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Abstract
It is now well established that two distinct types of motion occur in geophysical turbulence: slow motions associated with potential vorticity advection and fast oscillations due to inertiagravity waves (or acoustic waves). Many studies have theorized the existence of a flow for which the entire motion is controlled by the potential vorticity (or one 'master variable')  this is known as balance. In real geophysical flows, deviations from balance in the form of inertiagravity waves or 'imbalance' have often been found to be small. Here we examine the extent to which balance holds in rotating stratified turbulence which is nearly balanced initially.
Using the nonhydrostatic fluid dynamical equations under the Boussinesq approximation, we analyse properties of rotating stratified turbulence spanning a range of Rossby numbers (Ro equivalent to vertical bar zeta vertical bar(max)/f) and the frequency ratios (c equivalent to N/f) where is the relative vertical vorticity, f is the Coriolis frequency and N is the buoyancy frequency. Using a recently introduced diagnostic procedure, called 'optimal potential vorticity balance', we extract the balanced part of the flow in the simulations and assess how the degree of imbalance varies with the above parameters.
We also introduce a new and more efficient procedure, building upon a quasigeostrophic scaling analysis of the complete nonhydrostatic equations. This 'nonlinear quasigeostrophic balance' procedure expands the equations of motion to second order in Rossby number but retains the exact (unexpanded) definition of potential vorticity. This proves crucial for obtaining an accurate estimate of balanced motions. In the analysis of rotating stratified turbulence at Ro less than or similar to 1 and N/f >> 1, this procedure captures a significantly greater fraction of the underlying balance than standard (linear) quasigeostrophic balance (which is based on the linearized equations about a state of rest). Nonlinear quasigeostrophic balance also compares well with optimal potential vorticity balance, which captures the greatest fraction of the underlying balance overall.
More fundamentally, the results of these analyses indicate that balance dominates in carefully initialized simulations of freely decaying rotating stratified turbulence up to O(1) Rossby numbers when N/f >> 1. The fluid motion exhibits important quasigeostrophic features with, in particular, typical heighttowidth scale ratios remaining comparable to f/N.
Original language  English 

Pages (fromto)  201219 
Number of pages  19 
Journal  Journal of Fluid Mechanics 
Volume  596 
DOIs  
Publication status  Published  10 Feb 2008 
Keywords
 POTENTIALVORTICITY INVERSION
 ROSSBYNUMBER EXPANSIONS
 QUASIGEOSTROPHIC THEORY
 INERTIAGRAVITY WAVES
 GEOPHYSICAL FLOWS
 SLAVING PRINCIPLES
 BAROTROPIC MODEL
 EQUATIONS
 INITIALIZATION
 DYNAMICS
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Dive into the research topics of 'Balance in nonhydrostatic rotating stratified turbulence'. Together they form a unique fingerprint.Projects
 1 Finished

EPSRC GR/S69290/01: A new twist to rotating stratified turbulance
Dritschel, D. G. (PI)
1/03/04 → 28/02/07
Project: Standard