In this study, we report on turbulent mixing observed during the annual stratification cycle in the hypolimnetic waters of Lake Michigan (USA), highlighting stratified, convective, and transitional mixing periods. Measurements were collected using a combination of moored instruments and microstructure profiles. Observations during the stratified summer showed a shallow, wind‐driven surface mixed layer (SML) with locally elevated dissipation rates in the thermocline (
Estimates of turbulence kinetic energy (TKE) dissipation rate (
- NSF-PAR ID:
- 10390439
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Journal of Geophysical Research: Oceans
- Volume:
- 128
- Issue:
- 1
- ISSN:
- 2169-9275
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
more » « less
Abstract ) potentially associated with internal wave shear. Below the thermocline, turbulence was weak ( ) and buoyancy‐suppressed ( < 8.5), with low hypolimnetic mixing rates ( ) limiting benthic particle delivery. During the convective winter period, a diurnal cycle of radiative convection was observed over each day of measurement, where temperature overturns were directly correlated with elevated turbulence levels throughout the water column ( ; ). A transitional mixing period was observed for spring conditions when surface temperatures were near the temperature of maximum density ( T MD3.98 ) and the water column began to stably stratify. While small temperature gradients allowed strong mixing over the transitional period ( ), hypolimnetic velocity shear was overwhelmed by weakly stable stratification ( ; ), limiting the development of the SML. These results highlight the importance of radiative convection for breaking down weak hypolimnetic stratification and driving energetic, full water column mixing during a substantial portion of the year (>100 days at our sample site). Ongoing surface water warming in the Laurentian Great Lakes is significantly reducing the annual impact of convective mixing, with important consequences for nutrient cycling, primary production, and benthic‐pelagic coupling. -
more » « less
Abstract The air‐sea exchange of oxygen (O2) is driven by changes in solubility, biological activity, and circulation. The total air‐sea exchange of O2has been shown to be closely related to the air‐sea exchange of heat on seasonal timescales, with the ratio of the seasonal flux of O2to heat varying with latitude, being higher in the extratropics and lower in the subtropics. This O2/heat ratio is both a fundamental biogeochemical property of air‐sea exchange and a convenient metric for testing earth system models. Current estimates of the O2/heat flux ratio rely on sparse observations of dissolved O2, leaving it fairly unconstrained. From a model ensemble we show that the ratio of the seasonal amplitude of two atmospheric tracers, atmospheric potential oxygen (APO) and the argon‐to‐nitrogen ratio (Ar/O2), exhibits a close relationship to the O2/heat ratio of the extratropics (40–
). The amplitude ratio, / , is relatively constant within the extratropics of each hemisphere due to the zonal mixing of the atmosphere. / is not sensitive to atmospheric transport, as most of the observed spatial variability in the seasonal amplitude of APO is compensated by similar variations in (Ar/ ). From the relationship between /heat and / in the model ensemble, we determine that the atmospheric observations suggest hemispherically distinct /heat flux ratios of 3.3 0.3 and 4.7 0.8 nmol between 40 and in the Northern and Southern Hemispheres respectively, providing a useful constraint for and heat air‐sea fluxes in earth system models and observation‐based data products. -
more » « less
Abstract In field observations from a sinuous estuary, the drag coefficient
based on the momentum balance was in the range of , much greater than expected from bottom friction alone. also varied at tidal and seasonal timescales. was greater during flood tides than ebbs, most notably during spring tides. The ebb tide was negatively correlated with river discharge, while the flood tide showed no dependence on discharge. The large values of are explained by form drag from flow separation at sharp channel bends. Greater water depths during flood tides corresponded with increased values of , consistent with the expected depth dependence for flow separation, as flow separation becomes stronger in deeper water. Additionally, the strength of the adverse pressure gradient downstream of the bend apex, which is indicative of flow separation, correlated with during flood tides. While generally increased with water depth, decreased for the highest water levels that corresponded with overbank flow. The decrease in may be due to the inhibition of flow separation with flow over the vegetated marsh. The dependence of during ebbs on discharge corresponds with the inhibition of flow separation by a favoring baroclinic pressure gradient that is locally generated at the bend apex due to curvature‐induced secondary circulation. This effect increases with stratification, which increases with discharge. Additional factors may contribute to the high drag, including secondary circulation, multiple scales of bedforms, and shallow shoals, but the observations suggest that flow separation is the primary source. -
more » « less
Abstract Let
be integers with , and set . Erdős proved that when , each n ‐vertex nonhamiltonian graphG with minimum degreehas at most edges. He also provides a sharpness example for all such pairs . Previously, we showed a stability version of this result: for n large enough, every nonhamiltonian graphG onn vertices withand more than edges is a subgraph of . In this article, we show that not only does the graph maximize the number of edges among nonhamiltonian graphs with n vertices and minimum degree at leastd , but in fact it maximizes the number of copies of any fixed graphF whenn is sufficiently large in comparison withd and. We also show a stronger stability theorem, that is, we classify all nonhamiltonian n ‐vertex graphs withand more than edges. We show this by proving a more general theorem: we describe all such graphs with more than copies of for any k . -
more » « less
Abstract We consider the mapping properties of the integral operator arising in nonlocal slender body theory (SBT) for the model geometry of a straight, periodic filament. It is well known that the classical singular SBT integral operator suffers from high wavenumber instabilities, making it unsuitable for approximating the
slender body inverse problem , where the fiber velocity is prescribed and the integral operator must be inverted to find the force density along the fiber. Regularizations of the integral operator must therefore be used instead. Here, we consider two regularization methods: spectral truncation and the‐regularization of Tornberg and Shelley (2004). We compare the mapping properties of these approximations to the underlying partial differential equation (PDE) solution, which for the inverse problem is simply the Stokes Dirichlet problem with data constrained to be constant on cross sections. For the straight‐but‐periodic fiber with constant radius , we explicitly calculate the spectrum of the operator mapping fiber velocity to force for both the PDE and the approximations. We prove that the spectrum of the original SBT operator agrees closely with the PDE operator at low wavenumbers but differs at high frequencies, allowing us to define a truncated approximation with a wavenumber cutoff . For both the truncated and ‐regularized approximations, we obtain rigorous ‐based convergence to the PDE solution as : A fiber velocity with regularity gives convergence, while a fiber velocity with at least regularity yields convergence. Moreover, we determine the dependence of the ‐regularized error estimate on the regularization parameter .
