Vorticity waves in a shallow basin

Abstract

Observed oscillatory current patterns in the southern basin of Lake Michigan, with a distinctive peak in the energy spectrum at a period of about 90 h, are simulated using a linear potential vorticity conservation model. Solutions of the forced vorticity equation in a paraboloidal basin show rotational, oscillatory motions tuned to the low-frequency topographic modes that are very similar to the observed flow patterns. Topography-controlled vorticity waves are excited most effectively by wind episodes with frequency nearly in resonance with the topographic modes. Bottom resistance has no significant effect on the frequency equation; it simply decays the waves slowly in the open lake and more quickly near the coast. Flow patterns of both the gravest free vorticity wave and the corresponding forced wave consist of two opposite circulation cells separated by a null streamline through the center of the basin and rotating cyclonically near the free wave and atmospheric forcing frequencies, respectively. Interactions between the forced and free waves result in an apparent rotational pattern with a frequency the median of the two. A combination of elliptic—paraboloidal basin and shorter period forced modes can approximate the observed Lake Michigan response. Doppler shift, due to the persistence of cyclonic vorticity in the flow field, is also determined to be a factor in shifting the elliptical basin mode to a higher frequency.