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On the energetics of a two-layer baroclinic flow

Published online by Cambridge University Press:  08 March 2017

Thibault Jougla
Affiliation:
School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, UK
David G. Dritschel
Affiliation:
School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, UK
Corresponding
E-mail address:

Abstract

The formation, evolution and co-existence of jets and vortices in turbulent planetary atmospheres is examined using a two-layer quasi-geostrophic $\unicode[STIX]{x1D6FD}$ -channel shallow-water model. The study in particular focuses on the vertical structure of jets. Following Panetta & Held (J. Atmos. Sci., vol. 45 (22), 1988, pp. 3354–3365), a vertical shear arising from latitudinal heating variations is imposed on the flow and maintained by thermal damping. Idealised convection between the upper and lower layers is implemented by adding cyclonic/anti-cyclonic pairs, called hetons, to the flow, though the qualitative flow evolution is evidently not sensitive to this or other small-scale stochastic forcing. A very wide range of simulations have been conducted. A characteristic simulation which exhibits alternation between two different phases, quiescent and turbulent, is examined in detail. We study the energy transfers between different components and modes, and find the classical picture of barotropic/baroclinic energy transfers to be too simplistic. We also discuss the dependence on thermal damping and on the imposed vertical shear. Both have a strong influence on the flow evolution. Thermal damping is a major factor affecting the stability of the flow while vertical shear controls the number of jets in the domain, qualitatively through the Rhines scale $L_{Rh}=\sqrt{U/\unicode[STIX]{x1D6FD}}$ .

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© 2017 Cambridge University Press 

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Jougla et al. supplementary movie

This movie exhibits the upper layer flow (on the top) and the lower layer flow (on the bottom) corresponding to figures 3 and 4, but from $t=3500$ to $t=4500$. Left: normalised latitude $2y/\pi$ vs zonally-averaged zonal velocity $\bar{u}_i(y,t)$. Centre: PV field $q_i(x,y,t)$ over the entire domain. Right: equivalent latitude $y_e( \tilde{q},t)$ vs normalised PV $ \tilde{q}=(q-q_{\mathsf{min}})/(q_{\mathsf{max}}-q_{\mathsf{min}})$.

Download Jougla et al. supplementary movie(Video)
Video 8 MB

Jougla et al. supplementary movie

This movie exhibits the upper layer flow (on the top) and the lower layer flow (on the bottom) corresponding to figure 5, but from $t=9000$ to $t=10000$. Left: normalised latitude $2y/\pi$ vs zonally-averaged zonal velocity $\bar{u}_i(y,t)$. Centre: PV field $q_i(x,y,t)$ over the entire domain. Right: equivalent latitude $y_e( \tilde{q},t)$ vs normalised PV $ \tilde{q}=(q-q_{\mathsf{min}})/(q_{\mathsf{max}}-q_{\mathsf{min}})$.

Download Jougla et al. supplementary movie(Video)
Video 9 MB

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