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John Kroll

Abstract

The stability of Niiler's model of a deepening mixed layer was investigated assuming the deepening rate was negligible. Two basically different instability mechanisms appeared. One is a mixture of a Kelvin-Helmholtz type and parallel flow viscous type with a relatively small horizontal wavelength [O(1 km)]. The other depends on the perturbation of the bulk stress and is related to the inflection point type of instability of an inviscid shear model with a relatively long horizontal wavelength ]O(10 km)]. The former instability has its most unstable wave directed generally in the direction of the mean flow, while for the latter, it generally is perpendicular to the mean flow and opposite the wind. Each is likely to produce near-inertial motion. Though the former is potentially stronger than the latter, it is also less likely to occur for usual oceanic conditions.

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John Kroll

Abstract

In Part I we examined the stability of a model of the mixed layer, neglecting the deepening rate. Here we examine the effects of the deepening but neglect the oscillations in the steady state. We find that the two types of instability found previously are modified. The long wavelength [O(10) km] instability becomes more stable while the converse is true for the short wavelength [O(1) km] instability with the purely kinematic effect of the slowly deepening mixed layer on the equally slow vertically propagating near-inertial waves being of most importance. The short wavelength instability might be expected to be observed if the lateral friction is sufficiently large. There is also a different short wavelength instability which is basically independent of the ocean interior which might be expected to appear if friction is sufficiently small.

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John Kroll

Abstract

Over a deep barotropic ocean an isolated pressure cell, producing a wind stress curl, generates topographic Rossby waves which are incident on a continental shelf with a simple exponentially varying slope. It is shown that this energy appears as a distinct peak at low frequency on the energy spectrum on the shelf. A peak at 0.05 cycles per day (cpd) in the spectrum from data of Smith (1974) for the Oregon shelf is consistent with this effect. For the case where topography dominates the beta effect off the shelf, general equations are found to estimate the frequency and dominant wavelength of the energy peak. An interesting result of this analysis is that, for all parameters being equal, this frequency should be lower on an eastern shelf than a western shelf in the Northern Hemisphere due to the beta effect. The variation of the magnitude and frequency of this peak with the location on the shelf, the distance of the center of forcing from the shelf, and the scale of the pressure cell is then investigated for the Oregon shelf in particular.

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John Kroll and Pearn P. Niiler

Abstract

We know that long-period (>1 day) and long-wavelength (>100 km) topographical Rossby waves can be generated by a wind acting directly on a continental shelf (Adams and Buchwald, 1969). Here we examine the characteristics of them waves which can also be produced off the shelf by wind and current eddies and can propagate up to and onto the shelf. We use a shelf model which varies in depth in one direction only and assume that a shelf can be approximated by at most two breaks with the depth varying exponentially. We assume velocity-dependent bottom friction to determine the effect of frictional dissipation. The following results are derived by our analysis. The regression angle of scatter plots for topography-dominated waves should be small and the preponderant direction of the waves determined by the sign. The group velocity directed up the slope possesses an absolute maximum which occurs at a relatively short period. The ability of a wave moving up a slope to overcome friction correlates with this group velocity. The energy flux transmission across one and two breaks can be determined. It is suggested that the product of this flux transmission coefficient and the group velocity component up the shelf be the criterion to determine which wavelengths and frequencies penetrate nearest to shore. It is found, however, that the energy from off the shelf is likely to he decayed completely in bottom depths ≲25 m. A comparison of some results with data for the New England and west Florida shelf shows a general agreement.

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Sang-Ki Lee, J. L. Pelegrí, and John Kroll

Abstract

An analytic solution is presented for the steady-state depth-averaged western boundary current flowing over the continental slope by combining three highly idealized models: the Stommel model, the Munk model, and the arrested topographic wave model. The main vorticity balance over the slope is between planetary vorticity advection and the slope-induced bottom stress torque, which is proportional to r υ(h −1)x where r is the Rayleigh friction coefficient, h is the water depth, and υ is the meridional velocity. This slope-induced torque provides the necessary source of vorticity for poleward flow over the slope, its simple interpretation being that vorticity is produced because the bottom stress has to act over the seaward-deepening water column. The character of the solution depends on the slope α as well as on the assumed bottom drag coefficient, and the length scale of the boundary current is ∼2r/(βα). It is further shown that, if the depth-averaged velocity flows along isobaths, then the stretching of water columns associated with cross-isobath geostrophic flow, which compensates bottom Ekman transport, is identical to the slope-induced torque by the geostrophic velocities.

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