Research output: Contribution to journal › Article

**Balance in non-hydrostatic rotating stratified turbulence.** / Mckiver, William J.; Dritschel, David G.

Research output: Contribution to journal › Article

Mckiver, WJ & Dritschel, DG 2008, 'Balance in non-hydrostatic rotating stratified turbulence' *Journal of Fluid Mechanics*, vol. 596, pp. 201-219. https://doi.org/10.1017/S0022112007009421

Mckiver, W. J., & Dritschel, D. G. (2008). Balance in non-hydrostatic rotating stratified turbulence. *Journal of Fluid Mechanics*, *596*, 201-219. https://doi.org/10.1017/S0022112007009421

Mckiver WJ, Dritschel DG. Balance in non-hydrostatic rotating stratified turbulence. Journal of Fluid Mechanics. 2008 Feb 10;596:201-219. https://doi.org/10.1017/S0022112007009421

@article{7a75894e8ac3424bb719593b6dc34b46,

title = "Balance in non-hydrostatic rotating stratified turbulence",

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 inertia-gravity 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 inertia-gravity 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 non-hydrostatic 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 quasi-geostrophic scaling analysis of the complete non-hydrostatic equations. This 'nonlinear quasi-geostrophic 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) quasi-geostrophic balance (which is based on the linearized equations about a state of rest). Nonlinear quasi-geostrophic 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 quasi-geostrophic features with, in particular, typical height-to-width scale ratios remaining comparable to f/N.",

keywords = "POTENTIAL-VORTICITY INVERSION, ROSSBY-NUMBER EXPANSIONS, QUASI-GEOSTROPHIC THEORY, INERTIA-GRAVITY WAVES, GEOPHYSICAL FLOWS, SLAVING PRINCIPLES, BAROTROPIC MODEL, EQUATIONS, INITIALIZATION, DYNAMICS",

author = "Mckiver, {William J.} and Dritschel, {David G.}",

year = "2008",

month = "2",

day = "10",

doi = "10.1017/S0022112007009421",

language = "English",

volume = "596",

pages = "201--219",

journal = "Journal of Fluid Mechanics",

issn = "0022-1120",

publisher = "CAMBRIDGE UNIV PRESS",

}

TY - JOUR

T1 - Balance in non-hydrostatic rotating stratified turbulence

AU - Mckiver, William J.

AU - Dritschel, David G.

PY - 2008/2/10

Y1 - 2008/2/10

N2 - 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 inertia-gravity 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 inertia-gravity 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 non-hydrostatic 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 quasi-geostrophic scaling analysis of the complete non-hydrostatic equations. This 'nonlinear quasi-geostrophic 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) quasi-geostrophic balance (which is based on the linearized equations about a state of rest). Nonlinear quasi-geostrophic 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 quasi-geostrophic features with, in particular, typical height-to-width scale ratios remaining comparable to f/N.

AB - 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 inertia-gravity 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 inertia-gravity 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 non-hydrostatic 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 quasi-geostrophic scaling analysis of the complete non-hydrostatic equations. This 'nonlinear quasi-geostrophic 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) quasi-geostrophic balance (which is based on the linearized equations about a state of rest). Nonlinear quasi-geostrophic 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 quasi-geostrophic features with, in particular, typical height-to-width scale ratios remaining comparable to f/N.

KW - POTENTIAL-VORTICITY INVERSION

KW - ROSSBY-NUMBER EXPANSIONS

KW - QUASI-GEOSTROPHIC THEORY

KW - INERTIA-GRAVITY WAVES

KW - GEOPHYSICAL FLOWS

KW - SLAVING PRINCIPLES

KW - BAROTROPIC MODEL

KW - EQUATIONS

KW - INITIALIZATION

KW - DYNAMICS

UR - http://www.scopus.com/inward/record.url?scp=38349108857&partnerID=8YFLogxK

U2 - 10.1017/S0022112007009421

DO - 10.1017/S0022112007009421

M3 - Article

VL - 596

SP - 201

EP - 219

JO - Journal of Fluid Mechanics

T2 - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -

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David Gerard Dritschel (Editor)2005 → …Activity: Publication peer-review and editorial work types › Editor of research journal

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ID: 621313