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The persistence of balance in geophysical flows

Published online by Cambridge University Press:  14 October 2021

David G. Dritschel  and
Álvaro Viúdez
David G. Dritschel
Affiliation:
School of Mathematics and Statistics, University of St Andrews, St Andrews, UKdgd@mcs.st-and.ac.uk
Álvaro Viúdez
Affiliation:
Institut de Ciènces del Mar, CSIC, Barcelona, Spainaviudez@cmima.csic.es
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Abstract

Rotating stably stratified geophysical flows can exhibit a near ‘balanced’ evolution controlled by the conservative advection of a single scalar quantity, the potential vorticity (PV). This occurs frequently in the Earth's atmosphere and oceans where motions tend to be weak compared with the background planetary rotation and where stratification greatly inhibits vertical motion. Under these circumstances, both high-frequency acoustic waves and lower-frequency inertia–gravity waves (IGWs) contribute little to the flow evolution compared with the even-lower-frequency advection of PV. Moreover, this ‘slow’ PV-controlled balanced evolution appears unable to excite these higher-frequency waves in any significant way – i.e. balance persists.

The present work pushes the limits of balance by systematically exploring the evolution of a range of highly nonlinear flows in which motions are comparable with the background rotation. These flows do not possess a frequency separation between PV advection and IGWs. Nonetheless, the flows exhibit a remarkable persistence of balance. Even when flows are not initialized to minimize the amount of IGWs initially present, and indeed even when flows are deliberately seeded with significant IGW amplitudes, the flow evolution – over many inertial periods (days) – remains strongly controlled by PV advection.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 570 , 10 January 2007 , pp. 365 - 383
Copyright
Copyright © Cambridge University Press 2007

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