John R. Bennett

Accuracy of trajectory calculation in a finite-difference circulation model

Abstract The prediction of drifting object motion due to currents in an irregular body is a complex problem with a wide range of practical applications. Simple numerical methods for interpolating current velocity fields have spatial interpolation and time integration errors that result in misleading solutions. The method described in this paper minimizes these problems, yielding much more accurate predictions. This method can be easily implemented in other finite-difference models or finite-element models.

Comparison of a Two-Dimensional Wave Prediction Model with Synoptic Measurements in Lake Michigan

Abstract We compare results from a simple parametric, dynamical, deep-water wave prediction model with two sets of measured wave height maps of Lake Michigan. The measurements were made with an airborne laser altimeter under two distinctly different wind fields during November 1977. The results show that the model predicted almost all of the synoptic features. Both the magnitude and the general pattern of the predicted wave-height contours compared well with the measurements. The model also predicts the direction for wave propagation in conjunction with the wave height map, which is useful for practical ship routing and can be significantly different form the prevailing wind direction.

Calculation of the rotational normal modes of oceans and lakes with general orthogonal coordinates

Abstract A finite-difference method for computing the frequency and structure of the rotational modes of oscillation of enclosed seas is tested against known solutions for: (1) a circular basin with a parabolic depth law, (2) a circular, flat basin with a linear variation of the Coriolis parameter, and (3) an elliptic paraboloid. Several higher modes of the elliptic paraboloid are also calculated. The method uses the non-divergent assumption and solves the barotropic vorticity equation in general orthogonal coordinates generated by a conformal map of the shoreline onto the unit circle. The numerical procedure for calculating the conformal map of an arbitrarily shaped basin is presented.

Accuracy of a finite-difference method for computing lake currents

Abstract A semi-analytic model is used to assess the accuracy of a finite-difference model for computing lake currents. Both models solve the vorticity equation for two-dimensional, time-dependent flow to compute currents in a circular lake with a parabolic depth profile. The semi-analytic solution is obtained by using separation of variables to remove the azimuthal dependence and reduce the equations in cylindrical coordinates to a single equation in two variables, time and radius. This equation is then solved by a finite-difference technique for grid sizes small enough that the solution appears to converge. Comparison with the rectangular finite-difference solution shows a strong improvement in accuracy with decreasing grid size. It is found that about 20 grid points across a lake basin are required to adequately resolve winddriven flow.

The physics of sediment transport, resuspension, and deposition

The physics of sediment transport, resuspension and deposition is reviewed. First, the general problem is described and then emphasis is given to recent quantitative research in Lakes Ontario, Michigan and Erie. In this discussion, some original calculations are presented to show that Ekman layer sediment transport is important in determining the deposition areas in deep lakes.