To better understand lateral dispersion of buoyant and nonbuoyant pollutants within the surface waters of large lakes, two lateral dispersion experiments were carried out in Lake Michigan during the stratified period: (1) a dye tracking experiment lasting 1 d; and (2) a drifter tracking experiment lasting 24 d. Both the dye patch and drifters were surface-released at the center of Lake Michigan’s southern basin. Near-surface shear induced by near-inertial Poincaré waves partially explains elevated dye dispersion rates (1.5–4.2 m2 s−1). During the largely windless first 5 d of the drifter release, the drifters exhibited nearly scale-independent dispersion ( K ∼ L0.2), with an average dispersion coefficient of 0.14 m2 s−1. Scale-dependent drifter dispersion ensued after 5 d, with K ∼ L1.09 and corresponding dispersion coefficients of 0.3–2.0 m2 s−1 for length scales L = 1500–8000 m. The largest drifter dispersion rates were found to be associated with lateral shear-induced spreading along a thermal front. Comparisons with other systems show a wide range of spreading rates for large lakes, and larger rates in both the ocean and the Gulf of Mexico, which may be caused by the relative absence of submesoscale processes in offshore Lake Michigan.
In this work, we study mixed layer lateral dispersion that is enhanced by near-inertial internal Poincaré waves in the offshore region of a large stratified lake, Lake Michigan. We examine the hypothesis that the vertical shear created by near-inertial internal Poincaré waves is not only an energy source for vertical mixing in the thermocline and mixed layer, but also enhances horizontal dispersion via an unsteady shear flow dispersion mechanism. Complex empirical orthogonal function analysis reveals that the dominant shear structure is observed to mirror the thermal structure, with the location of maximum shear gradually lowered as the mixed layer deepens. This changing structure of shear and vertical mixing produces different characteristics in shear flow dispersion between the early and later stratified periods. The estimated depth-averaged surface layer vertical turbulent diffusivity grows from 10-5 m2s-1 to 10-3 m2s-1 over the stratified period, and the associated lateral dispersion coefficients are estimated as 0.1 – 40 m2s-1. The Poincaré waves are found to enhance greatly lateral dispersion for times less than the inertial period following release. In contrast, sub-inertial shear is the dominant mechanism responsible for shear dispersion for times greater than the inertial period. A simple approximation of the dispersion coefficient for lateral dispersion is developed, which scales as the product of surface current velocity (or wind friction velocity) and mixed layer depth. The calculated dispersion coefficients agree well with Okubo’s diffusion diagram for times up to a week, which suggests that unsteady shear dispersion is a plausible mechanism to explain observed dispersion rates in the mixed layer for early times after release.
In this paper we examine the characteristics of near-inertial internal Poincaré waves in Lake Michigan (USA) as discerned from field experiments and hydrodynamic simulations. The focus is on the determination of the lateral and vertical structure of the waves. Observations of near-inertial internal wave properties are presented from two field experiments in southern Lake Michigan conducted during the years 2009 and 2010 at Michigan City (IN, USA) and Muskegon (MI, USA), respectively. Spectra of thermocline displacements and baroclinic velocities show that kinetic and potential baroclinic energy is dominated by near-inertial internal Poincaré waves. Vertical structure discerned from empirical orthogonal function analysis shows that this energy is predominantly vertical mode 1. Idealized hydrodynamic simulations using stratifications from early summer (June), mid-summer (July) and fall (September) identify the basin-scale internal Poincaré wave structure as a combination of single- and two-basin cells, similar to those identified in Lake Erie by Schwab, with near-surface velocities largest in the center of the northern and southern basins. Near-inertial bottom kinetic energy is seen to have roughly constant magnitude over large swathes across the basin, with higher magnitude in the shallower areas like the Mid-lake Plateau, as compared with the deep northern and southern basins. The near-bottom near-inertial kinetic energy when mapped appears similar to the bottom topography map. The wave-induced vertical shear across thermocline is concentrated along the longitudinal axis of the lake basin, and both near-bottom velocities and thermocline shear are reasonably explained by a simple conceptual model of the expected transverse variability.
A unique set of full year, deep water observations from the middle of Lake Michigan’s southern basin are analyzed to quantify the seasonal variability of the dominant near-inertial internal Poincaré wave. At this mid-lake location, the Poincaré wave is seen to describe more than 80% of the observed surface current variability for much of the year, with characteristic near-inertial frequency and clockwise-rotating velocities. The dominance of the near-inertial seiche on the flow decreases with depth. The wave persists during the “stratified period,” roughly May through late December, and is supported by as few as 1–2 degrees of thermal stratification over 150 m; only after complete water column mixing does the wave go dormant for January through April. The strongest Poincaré wave activity is seen to correspond to the period of strongest summer thermal stratification (August), in spite of the relatively weak winds at this time. A simple inertial slab model optimized with linear friction is shown to capture the seasonal variability of the near-inertial energy at this location reasonably well. The vertical structure of the wave shows good agreement with that calculated with a standard normal modes formulation, which is in turn used to characterize the potential shear and mixing caused by the wave. Late-spring and summer events of elevated Poincaré wave activity are shown to generate sufficiently strong shear with persistent periods of sub-1 Richardson numbers within the thermocline, suggesting that the near-inertial seiche is likely generating thermocline instabilities in the lake’s interior.
Results from a field experiment in southern Lake Michigan are used to quantify the cross-shelf nearshore variability in Great Lakes temperatures during the stratified season. The experiment was conducted along the Indiana coast of southern Lake Michigan, with temperature and velocity moorings arranged in a cross-shelf transect that extended to approximately 20 km from shore (40 m depth). The field site is noteworthy because of its location at the end of a major axis of an elliptical Great Lake, the relatively mild bathymetric slope, and local shoreline orientation that is perpendicular relative to the dominant summer winds. Measurements demonstrate that the location of the thermocline-bottom intersection is highly variable, causing a wide zone of extreme thermal variability in the nearshore region with time scales of variability ranging from hours to months. Near-inertial internal Poincaré waves are shown to cause large thermocline excursions but primarily only during periods of elevated activity. Several full upwelling events were observed, but in general, they were brief, lasting only 1–2 days, and had very limited spatial extent (2.5 km or less). Nonetheless, the offshore extent of the upwelling front was shown to be reasonably estimated with a simple estimate of the cross-shelf transport caused by alongshore wind events. A persistent feature that determined the zone of elevated thermal variability (the thermocline-shelf intersection point) was the strongly tilted thermocline, which resulted in the thermocline being located very close to shore. No evidence was found to support the hypothesis that internal Kelvin waves affect thermal variability at the study location.