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The Wave-Driven Ocean Circulation

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  • 1 Department of Atmospheric Sciences and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, Los Angeles, California
  • | 2 Department of Mathematics and Program in Applied Mathematics, The University of Arizona, Tucson, Arizona
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Abstract

Oceanic surface gravity waves have a mean Lagrangian motion, the Stokes drift. The dynamics of wind-driven, basin-scale oceanic currents in the presence of Stokes drift are modified by the addition of so-called vortex forces and wave-induced material advection, as well by wave-averaged effects in the surface boundary conditions for the dynamic pressure, sea level, and vertical velocity. Some theoretical analyses previously have been made for the gravity wave influences on boundary-layer motions, including the Ekman currents. The present paper extends this theory to the basin-scale, depth-integrated circulation in a bounded domain. It is shown that the Sverdrup circulation relation, with the meridional transport proportional to the curl of the surface wind stress, applies to Lagrangian transport, while the associated Eulerian transport is shown to have a component opposite to the Stokes-drift transport. A wave-induced correction to the relation between sea level and surface dynamic pressure is also derived. Preliminary assessments are made of the relative importance of these influences using a global wind climatology and an empirical relationship between the wind and wave fields. Recommendations are made for further development and testing of this theory and for its inclusion in general circulation models.

Corresponding author address: Dr. James C. McWilliams, Dept. of Atmospheric Sciences, University of California, Los Angeles, 405 Hilgard Ave., Los Angeles, CA 90095-1565.

Email: jcm@atmos.ucla.edu

Abstract

Oceanic surface gravity waves have a mean Lagrangian motion, the Stokes drift. The dynamics of wind-driven, basin-scale oceanic currents in the presence of Stokes drift are modified by the addition of so-called vortex forces and wave-induced material advection, as well by wave-averaged effects in the surface boundary conditions for the dynamic pressure, sea level, and vertical velocity. Some theoretical analyses previously have been made for the gravity wave influences on boundary-layer motions, including the Ekman currents. The present paper extends this theory to the basin-scale, depth-integrated circulation in a bounded domain. It is shown that the Sverdrup circulation relation, with the meridional transport proportional to the curl of the surface wind stress, applies to Lagrangian transport, while the associated Eulerian transport is shown to have a component opposite to the Stokes-drift transport. A wave-induced correction to the relation between sea level and surface dynamic pressure is also derived. Preliminary assessments are made of the relative importance of these influences using a global wind climatology and an empirical relationship between the wind and wave fields. Recommendations are made for further development and testing of this theory and for its inclusion in general circulation models.

Corresponding author address: Dr. James C. McWilliams, Dept. of Atmospheric Sciences, University of California, Los Angeles, 405 Hilgard Ave., Los Angeles, CA 90095-1565.

Email: jcm@atmos.ucla.edu

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