Application of a Log-Linear Element to a Finite-Element Boundary-Layer Flow Model

The finite element method was used to develop a class of boundary elements for the modeling of geophysical flows. These elements have both logarithmic and linear terms for the vertical direction and a quadratic function in the streamwise direction to permit a more accurate representation of the logarithmic velocity profile normal to the boundary. The log-linear element was tested against a conventional (9-node) element in a one-dimensional time-dependent simulation of diffusion-dominated flow of 50 m depth over a surface of assumed roughness. The result of the single log-linear element and results from the conventional method using two grids of 6 and 10 quadratic elements were compared with the analytic solution. The present element demonstrates superior accuracy. Nearly identical results were obtained in one-dimensional high-resolution simulations of neutral flow in the lowest 1500 m with and without the log-linear boundary element. The influence on the flow produced by cooling at the earth's surface is also studied.