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QUANTITATIVE SKILL ASSESSMENT FOR COASTAL OCEAN MODELS, COASTAL AND ESTUARINE STUDIES, VOL. 47, PAGES 125–152, 1995

Depth Dependent Analytical and Numerical Solutions for Wind-Driven Flow in the Coastal Ocean

Charles G. Hannah and Daniel G. Wright


Abstract

We develop a linear depth-dependent analytical solution for wind-driven flow in the coastal ocean which is valid for a wide range of frequencies and wavelengths. While there can be no along-shelf variations in the topography, features such as off‐shore ridges can be represented. The steady, long-wave, depth-independent limit of our solution is the arrested topographic wave [Csanady, 1978].

The analytical solution is used to test a finite element numerical model which solves an equivalent mathematical system. The numerical model performs very well. The largest differences occur at the the coast where the velocity estimate of the numerical model degenerates to first order in the grid resolution. The next largest source of error is associated with the abrupt changes in bottom slope which were introduced for analytical convenience. An amplification of the relative errors in velocity compared to those in the pressure gradient is also observed, and a simple explanation is given.

The development of a cross‐shelf vertical overturning circulation is favoured by steep slopes, large along-shelf scales, strong bottom friction, and small vertical eddy viscosities. Momentum blocking by dissipation in shallow water requires a thick Ekman layer and that the time scale on which momentum is removed by the bottom stress is short compared to the inertial period. Under these conditions an offshore ridge can effectively block the flow and the placement of a vertical wall at the coast places no additional constraints on the solution.

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Citation: Hannah, C. G., and Daniel G. Wright (1995), Depth Dependent Analytical and Numerical Solutions for Wind-Driven Flow in the Coastal Ocean, in Quantitative Skill Assessment for Coastal Ocean Models, Coastal Estuarine Stud., vol. 47, edited by D. R. Lynch and C. N. K. Mooers, pp. 125-152, AGU, Washington, D. C.