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K. H. Brink

Abstract

Using a geometry which roughly approximates that of a typical continental shelf and slope, the effects of a random bottom topography on free barotropic shelf waves are found. The bathymetric irregularity induces damping of the coherent wave due to scattering, as well as Phase velocity Changes. For a representative realization of the bottom topography, the damping of low-mode long waves due to scattering is apparently comparable to that due to turbulent bottom friction. Damping peaks occur at frequencies where the coherent wave scatters into modes having a zero group velocity. Generally, the breadth of the peaks is a maximum when the alongshore topographic scale and the zero group velocity wavelength are comparable. Strong scattering to high modes, which have low phase velocities, may be prevented by the presence of a mean alongshore flow.

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K. H. Brink

Abstract

A perturbative method is presented for estimating the decay time of subinertial coastal-trapped waves under a wide range of conditions where damping is relatively weak. Bottom friction is sometimes much more important than “long-wave” results would suggest, even in the parameter range where the waves are approximately non-dispersive. The presence of a mean flow can greatly change the effect of bottom friction. Specifically, if the mean flow over the shelf has positive (negative) relative vorticity in the Northern (Southern) Hemisphere, wave damping increases. This mean flow effect appears to account for the failure of coastal-trapped waves to propagate into the Agulhas between Port Elizabeth and Durban, South Africa.

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K. H. Brink

Abstract

When steady flow in a stratified ocean passes between the continental slope and open ocean, its ability to cross isobaths is potentially limited by buoyancy arrest. If the bottom Ekman transport vanishes and there are no interior stresses, then steady linear flow on an f plane must be geostrophic and follow isobaths exactly. The influence of arrest on cross-shelf transport is investigated here to establish 1) whether there are substantial penetration asymmetries between cases with upwelling and downwelling in the bottom boundary layer; 2) over what spatial scales, hence in what parameter regime, buoyancy arrest is important; and 3) the effects of depth-dependent interior flow. The problem is approached using scalings and idealized numerical models. The results show that there is little or no asymmetry introduced by bottom boundary layer behavior. Further, if the stratification is weak or moderate, as measured by a slope Burger number s = αN/f (where α is the bottom slope, N is buoyancy frequency, and f is the Coriolis parameter), buoyancy arrest does not exert a strong constraint on cross-isobath exchange.

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K. H. Brink

Abstract

Models show that surface cooling over a sloping continental shelf should give rise to baroclinic instability and thus tend toward gravitationally stable density stratification. Less is known about how alongshore winds affect this process, so the role of surface momentum input is treated here by means of a sequence of idealized, primitive equation numerical model calculations. The effects of cooling rate, wind amplitude and direction, bottom slope, bottom friction, and rotation rate are all considered. All model runs lead to instability and an eddy field. While instability is not strongly affected by upwelling-favorable alongshore winds, wind-driven downwelling substantially reduces eddy kinetic energy, largely because the downwelling circulation plays a similar role to baroclinic instability by flattening isotherms and so reducing available potential energy. Not surprisingly, cross-shelf winds appear to have little effect. Analysis of the model runs leads to quantitative relations for the wind effect on eddy kinetic energy for the equilibrium density stratification (which increases as the cooling rate increases) and for eddy length scale.

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K. H. Brink

Abstract

This study attempts to isolate the physics peculiar to a submarine bank. The particular model is barotropic and contains an infinitely long straight bank within an unbounded ocean basin. The low-frequency, free wave solutions consist of two infinite sets of model analogous to barotropic continental shelf waves, one set trapped to each side of the bank. In addition, a severely distorted double Kelvin wave is associated with the net depth difference across the bank. Inclusion of bottom friction representative of Georges Bank suggests that only one free wave (westward propagating on the South side) will have a sufficiently long decay time to be likely to be observed in nature. The spatial variation in local spindown time also causes the lines of constant wave phase to be no longer perpendicular to the isobaths. Steady, forward motions are considered for winds which vary slowly in the alongbank direction. When the Ekman scale depth is the same order as the minimal depth over the bank, the primary driving mechanism is related to the disruption of surface Ekman transport by bottom friction. Alongbank wind stress is shown to be a fairly ineffectivc driving agent, while crossbank winds drive geostrophic currents relatively effectively. Also, since the crossbank winds vary in the alongbank direction, the resulting stress curl drives motions in the entire ocean. These large-scale currents are closed in boundary layers on the outer edges of the bank, thus isolating the inner bank from deep ocean influence.

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K. H. Brink

Abstract

The characteristics of long, gravest mode trench waves in the presence of realistic stratification are investigated. Two examples are computed, representing cases with widely differing importance of baroclinic effects. In both cases the wave-related alongshore velocity structure becomes noticeably bottom intensified, but much less so for the high latitude (smaller internal Rossby radius of deformation) Aleutian trench example than for the low latitude (larger Rossby radius) Peru trench example. Some consequences of the bottom trapping are then discussed.

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K. H. Brink

Abstract

A barotropic model is formulated to investigate the topographic drag due to steady barotropic alongshore flow over the continental shelf and slope. The topography is extensive, irregular and of small amplitude. Topographic drag is in general only appreciable when the mean flow runs counter to the direction of free shelf-wave phase propagation. The cross-shelf structure of the drag is determined by which mode lee waves dominate. This selection is determined by the projection of the topographic structure onto the wave mode, and by the degree of matching between dominant topographic length scale and natural lee wave wavelength.

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K. H. Brink

Abstract

In September 1985, the eye of Hurricane Gloria passed within about 100 km of a current meter mooring in the western North Atlantic. Data from this mooring provide a clear view of the vertical structure of the near-inertial wake in the main thermocline. The response at 159 m was strong (>25 cm s−1 amplitude) and lasted about 18 days. At greater depths, the response was weaker and more irregular. The phase of the near-inertial currents increased with depth, consistent with the downward spreading of enemy. The total phase change across the thermocline reached about a half cycle seven days after the hurricane's passage, indicating a large vertical scale of the response. The observations are briefly compared with other time series measurements (on the continental margin) and with models.

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K. H. Brink

Abstract

A consideration of energy conservation for coastal-trapped waves shows that, for a slowly varying medium, the normalization of the wave modes is not arbitrary. Errors related to incorrect normalization are demonstrated for a simple analytic example and for a realistic case. If alongshore changes in latitude, topography or stratification are substantial, then predicted time series are shown by example to have amplitude errors of as much as 50% if an incorrect normalization is applied.

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K. H. Brink

Abstract

There exists a good deal of indirect evidence, from several locations around the world, that there is a substantial eddy field over continental shelves. These eddies appear to have typical swirl velocities of a few centimeters per second and have horizontal scales of perhaps 5–10 km. These eddies are weak compared to typical, wind-driven, alongshore flows but often seem to dominate middepth cross-shelf flows. The idea that motivates the present contribution is that the alongshore wind stress ultimately energizes these eddies by means of baroclinic instabilities, even in cases where obvious intense fronts do not exist. The proposed sequence is that alongshore winds over a stratified ocean cause upwelling or downwelling, and the resulting horizontal density gradients are strong enough to fuel baroclinic instabilities of the requisite energy levels. This idea is explored here by means of a sequence of idealized primitive equation numerical model studies, each driven by a modest, nearly steady, alongshore wind stress applied for about 5–10 days. Different runs vary wind forcing, stratification, bottom slope, bottom friction, and Coriolis parameter. All runs, both upwelling and downwelling, are found to be baroclinically unstable and to have scales compatible with the underlying hypothesis. The model results, combined with physically based scalings, show that eddy kinetic energy generally increases with bottom slope, stratification, wind impulse (time integral of the wind stress), and inverse Coriolis parameter. The dominant length scale of the eddies is found to increase with increasing eddy kinetic energy and to decrease with Coriolis parameter.

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