On the Calculation of Tidal Currents in Homogeneous Estuaries

Carl E. Pearson Department of Aeronautics and Astronautics and Department of Oceanography, University of Washington, Seattle 98195

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Donald F. Winter Department of Aeronautics and Astronautics and Department of Oceanography, University of Washington, Seattle 98195

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Abstract

This paper describes a new approach to the computation of tidal flow in homogeneous estuaries with irregular boundary configurations and of arbitrary depth. The governing equations are the standard vertically integrated expressions of momentum and mass conservation including the effects of Coriolis acceleration, surface wind stress and bottom friction. The motion is assumed to be periodic and the original time-dependent equations are replaced by a set of modal equations obtained by Fourier decomposition, with the nonlinear terms being treated by an iteration technique. Two types of boundary conditions at the junction of the estuary with the sea are considered. 1) the specification of tidal height as a function of time across the mouth, and 2) continuity of height and velocity at the mouth when a source at sea generates waves propagating toward the estuary. It is shown that the boundary value problems as expressed by the modal equations and the boundary conditions in each case can be rephrased in term of variational principles. The variational principle is then used together with a finite element method to solve for the unknown variables—water surface height and depth-averaged velocities.

For the purpose of illustration the method is applied to estuaries with semi-elliptical boundaries and various bottom profiles. It appears that the method can provide both computational speed and numerical accuracy in a wide variety of problems of practical interest.

Abstract

This paper describes a new approach to the computation of tidal flow in homogeneous estuaries with irregular boundary configurations and of arbitrary depth. The governing equations are the standard vertically integrated expressions of momentum and mass conservation including the effects of Coriolis acceleration, surface wind stress and bottom friction. The motion is assumed to be periodic and the original time-dependent equations are replaced by a set of modal equations obtained by Fourier decomposition, with the nonlinear terms being treated by an iteration technique. Two types of boundary conditions at the junction of the estuary with the sea are considered. 1) the specification of tidal height as a function of time across the mouth, and 2) continuity of height and velocity at the mouth when a source at sea generates waves propagating toward the estuary. It is shown that the boundary value problems as expressed by the modal equations and the boundary conditions in each case can be rephrased in term of variational principles. The variational principle is then used together with a finite element method to solve for the unknown variables—water surface height and depth-averaged velocities.

For the purpose of illustration the method is applied to estuaries with semi-elliptical boundaries and various bottom profiles. It appears that the method can provide both computational speed and numerical accuracy in a wide variety of problems of practical interest.

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