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Beyond Lighthill: three ways to stay close to balance

McIntyre, ME (Cambridge)
Wednesday 10 December 2008, 09:30-10:00

Seminar Room 1, Newton Institute


This talk proposes to discuss the recently discovered cases of hybrid propagating structures consisting of vortex dipoles and co-moving gravity waves undergoing wave capture. It is shown how these cases fall outside the scope of the Lighthill theory of spontaneous imbalance and, concomitantly, outside the scope of shallow-water dynamics. Besides the fact that going from shallow water to continuous stratification allows disparate vertical scales -- small for inertia-gravity waves and large for vortical motion -- the key points are (a) that in contrast with cases covered by the Lighthill theory the wave source in these cases feels an order-unity radiation reaction, hence cannot be prescribed in advance, when Rossby numbers R \sim 1; (b) that cases of this sort will supply exceptions to the general rule that spontaneous imbalance is exponentially small in R; and (c) that unsteady vortical motion in continuous stratification can stay close to balance thanks to three quite separate mechanisms. These are (1) the near-suppression, by Lighthill interference, of large-scale imbalance (inertia-gravity waves of large horizontal scale) where "large" means relative to Rossby deformation lengths L_D characterizing the vortical motion, (2) the low-group-velocity flaccidity hence near-steadiness of L_D-wide jets that meander and form loops, Gulf-Stream-like, on streamwise scales >> L_D, and (3) the dissipation of small-scale imbalance by wave capture leading to wave breaking, generically likely in an environment of random shear and straining. Shallow-water models include the first two mechanisms but exclude the third.


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