David G Dritschel, Jemma Shipton & Will McKiver
Mathematical Institute, University of St Andrews, Scotland
Recently, a powerful new procedure was introduced to separate balanced vortical motions from imbalanced (inertia-)gravity wave motions in flows with O(1) Rossby and Froude numbers (Viudez and Dritschel, J. Fluid Mech., vol. 521, 2004, p. 343). This procedure, called "Optimal PV (OPV) balance", has proved effective in isolating weak-amplitude gravity waves in a variety of flows ranging from shallow water to three-dimensional non-hydrostatic. It attributes significantly less - often orders of magnitude less - of the motion to gravity waves than conventional balance methods, e.g. those based on quasi-geostrophy or extensions thereof. The amplitude of the unbalanced motions (the gravity waves) is astonishingly weak in many circumstances. Just what impact do they have then? We quantify this using OPV balance, recursively, to measure the rate of generation of imbalance in a series of complex flows. The impact varies most strongly with the Froude number, but remains very weak for Froude numbers less than unity.