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Abstract
Wind forcing of the ocean generates a spectrum of inertiagravity waves that is sharply peaked near the local inertial (or Coriolis) frequency. The corresponding nearinertial waves (NIWs) are highly energetic and play a significant role in the slow, largescale dynamics of the ocean. To analyse this role, we develop a new model of the nondissipative interactions between NIWs and balanced motion. The model is derived using the generalisedLagrangianmean (GLM) framework (specifically, the glm variant of Soward & Roberts (2010)), taking advantage of the timescale separation between the two types of motion to average over the short NIW period.
We combine Salmon's (2013) variational formulation of GLM with Whitham averaging to obtain a system of equations governing the joint evolution of NIWs and mean flow. Assuming that the mean flow is geostrophically balanced reduces this system to a simple model coupling Young & Ben Jelloul's (1997) equation for NIWs with a modified quasigeostrophic equation. In this coupled model, the mean flow affects the NIWs through advection and refraction; conversely, the NIWs affect the mean flow by modifying the potentialvorticity inversion  the relation between advected potential vorticity and advecting mean velocity  through a quadratic wave term, consistent with the GLM results of Buhler & McIntyre (1998).
The coupled model is Hamiltonian and its conservation laws, for wave action and energy in particular, prove illuminating: on their basis, we identify a new interaction mechanism whereby NIWs forced at large scales extract energy from the balanced flow as their horizontal scale is reduced by differential advection and refraction so that their potential energy increases. A rough estimate suggests that this mechanism could provide a significant sink of energy for mesoscale motion and play a part in the global energetics of the ocean.
We combine Salmon's (2013) variational formulation of GLM with Whitham averaging to obtain a system of equations governing the joint evolution of NIWs and mean flow. Assuming that the mean flow is geostrophically balanced reduces this system to a simple model coupling Young & Ben Jelloul's (1997) equation for NIWs with a modified quasigeostrophic equation. In this coupled model, the mean flow affects the NIWs through advection and refraction; conversely, the NIWs affect the mean flow by modifying the potentialvorticity inversion  the relation between advected potential vorticity and advecting mean velocity  through a quadratic wave term, consistent with the GLM results of Buhler & McIntyre (1998).
The coupled model is Hamiltonian and its conservation laws, for wave action and energy in particular, prove illuminating: on their basis, we identify a new interaction mechanism whereby NIWs forced at large scales extract energy from the balanced flow as their horizontal scale is reduced by differential advection and refraction so that their potential energy increases. A rough estimate suggests that this mechanism could provide a significant sink of energy for mesoscale motion and play a part in the global energetics of the ocean.
Original language  English 

Pages (fromto)  143169 
Journal  Journal of Fluid Mechanics 
Volume  774 
Early online date  4 Jun 2015 
DOIs  
Publication status  Published  Jul 2015 
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 2 Finished


Science and Innovation: Numerical Algorithms and Intelligent Software for the Evolving HPC Platform
1/08/09 → 31/07/14
Project: Research
Profiles

Jacques Vanneste
 School of Mathematics  Personal Chair in Fluid Dynamics
Person: Academic: Research Active