Author(s): J. Van De Kreeke; A. A. Chiu

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Abstract: For a square bight (= square basin with two neighboring open boundaries) residual flows are computed 1) by (semi-analytically) solving the time averaged tidal equations, 2) by numerically solving the tidal equations and time averaging the tidal flows. For a semi-enclosed basin, residual flows are computed by numerically solving the tidal equations. An explicit finite difference technique is used for the numerical solutions. The numerical computations for the square bight are carried out using three different approaches (approximations) to accomodate the cross-differentiated terms at the open boundaries. When restricting attention to the interior, for all three approximations good agreement is found between the residual flows computed with the methods 1 and 2. When inconsistent with the true (= semi-analytical solution) the approximations lead to an erroneous residual flow pattern adjacent to the boundary. Numerically computed residual flow patterns for the semi-enclosed basin show large eddies. Eddies are not present in the tidal flow. Because of the relatively large values of the advective terms and the applied finite difference formulation the computed flow patterns for the semi-enclosed basin should be regarded as tentative. The relation between residual flow, Eulerian mean velocity, Lagrangian mean velocity and the Stokes velocity is discussed. Contrary to one-dimensional tidal flow, for two-dimensional flow the Lagrangian mean velocity is not the equivalent of the residual flow divided by the mean depth. However, computations for the square bight show the difference to be small. Using the time-averaged tidal equations, the role of the residual stresses in generating residual flow is discussed.

DOI: https://doi.org/10.1080/00221688109499517

Year: 1981