HR: 13:40h
AN: OS23E-01 INVITED     [Abstracts]
TI: An Asymptotic and Stochastic Theory for the Effects of Surface Gravity Waves on Currents and Infragravity Waves
AU: * McWilliams, J C
EM: jcm@atmos.ucla.edu
AF: IGPP, UCLA , 405 Hilgard Ave. , Los Angeles, CA 90095-1567 United States
AU: Lane, E
EM: elane@grad.math.arizona.edu
AF: IGPP, UCLA , 405 Hilgard Ave. , Los Angeles, CA 90095-1567 United States
AU: Lane, E
EM: elane@grad.math.arizona.edu
AF: Math. Dept., Univ. of Arizona, Tucson, AZ 85721 United States
AU: Melville, K
EM: kmelville@ucsd.edu
AF: ORD, SIO, UCSD 9500 Gilman Drive, 0210, La Jolla, CA 92093-0210 United States
AU: Restrepo, J
EM: restrepo@math.arizona.edu
AF: Math. Dept., Univ. of Arizona, Tucson, AZ 85721 United States
AU: Sullivan, P
EM: pps@ncar.ucar.edu
AF: MMM, NCAR , P.O. Box 3000, Boulder, CA 80307
AB: Oceanic surface gravity waves are approximately irrotational, weakly nonlinear, and conservative, and they have a much shorter time scale than oceanic currents and longer waves (e.g., infragravity waves) --- except where the primary surface waves break. This provides a framework for an asymptotic theory, based on separation of time (and space) scales, of wave-averaged effects associated with the conservative primary wave dynamics combined with a stochastic representation of the momentum transfer and induced mixing associated with non-conservative wave breaking. Such a theory requires only modest information about the primary wave field from measurements or operational model forecasts and thus avoids the enormous burden of calculating the waves on their intrinsically small space and time scales. For the conservative effects, the result is a vortex force associated with the primary wave's Stokes drift; a wave-averaged Bernoulli head and sea-level set-up; and an incremental material advection by the Stokes drift. This can be compared to the "radiation stress" formalism of Longuet-Higgins, Stewart, and Hasselmann; it is shown to be a preferable representation since the radiation stress is trivial at its apparent leading order. For the non-conservative breaking effects, a population of stochastic impulses is added to the current and infragravity momentum equations with distribution functions taken from measurements. In offshore wind-wave equilibria, these impulses replace the conventional surface wind stress and cause significant differences in the surface boundary layer currents and entrainment rate, particularly when acting in combination with the conservative vortex force. In the surf zone, where breaking associated with shoaling removes nearly all of the primary wave momentum and energy, the stochastic forcing plays an analogous role as the widely used nearshore radiation stress parameterizations. This talk describes the theoretical framework and presents some preliminary solutions using it. McWilliams, J.C., J.M. Restrepo, & E.M. Lane, 2004: An asymptotic theory for the interaction of waves and currents in coastal waters. J. Fluid Mech. 511, 135-178. Sullivan, P.P., J.C. McWilliams, & W.K. Melville, 2004: The oceanic boundary layer driven by wave breaking with stochastic variability. J. Fluid Mech. 507, 143-174.
DE: 4512 Currents
DE: 4546 Nearshore processes
DE: 4560 Surface waves and tides (1255)
SC: Ocean Sciences [OS]
MN: 2004 AGU Fall Meeting