TY - JOUR

T1 - Impeded inverse energy transfer in the Charney--Hasegawa--Mima model of quasi-geostrophic flows

AU - Tran, Chuong Van

AU - Dritschel, David Gerard

PY - 2006/3/25

Y1 - 2006/3/25

N2 - The behaviour of turbulent flows within the single-layer quasi-geostrophic (Charney-Hasegawa-Mima) model is shown to be strongly dependent on the Rossby deformation wavenumber lambda (or free-surface elasticity). Herein, we derive a bound oil the inverse energy transfer, specifically on the growth rate dl/dt of the characteristic length scale e representing the energy centroid. It is found that dl/dt <= 2 parallel to q parallel to(infinity)/(l(s)lambda(2)), where parallel to q parallel to(infinity) is the supremum of the potential vorticity and l(s) represents the potential enstrophy centroid of the reservoir, both invariant. This result implies that in the potential-energy-dominated regime (l >= l(s) >> lambda(-1)) the inverse energy transfer is strongly impeded, in the sense that under the usual time scale no significant transfer of energy to larger scales occurs. The physical implication is that the elasticity of the free surface impedes turbulent energy transfer in wavenumber space, effectively rendering large-scale vortices long-lived and inactive. Results from numerical simulations of forced-dissipative turbulence confirm this prediction.

AB - The behaviour of turbulent flows within the single-layer quasi-geostrophic (Charney-Hasegawa-Mima) model is shown to be strongly dependent on the Rossby deformation wavenumber lambda (or free-surface elasticity). Herein, we derive a bound oil the inverse energy transfer, specifically on the growth rate dl/dt of the characteristic length scale e representing the energy centroid. It is found that dl/dt <= 2 parallel to q parallel to(infinity)/(l(s)lambda(2)), where parallel to q parallel to(infinity) is the supremum of the potential vorticity and l(s) represents the potential enstrophy centroid of the reservoir, both invariant. This result implies that in the potential-energy-dominated regime (l >= l(s) >> lambda(-1)) the inverse energy transfer is strongly impeded, in the sense that under the usual time scale no significant transfer of energy to larger scales occurs. The physical implication is that the elasticity of the free surface impedes turbulent energy transfer in wavenumber space, effectively rendering large-scale vortices long-lived and inactive. Results from numerical simulations of forced-dissipative turbulence confirm this prediction.

KW - Drift-wave turbulence

KW - 2-dimensional turbulence

KW - Spectral distribution

KW - Vortices

KW - Cascade

KW - Fluid

KW - Plane

UR - http://www.scopus.com/inward/record.url?scp=33646791856&partnerID=8YFLogxK

U2 - 10.1017/S0022112005008384

DO - 10.1017/S0022112005008384

M3 - Article

SN - 0022-1120

VL - 551

SP - 435

EP - 443

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

ER -