Inertial oscillations and related internal beat pulsations and surges in Lakes Michigan and Ontario

Records of water temperature, current, and wind, made during campaigns on Lakes Michigan 1963 and Ontario 1972, are searched for inertial responses to wind action: (i) circle-tracking currents; and (ii) isothermdepth undulations, i.e., long internal wave manifestations of forcing by wind. With stratification absent in winter, only response (i) is seen (and then only rarely) with periods very close to the local inertial period, Tin. After wholebasin stratification is complete, both responses (i) and (ii) occur frequently, as internal Kelvin waves (shoretrapped and not further treated here) and cross-basin Poincaré internal seiche modes. Mode periods range between 1% and 15% less than Tin, depending on which of the here-modeled modes have responded and on differences between modes in their partitioning of kinetic and potential energy. When, in both lakes, shortduration wind impulses were followed by a week or more of relative calm, Poincaré mode combinations produced beat pulsations in both responses (i) and (ii), diagnostic features of which sometimes permitted participating modes to be identified. At a nearshore downwelled front in Lake Ontario, another type of poststorm adjustment was seen. Periodically released from the front, internal surges migrated across the basin through fields of inertially rotating, response (i) currents. Long internal waves, responding to wind action and the earth’s rotation in basins of the size considered here, fall into two classes: shore-hugging Kelvin waves of very long period; and Poincaré wave modes, occupying the whole basin and displaying periods close to but always less than Tin, the local inertial period. Features of these two wave classes were illustrated for a (two-layered) flat-bottomed model of Lake Ontario (Schwab 1977, Kelvin period 598 h, Poincaré period 17.35 h) and for two-layered channels in Mortimer (2004). There it was shown that internal Kelvin wave amplitude, maximal at the shore, falls to about 2% at a distance of four internal Rossby (1937, 1938) radii (<16 km) offshore in Lake Michigan. Kelvin waves are therefore restricted to within the nearshore hatched areas in the Fig. 2B model and are not further treated here. Such neglect is not possible in lakes one size-order smaller than Michigan, for example Lakes Kinneret (Antenucci and Imberger 2001, 2003) and Geneva (Lemmin et al. 2005). In those basins, approximately two Rossby radii wide for internal waves, both Kelvin and Pointcaré waves occupy the whole basins. The treatment here of near-inertial motions, principally internal Poincaré modes, is largely descriptive; but references to more advanced models and analytical theory are given in the summary, which also poses further questions. When motion of a water mass is governed by inertia alone, its track (as seen by an observer on the rotating earth) is not a straight line, but one that veers to the right in the northern hemisphere. In a large lake or ocean, remote from shore, the observer sees that track as an inertial circle, completed in an inertial period 12 (sin W)21 h at latitude Wu. In this paper, that period is designated as Tin. It is 17.4 and 18.0 h, respectively, at the north and south ends of Lake Michigan. Radii of inertial circles are proportional to current speed. At 10 cm s21, at the latitudes here considered, the radius is close to 1 km. Inertial circling is often combined with other currents, which vary little or not at all in direction. The combined current track is, then, ‘‘looping,’’ ‘‘waltzing,’’ or ‘‘meandering,’’ as commonly