Dynamics of dense water cascades at the shelf edge
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Plumes of dense shelf water cascade down continental slopes in many parts of the world's oceans and provide a mechanism for shelf-ocean exchange. In this paper a nonlinear process-orientated theory is developed and used to examine the dynamics of cascading. The theory is formulated in terms of a "11/2-layer" model and incorporates bottom topography, earth rotation, internal and bottom friction, and entrainment as well as externally imposed pressure gradients. The theory occupies a niche between the stream tube class of model (which considers only bulk properties of a plume) and the full three-dimensional primitive equation approach. The model provides useful insights into the complex interplay between the controlling forces, and it allows one to recover the shape and trajectory of dense plumes as well as the three-dimensional flow field inside the bottom layer. Asymptotic limits are investigated and lead to several basic results. A typical thickness of a fully developed plume is found to be twice the bottom Ekman layer scale, corresponding to reported observations. The relative importance of downslope density-driven cascading and downslope drainage forced by interior currents is assessed. It is found that vertical mixing always assists downslope plume propagation, while an interior current may assist or inhibit cascading. The model is applied to some recent observations at the Hebridean shelf edge west of the British Isles and is used to infer the characteristics of an observed cascade. The model could also be applied to double frontal currents such as the Mediterranean outflow.
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