Length Scales in a Rotating Stratified Fluid on the Beta Plane

Abstract

Abstract The relationships between vertical and horizontal length scales in a rotating stratified fluid on the beta plane are discussed in an attempt to unify the results of previous papers. The model is steady, linear and Boussinesq, but allows for different coefficients for the horizontal and vertical eddy mixing processes. The boundary layers in previous papers together with a new physical scale are analyzed with respect to their physical balances, length scale, and existence in a parameter space. The results are summarized in a three-part schematic graph, which shows the relations between dimensionless horizontal and vertical scales, and in a table, which contains the relevant physical balances for each relation. Three internal dimensionless parameters are considered, namely S a measure of the importance of stratification relative to rotation, δ a measure of the magnitudes of vertical to horizontal mixing processes, and βE½ a ratio of the length scales over which lateral friction and the beta effect a...