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The Rossby wave paradigm and its problems

The Rossby wave paradigm and its problems. Ian James School of Mathematics, Meteorology and Physics University of Reading. Basic properties. Transverse wave motion in a fluid with a gradient of potential vorticity Dispersion relationship: Highly dispersive; anisotropic propagation

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The Rossby wave paradigm and its problems

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  1. The Rossby wave paradigm and its problems Ian James School of Mathematics, Meteorology and Physics University of Reading

  2. Basic properties • Transverse wave motion in a fluid with a gradient of potential vorticity • Dispersion relationship: • Highly dispersive; anisotropic propagation • Basic paradigm of low frequency flow

  3. Physical picture • Displaced parcel acquires vorticity relative to environment. • “Action at a distance” x < 0 x < 0 A B x > 0

  4. Ray tracing • Packets propagate with group velocity (WKBJ) • “Refractive index” m • Pacific-North American pattern (w=0 Rossby wave)

  5. Positive feedback between trains of Rossby waves Stationary wrt each other: sheared flow, change of sign of [q]y Barotropic instability (horizontal) Baroclinic instability (vertical) Fluid instability

  6. Definition of PV gradient • Quasi-geostrophic form: • Barotropic: if then U [q]y

  7. Towards a Rossby wave programme • Rationale for smoothing of PV field? • How do Rossby waves propagate in the presence of small scale [q]yanomalies? • Scattering of Rossby waves in an inhomogeneous medium?

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