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David Rubenstein

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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David Rubenstein

Abstract

Interactions between near-inertial waves and rough bathymetry are studied theoretically and numerically. Rough bathymetric features cause scattering, even when their length scales are much smaller than the wavelengths of the incident waves. The scattering efficiency depends on the relative slopes of the incident wave propagation and bottom features. Scattered wavelength are comparable to wavelengths of the bathymetry. In a steady-state situation over an isolated bump, most of the kinetic energy is associated with upward propagating waves, in agreement with observations. A spectral model shows that first-mode incident waves with wavelengths >150 km, and second-mode waves with wavelengths >50 km are completely scattered into smaller wavelengths, primarily into wavelengths smaller than the bathymetry spectrum roll-off, 40 km. This model is applied to a spectrum of incident internal waves. The principal interactions involve the scattering of low-frequency, low-wavenumber incident waves into higher wavenumbers. Because of its higher wavenumbers, the scattered wave field has elevated shear levels and a Richardson number that is reduced by a factor of about 3.6 with respect to the incident wave field. A time-dependent numerical model simulates the evolution of wind-induced waves over rough bathymetry. All of the first vertical mode, containing about 35% of the initial energy, is scattered into higher modes after 40 inertial periods.

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David M. Rubenstein

Abstract

We present a combined observational and theoretical study of the daytime evolution of the equatorial East African low-level jet stream. During the daytime, as the flow advects from a suppressed marine environment across the East African coastline to an actively convective environment, a mixed layer grows in depth. Using measurements taken aboard a research aircraft, the turbulence flux profiles of heat and momentum are computed. These profiles are used to descriptively analyze the daytime evolution of the jet structure.

A nonlinear entrainment model is developed to describe the evolution of the mixed layer in both time and space. Sensitivity tests examine the relative importance of the factors that influence the character and growth of the mixed layer.

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David M. Rubenstein and Glyn O. Roberts

Abstract

Recent observations suggest that the space-time spectrum of near-inertial motions is strongly modulated by ocean fronts and geostrophic shear. This paper postulates a mechanism that may be responsible for generating much of this variability in the vicinity of fronts. The effective inertial frequency is variable because of gradients in the mean flow associated with a front. As a result, phase differences accumulate in inertial oscillations over short length scales of order tens of kilometers. Inertial pumping ensures, and near-inertial waves propagate away from the front in various directions. Inertial energy in the mixed layer disperses more rapidly in the vicinity of the front, and the mixed layer depth assumes strong across-front variations. In the thermocline, scattered internal waves develop a modulated pattern of amplitude, within the front and in its vicinity.

In order to investigate this mechanism, a two-dimensional numerical model is developed. The model simulates a mixed layer sitting over a stratified interior, and a barotropic jet. Solutions are suggestive of patterns of variability that have been observed in the ocean.

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David Rubenstein, Fred Newman, and Walt Grabowski

Abstract

We derive a statistical model or shear to predict how measurement of mean-square shear vary with stratification and with vertical separation Δz between moored current meters. Our model is based on a simplified version of the vertical wavenumber-shear spectrum proposed by Gargett et al. We compare the model predictions with shear derived from current measurements in the seasonal thermocline, from the MILE-1 mooring. The comparison is favorable and provides us with a framework for evaluating the vertical length scales of shear from current meter time series.

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