Large-scale motion in the Great Lakes

Abstract

Large-scale motion in the Great Lakes can be assumed to be of small Rossby number, so that the equations of motion can be linearized and at the same time the variation of the Coriolis parameter with latitude can be neglected. When applied to a two-layer lake model, the equations become identical with the equations governing the behavior of surface and internal seiches in lakes, but now ‘current-like,’ as well as ‘wave-like’ solutions to these equations become of interest. The four equations of motion in the horizontal (assuming hydrostatic pressure distribution in the vertical) and the two continuity equations can be reduced to two independent sets of equations for the principal ‘internal’ and ‘surface’ modes. The solutions of each of these comprise one stationary mode, possibly some very slow periodic modes akin to Kelvin waves (but only if the basin is large enough) and some faster periodic modes corresponding to surface and internal seiches which rotate around the basin. When applied to a circular basin, constant depth ‘model Great Lake’ (of dimensions and other characteristics appropriate to the Great Lakes) the theory suggests the existence of (1) baroclinic ‘coastal jets’ during the summer stratification; (2) slow counterclockwise rotating internal waves of a period many times the half-pendulum day; and (3) surface and internal seiches rotating in either direction and having a period of at most several hours (surface modes) or up to within a small fraction of the inertial period (internal modes). An examination of the available observational material indeed suggests that these features are detectable in the Great Lakes.