Journal of Fluid Mechanics


Spontaneous inertia-gravity-wave generation by surface-intensified turbulence

E. Daniouxa1 p1, J. Vannestea1, P. Kleina2 and H. Sasakia3

a1 School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, King’s Buildings, Edinburgh EH9 3JZ, UK

a2 Laboratoire de Physique des Océans, Ifremer-CNRS-UBO-IRD, 29280 Plouzané, France

a3 Earth Simulator Center, JAMSTEC, 3173-25 Showa-machi, Kanazawa-ku, Yokohama, Kanagawa 236-0001, Japan


The spontaneous generation of inertia-gravity waves (IGWs) by surface-intensified, nearly balanced motion is examined using a high-resolution simulation of the primitive equations in an idealized oceanic configuration. At large scale and mesoscale, the dynamics, which is driven by baroclinic instability near the surface, is balanced and qualitatively well described by the surface quasi-geostrophic model. This however predicts an increase of the Rossby number with decreasing spatial scales and, hence, a breakdown of balance at small scale; the generation of IGWs is a consequence of this breakdown. The wave field is analysed away from the surface, at depths where the associated vertical velocities are of the same order as those associated with the balanced motion. Quasi-geostrophic relations, the omega equation in particular, prove sufficient to separate the IGWs from the balanced contribution to the motion. A spectral analysis indicates that the wave energy is localized around dispersion relation for free IGWs, and decays only slowly as the frequency and horizontal wavenumber increase. The IGW generation is highly intermittent in time and space: localized wavepackets are emitted when thin filaments in the surface density are formed by straining, leading to large vertical vorticity and correspondingly large Rossby numbers. At depth, the IGW field is the result of a number of generation events; away from the generation sites it takes the form of a relatively homogeneous, apparently random wave field. The energy of the IGW field generated spontaneously is estimated and found to be several orders of magnitude smaller than the typical IGW energy in the ocean.

(Received March 30 2011)

(Reviewed November 22 2011)

(Accepted February 14 2012)

(Online publication April 24 2012)

Key Words:

  • internal waves;
  • quasi-geostrophic flows;
  • wave–turbulence interactions


p1 Present address: Northwest Research Associates, Bellevue, WA 98009-3027, USA. Email address for correspondence: