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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

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

An approximate technique is presented for including the effect of turbulent bottom friction in the forced first-order wave equation governing long generalized coastal trapped waves. The resulting governing equations include both damping and a cross-shelf and vertical phase shift. A set of examples shows that damping of free waves decreases as the static stability increases, consistent with the inhibition of vertical motions by stratification.

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K. H. Brink

Abstract

The agreement between coastal trapped wave theory and observation is studied for the case of observations made off Peru during the 1977 CUEA JOINT-II experiment. Wave properties are calculated using a numerical model with realistic, horizontally uniform stratification and realistic bottom topography. These properties are then explored as a function of the ratio of the first internal Rossby radius of deformation to the shelf-slope width. The agreement of observed and calculated first-mode, free wave phase speeds (230 cm s−1) is excellent, while modal structures agree more poorly. A forced wave calculation, using observed winds and currents as input, is used to hindcast alongshore currents and sea level in the frequency band where Smith (1978) observed free coastal trapped waves during 1977. The model suggests that most of the observed sea level and alongshore velocity fluctuations in the 5–10 day period band are due to free waves originating equatorward of 5&deg's, while winds between 5&deg's and 15&deg's contribute little to the observed variance. Finally, free coastal trapped wave, calculations are briefly compared with CUEA observations from off Northwest Africa and Oregon. Generally, the wave calculations appear to be a useful tool in interpretation of the field observations.

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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

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 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

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 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

A linear numerical model of an island or a tall seamount is used to explore superinertial leaky resonances forced by ambient vertically and horizontally uniform current fluctuations. The model assumes a circularly symmetric topography (including a shallow reef) and allows realistic stratification and bottom friction. As long as there is substantial stratification, a number of leaky resonances are found, and when the island’s flanks are narrow relative to the internal Rossby radius, some of the near-resonant modes resemble leaky internal Kelvin waves. Other “resonances” resemble higher radial mode long gravity waves as explored by Chambers. The near-resonances amplify the cross-reef velocities that help fuel biological activity. Results for cases with the central island replaced by a lagoon do not differ greatly from the island case which has land at the center. As an aside, insight is provided on the question of offshore boundary conditions for superinertial nearly trapped waves along a straight coast.

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