1. University of Reading School of Mathematics Meteorology & Physics Ian N. James I.N.James@reading.ac.uk 1 The Rossby wave paradigm and its problems Ian James School of Mathematics, Meteorology and Physics University of Reading

2. School of Mathematics Meteorology & Physics Ian N. James I.N.James@reading.ac.uk 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. University of Reading School of Mathematics Meteorology & Physics Ian N. James I.N.James@reading.ac.uk 3 Physical picture Displaced parcel acquires vorticity relative to environment. “Action at a distance”  < 0  > 0  < 0 A B

4. University of Reading School of Mathematics Meteorology & Physics Ian N. James I.N.James@reading.ac.uk 4 Ray tracing Packets propagate with group velocity (WKBJ) “Refractive index”  Pacific-North American pattern (  =0 Rossby wave)

5. University of Reading School of Mathematics Meteorology & Physics Ian N. James I.N.James@reading.ac.uk 5 Fluid instability 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)

6. University of Reading School of Mathematics Meteorology & Physics Ian N. James I.N.James@reading.ac.uk 6 Definition of PV gradient Quasi-geostrophic form: Barotropic: if then U [q] y

7. University of Reading School of Mathematics Meteorology & Physics Ian N. James I.N.James@reading.ac.uk 7 Towards a Rossby wave programme Rationale for smoothing of PV field? How do Rossby waves propagate in the presence of small scale [q] y anomalies? Scattering of Rossby waves in an inhomogeneous medium?