A Spectral Model of Wind-Forced Internal Waves

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  • 1 Science Applications International Corp., McLean, Virginia
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Abstract

It is hypothesized that wind forcing is a dominant generator of internal waves. A linear model is derived for the transfer of wind stress into vertical motions associated with internal waves. Two key assumptions are made in order to develop a wavenumber-frequency spectrum of wind stress. The first assumption is that the two-dimensional wavenumber spectrum is separable into two components, one parallel to the direction of mean synoptic flow and the other normal to it. A spectra form for each wavenumber component is hypothesized, based on aircraft measurements of mesoscale wind fields. The second key assumption is that the mesoscale wind field is frozen and advects with a uniform velocity associated with synoptic-scale motions. With these assumptions, the dynamics can be cast into a stationary reference frame-yielding a wavenumber-frequency spectrum-or into a moving reference frame-yielding a 2D wavenumber spectrum.

The resulting internal wave spectrum for vertical velocity is cast into various projections, and compared with the Garrett and Munk spectrum. With the proper choice of model parameters, excellent agreement between frequency spectra is obtained. It is found that the wind stress divergence dominates over wind stress curl in the generation of the internal wave continuum. Various sensitivities to model parameters are explored. A Rayleigh distribution of wind field advection speeds (as observed in synoptic scale weather maps) yields a response very similar to a single, average advection speed (11 m s−1). The lowest vertical mode is the most energetic for conditions where the surface mixed layer depth is greater than about 300 m. For a mixed layer depth of 100 m, the third vertical mode is most energetic.

Abstract

It is hypothesized that wind forcing is a dominant generator of internal waves. A linear model is derived for the transfer of wind stress into vertical motions associated with internal waves. Two key assumptions are made in order to develop a wavenumber-frequency spectrum of wind stress. The first assumption is that the two-dimensional wavenumber spectrum is separable into two components, one parallel to the direction of mean synoptic flow and the other normal to it. A spectra form for each wavenumber component is hypothesized, based on aircraft measurements of mesoscale wind fields. The second key assumption is that the mesoscale wind field is frozen and advects with a uniform velocity associated with synoptic-scale motions. With these assumptions, the dynamics can be cast into a stationary reference frame-yielding a wavenumber-frequency spectrum-or into a moving reference frame-yielding a 2D wavenumber spectrum.

The resulting internal wave spectrum for vertical velocity is cast into various projections, and compared with the Garrett and Munk spectrum. With the proper choice of model parameters, excellent agreement between frequency spectra is obtained. It is found that the wind stress divergence dominates over wind stress curl in the generation of the internal wave continuum. Various sensitivities to model parameters are explored. A Rayleigh distribution of wind field advection speeds (as observed in synoptic scale weather maps) yields a response very similar to a single, average advection speed (11 m s−1). The lowest vertical mode is the most energetic for conditions where the surface mixed layer depth is greater than about 300 m. For a mixed layer depth of 100 m, the third vertical mode is most energetic.

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