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The evolution of a front in turbulent thermal wind balance. Part 1. Theory

Published online by Cambridge University Press:  04 July 2018

Matthew N. Crowe  and
John R. Taylor Open the ORCID record for John R. Taylor [Opens in a new window]
Matthew N. Crowe
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
John R. Taylor*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: J.R.Taylor@damtp.cam.ac.uk
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Abstract

Here, we examine the influence of small-scale turbulence on the evolution of fronts in the ocean and atmosphere. Specifically, we consider the evolution of an initially balanced density front subject to an imposed viscosity and diffusivity as a simple analogue for small-scale turbulence. At late times, the dominant balance is found to be the quasisteady turbulent thermal wind balance with time evolution due to an advection–diffusion balance in the buoyancy equation. We use the leading-order balance to determine analytical similarity solutions for the spreading of a front and find that the spreading rate is maximum for an intermediate value of the Ekman number, with the spreading resulting from shear dispersion associated with the cross-front flow and vertical diffusion of density. In response to shear dispersion, the front evolves towards a density profile that is nearly linear in the cross-front coordinate. At the edges of the frontal zone, the density field develops large curvature, and these regions are associated with narrow bands of intense vertical velocity.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Ocean processes Geophysical and Geological Flows: Rotating flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 850 , 10 September 2018 , pp. 179 - 211
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Copyright
© 2018 Cambridge University Press 

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