waves from satellite altimeter data. Compare these observations with theoretical models of geostrophic turbulence using Quasi-Geostrophic theory.

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Understanding Barotropic and Baroclinic Rossby Waves: Observations and Theory

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  1. (N2 H/g)*1/(nH) = tan(nH) where n=(p/H)*i and i=1,2,… hyperbola tan N2H/g ≈ Dr/r0 • • • “mode” 0 1 2 For barotropic (i=0) mode: tan(nH)~nH  (nH)2 ≈ Dr/r0<<1

  2. w = -b0l / (l2+m2+1/Ri) Rossby wave dispersion relation Ri=[NH/f0]/(ip) = LD/(ip) Mode-i Rossby deformation radius

  3. Long wave  Fast phase speed wmax l2=a2=gH/f Long waves: Non-dispersive cp=cg=-b0a2 Short wave  Slow phase speed eastward group velocity westward group velocity

  4. Phase propagation Mode-0 (barotropic) Rossby Wave Physics (planetary b-effect) v0=g/f h/x div. conv. div.

  5. Mode-1 baroclinic Rossby wave: Note: Unlike reduced gravity model, both layers move! Westward phase propagation b0v ≈ ∂w/∂z = -(∂u/∂x + ∂v/∂y) v>0 --> convergence

  6. Mid-Latitude Rossby Waves from Satellite Altimeter from Chelton and Schlax (1996)

  7. Equatorial Rossby Waves from Satellite Altimeter from Chelton and Schlax (1996)

  8. Rossby Wave: Observations vs. Theory

  9. Geostrophic turbulence from QG-theory: q=q(x,y,t=const.,z=const.)

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