Water quality estimation of river plumes in southern Lake Michigan using hyperion

This study focuses on the calibration of an existing bio-geo-optical model for studying the spatial variability of water quality parameters including chlorophyll (CHL), non-algal particles (NAP), and colored dissolved organic matter (CDOM) in episodic river plumes. The geographic focus is the St. Joseph River plume in southern Lake Michigan. One set of EO-1 Hyperion imagery and one set of boat-based spectrometer measurements were successfully acquired to capture episodic plume events. Coincident water quality measurements were also collected during these plume events. In this study, a database of inherent optical properties (IOPs) measurements and spectral signatures was generated and used to calibrate the bio-geo-optical model. Field measured concentrations of NAP and CDOM at 67% of the sampled sites fall within one standard deviation of the retrieved means using the spectrometer measurements. The percentage of sites, 88%, is higher for the estimation of CHL concentrations. Despite the dynamic nature of the observed plume and the time lag during field sampling, 77% of the sampled sites show field measured CHL and NAP concentrations falling within one standard deviation of the Hyperion derived values. The spatial maps of water quality parameters generated from the Hyperion image provided a synoptic view of water quality conditions. Results show that concentrations of NAP, CHL, and CDOM were more than three times higher in conjunction with river outflow, and inside the river plumes, than in ambient water. It is concluded that the storm-initiated plume is a significant source of sediments, carbon and chlorophyll to Lake Michigan.

Shear dispersion from near‐inertial internal Poincaré waves in large lakes

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.

Spatial structure of internal Poincaré waves in Lake Michigan

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 Year of Internal Poincaré Waves in Southern Lake Michigan

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.

Cross-shelf thermal structure in Lake Michigan during the stratified periods

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.

The mixing efficiency of interfacial waves breaking at a ridge. Part I: Overall mixing efficiency

The overall mixing efficiency of periodic, interfacial waves breaking at a Gaussian ridge is investigated through laboratory experiments. Cumulative measurements are used to investigate the fraction of the wave energy lost in the breaking event that contributes to irreversible mixing of the background density gradient. Using the tank as a control volume, the distribution of energy into reflected waves, transmitted waves, and dissipation and irreversible mixing from the breaking event is determined. The overall fraction of wave energy lost in the breaking event that is converted irreversibly to mixing is found to be 3–8%, which is low compared with typical values of around 20% for steady, parallel, stratified shear instabilities. Spatial variability in the mixing event may contribute to the relatively low overall efficiency of the event.

The mixing efficiency of interfacial waves breaking at a ridge. Part II: Local Energetics

The efficiency with which internal wave energy is converted irreversibly to diapycnal mixing in bathymetry-induced mixing events is of great importance to larger-scale ocean modeling efforts. High-resolution laboratory measurements are used to investigate the spatial and temporal variability of interfacial wave breaking events at a submerged bathymetric ridge. From high spatial resolution measurements, it appears the local efficiency can vary significantly. Parameterizations based on the turbulent Reynolds number and Froude number suggest that the local mixing efficiency within the overturning patch at the interface is 10–17% but the local efficiency is near zero within the relatively homogenous layers. When the local mixing efficiency is integrated over the entire event, the resulting overall efficiency is consistent with the result from Part 1 that the overall event efficiency is 3–8%. This spatial variation in the mixing efficiency reinforces the importance of dynamic mixing efficiency parameterizations based on local stratified turbulence parameters.

The breaking of interfacial waves at a submerged bathymetric ridge

The breaking of periodic progressive two-layer interfacial waves at a Gaussian ridge is investigated through laboratory experiments. Length scales of the incident wave and topography are used to parameterize when and how breaking occurs. Qualitative observations suggest both shear and convection play a role in the instability of waves breaking at the ridge. Simultaneous particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) measurements are used to calculate high resolution, two-dimensional velocity and density fields from which the local gradient Richardson number Rig is calculated. The transition to breaking occurred when 0.2 ≤ Rig ≤ 0.4. In these wave-ridge breaking events, the destabilizing effects of waves steepening in shallow layers may be responsible for breaking at higher Rig than for similar waves breaking through shear instability in deep water (Troy & Koseff, J. Fluid Mech., vol. 543, 2005b, p. 107). Due to the effects of unsteadiness, nonlinear shoaling and flow separation, the canonical Rig > 0.25 is not sufficient to predict the stability of interfacial waves. A simple model is developed to estimate Rig in waves between finite depth layers using scales of the incident wave scale and topography. The observed breaking transition corresponds with a constant estimated value of Rig from the model, suggesting that interfacial shear plays an important role in initial wave instability. For wave amplitudes above the initial breaking transition, convective breaking events are also observed.

The viscous decay of progressive interfacial waves

The viscous damping of progressive, two-layer interfacial waves is examined theoretically and experimentally. Traditional water wave theory is modified to derive the damping rates associated with interfacial wave propagation in a rectangular channel. The individual wave damping contributions are considered from the bottom, side, and interfacial boundary layers, as well as the damping associated with the wave-induced velocities within the homogenous fluid layers. These results show that for most laboratory-scale experiments, sidewall friction plays the dominant role in wave damping. Laboratory experiments are conducted to verify the damping rates for progressive two-layer internal waves in a rectangular channel. Experiments are conducted on both monochromatic and polychromatic wave trains. The results of these experiments are in good agreement with the derived damping rates, but show poorer agreement for large-amplitude waves when the sidewall boundary layers become turbulent. More work is necessary to quantify the damping associated with nonlinear internal waves in order to allow for accurate interpretation of the results from laboratory experiments.

The instability and breaking of long internal waves

Laboratory experiments are carried out to determine the nature of internal wave breaking and the limiting wave steepness for progressive, periodic, lowest-mode internal waves in a two-layer, miscible density stratification. Shoaling effects are not considered. The waves investigated here are long relative to the thickness of the density interface separating the two fluid layers. Planar laser-induced fluoresence (PLIF) flow visualization shows that wave breaking most closely resembles a Kelvin–Helmholtz shear instability originating in the high-shear wave crest and trough regions. However, this instability is strongly temporally and spatially modified by the oscillations of the driving wave shear. Unlike a steady stratified shear layer, the wave instability discussed here is not governed by the canonical $it Ri{=}1/4$ stability limit. Instead, the wave time scale (the time scale of the destabilizing shear) imposes an additional constraint on instability, lowering the critical Richardson number below 1/4. Experiments were carried out to quantify this instability threshold, and show that, for the range of wavenumbers considered in this study, the critical wave steepness at which the wave breaking occurs is wavenumber-dependent (unlike surface waves). The corresponding critical wave Richardson numbers at incipient wave breaking are well below 1/4, in consonance with a modified instability analysis based on results from stratified shear flow instability theory.