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Wave turbulence in the two-layer ocean model

Published online by Cambridge University Press:  01 September 2014

Katie L. Harper ,
Sergey V. Nazarenko ,
Sergey B. Medvedev  and
Colm Connaughton
Katie L. Harper*
Affiliation:
Mathematics Institute, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
Sergey V. Nazarenko
Affiliation:
Mathematics Institute, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK Laboratoire SPHYNX, Service de Physique de l’Etat Condense, DSM, IRAMIS, CEA, Saclay, CNRS URA 2464, 91191, Gif-sur-Yvette, France
Sergey B. Medvedev
Affiliation:
Institute of Computational Technologies SD RAS, Lavrentjev Avenue 6, Novosibirsk, 630090, Russia
Colm Connaughton
Affiliation:
Mathematics Institute, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK Centre for Complexity Science, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK Okinawa Institute of Science and Technology Graduate University, 1919-1 Tancha Onna-son, Okinawa 904-0495, Japan
*
†Email address for correspondence: Katie.Harper@warwick.ac.uk
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Abstract

This paper looks at the two-layer ocean model from a wave-turbulence (WT) perspective. A symmetric form of the two-layer kinetic equation for Rossby waves is derived using canonical variables, allowing the turbulent cascade of energy between the barotropic and baroclinic modes to be studied. It is already well known that in two-layers, energy is transferred via triad interactions from the large-scale baroclinic modes to the baroclinic and barotropic modes at the Rossby deformation scale, where barotropization takes place, and from there to the large-scale barotropic modes via an inverse transfer. However, by applying WT theory, we find that energy is transferred via dominant $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\{+--\}$ triads with one barotropic component and two baroclinic components, and that the direct transfer of energy is local and the inverse energy transfer is non-local. We study this non-locality using scale separation and obtain a system of coupled equations for the small-scale baroclinic component and the large-scale barotropic component. Since the total energy of the small-scale component is not conserved, but the total barotropic plus baroclinic energy is conserved, the baroclinic energy loss at small scales will be compensated by the growth of the barotropic energy at large scales. Using the frequency resonance condition, we show that in the presence of the beta-effect this transfer is mostly anisotropic and mostly to the zonal component.

JFM classification

Geophysical and Geological Flows: Quasi-geostrophic flows Turbulent Flows: Wave-turbulence interactions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 756 , 10 October 2014 , pp. 309 - 327
Copyright
© 2014 Cambridge University Press 

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