Linear Stability Models of Shelfbreak Fronts

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  • 1 College of Marine Studies, University of Delaware, Newark, Delaware
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Abstract

The stability of inviscid frontally trapped waves along a shelfbreak is examined to determine whether frontal instabilities may contribute to the alongfront variability frequently observed. Three different basic states with increasingly complex stratification are treated. In each case, the shelfbreak occurs where a constant depth shelf meets a slope region with linearly increasing depth.

The first basic state consists of an unstratified flow with a velocity discontinuity located at the shelfbreak. The resulting shear waves are stable for the velocity shear and topography typical of the Middle Atlantic Bight. Next, a two-layer, geostrophically balanced front located at the shelfbreak is considered. This is similar to the configuration of Flagg and Beardsley, but with an unbounded bottom topography offshore beyond the frontal region. For parameters typical of the Middle Atlantic Bight in winter, the most unstable wave is surface-trapped with a typical e-olding growth time scale of 9.5 days. The most unstable wavelength, 25 km, is roughly 20 percent more unstable using the unbounded topography seaward of the front versus using a flat bottom seaward of the frontal region.

The third case simulates the summer configuration of the shelfbreak front in the Middle Atlantic Bight. A subsurface two-layer front in geostrophic balance is overlain by a uniformly buoyant surface layer containing a horizontal velocity discontinuity. Pycnocline-trapped waves are the most unstable, and the wavelength of the most unstable wave is 25 km. Depending on the choice of density difference across the subsurface front, the e-folding time scale for growth may vary from 4.0 to 7.6 days. The only available observation for comparison had a time scale for growth of one day. The model growth time scale for summer is less than the growth time scale of the winter front. The model predicts that the front south of Georges Bank should be more stable than the front south of New England. The model is also applied to the eastern Bering Sea and the Iceland–Faroe front. The model results indicate that shelfbreak frontal instabilities have seasonal and regional variations that depend on the stratification and velocity shear.

Abstract

The stability of inviscid frontally trapped waves along a shelfbreak is examined to determine whether frontal instabilities may contribute to the alongfront variability frequently observed. Three different basic states with increasingly complex stratification are treated. In each case, the shelfbreak occurs where a constant depth shelf meets a slope region with linearly increasing depth.

The first basic state consists of an unstratified flow with a velocity discontinuity located at the shelfbreak. The resulting shear waves are stable for the velocity shear and topography typical of the Middle Atlantic Bight. Next, a two-layer, geostrophically balanced front located at the shelfbreak is considered. This is similar to the configuration of Flagg and Beardsley, but with an unbounded bottom topography offshore beyond the frontal region. For parameters typical of the Middle Atlantic Bight in winter, the most unstable wave is surface-trapped with a typical e-olding growth time scale of 9.5 days. The most unstable wavelength, 25 km, is roughly 20 percent more unstable using the unbounded topography seaward of the front versus using a flat bottom seaward of the frontal region.

The third case simulates the summer configuration of the shelfbreak front in the Middle Atlantic Bight. A subsurface two-layer front in geostrophic balance is overlain by a uniformly buoyant surface layer containing a horizontal velocity discontinuity. Pycnocline-trapped waves are the most unstable, and the wavelength of the most unstable wave is 25 km. Depending on the choice of density difference across the subsurface front, the e-folding time scale for growth may vary from 4.0 to 7.6 days. The only available observation for comparison had a time scale for growth of one day. The model growth time scale for summer is less than the growth time scale of the winter front. The model predicts that the front south of Georges Bank should be more stable than the front south of New England. The model is also applied to the eastern Bering Sea and the Iceland–Faroe front. The model results indicate that shelfbreak frontal instabilities have seasonal and regional variations that depend on the stratification and velocity shear.

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