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John R. Taylor

Abstract

The influence of submesoscale currents on the distribution and subduction of passive, buoyant tracers in the mixed layer is examined using large-eddy simulations. Submesoscale eddies are generated through an ageostrophic baroclinic instability associated with a background horizontal buoyancy gradient. The simulations also include various levels of surface cooling, which provides an additional source of three-dimensional turbulence. Submesoscales compete against turbulent convection and restratify the mixed layer while generating strong turbulence along a submesoscale front. Buoyant tracers accumulate at the surface along the submesoscale front where they are subducted down into the water column. The presence of submesoscales strongly modifies the vertical tracer flux, even in the presence of strong convective forcing. The correlation between high tracer concentration and strong downwelling enhances the vertical diffusivity for buoyant tracers.

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John R. Taylor

Abstract

An understanding of the structure of the vertical temperature and salinity profiles in salt fingers is required to identify the occurrence of fingers in vertical profiles of oceanic microstructure and hence to make estimates of the contribution of fingers to vertical mixing in the ocean. With this in mind, a laboratory experiment was set up in which the vertical temperature and conductivity profiles through salt fingers were measured and compared with horizontal profiles of the same quantities. It was found that the vertical component of the temperature gradient in salt fingers had few zero crossings, so was quite different from the temperature gradient that would result from turbulence. On the other hand, the conductivity gradient (which is dominated by changes in salt concentration in our experiments) had numerous zero crossings even when the salt fingers were relatively weak. For density ratios Rp < 5 (where Rp = αθ¯z/βS̄z and θ¯z and S̄z are the mean vertical gradients of potential temperature and salinity) the average value of the ratio of the wavenumbers where the amplitudes of the vertical and horizontal temperature gradient spectra were maximum (when the spectra were plotted in variance-preserving form) was 0.58. Scaling of the temperature variance equation shows that the ratio of the vertical to one horizontal component of the Cox number C 3/C 1 should vary as the square of the ratio of the horizontal to vertical finger length scales. If the wavenumber ratio described above is a measure of this length-scale ratio, then C 3/C 1 should be (0.58)2. This is to be compared with the measured average of C 3/C 1, 0.25.

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John R. Taylor and Sutanu Sarkar

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A stratified bottom Ekman layer over a nonsloping, rough surface is studied using a three-dimensional unsteady large eddy simulation to examine the effects of an outer layer stratification on the boundary layer structure. When the flow field is initialized with a linear temperature profile, a three-layer structure develops with a mixed layer near the wall separated from a uniformly stratified outer layer by a pycnocline. With the free-stream velocity fixed, the wall stress increases slightly with the imposed stratification, but the primary role of stratification is to limit the boundary layer height. Ekman transport is generally confined to the mixed layer, which leads to larger cross-stream velocities and a larger surface veering angle when the flow is stratified. The rate of turning in the mixed layer is nearly independent of stratification, so that when stratification is large and the boundary layer thickness is reduced, the rate of veering in the pycnocline becomes very large. In the pycnocline, the mean shear is larger than observed in an unstratified boundary layer, which is explained using a buoyancy length scale, u */N(z). This length scale leads to an explicit buoyancy-related modification to the log law for the mean velocity profile. A new method for deducing the wall stress based on observed mean velocity and density profiles is proposed and shows significant improvement compared to the standard profile method. A streamwise jet is observed near the center of the pycnocline, and the shear at the top of the jet leads to local shear instabilities and enhanced mixing in that region, despite the fact that the Richardson number formed using the mean density and shear profiles is larger than unity.

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John R. Taylor and Raffaele Ferrari

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In this study, the influence of a geostrophically balanced horizontal density gradient on turbulent convection in the ocean is examined using numerical simulations and a theoretical scaling analysis. Starting with uniform horizontal and vertical buoyancy gradients, convection is driven by imposing a heat loss or a destabilizing wind stress at the upper boundary, and a turbulent layer soon develops. For weak lateral fronts, turbulent convection results in a nearly homogeneous mixed layer (ML) whose depth grows in time. For strong fronts, a turbulent layer develops, but this layer is not an ML in the traditional sense because it is characterized by persistent horizontal and vertical gradients in density. The turbulent layer is, however, nearly homogeneous in potential vorticity (PV), with a value near zero. Using the PV budget, a scaling for the depth of the turbulent low PV layer and its time dependence is derived that compares well with numerical simulations. Two dynamical regimes are identified. In a convective layer near the surface, turbulence is generated by the buoyancy loss at the surface; below this layer, turbulence is generated by a symmetric instability of the lateral density gradient. This work extends classical scalings for the depth of turbulent boundary layers to account for the ubiquitous presence of lateral density gradients in the ocean. The new results indicate that a lateral density gradient, in addition to the surface forcing, can affect the stratification and the rate of growth of the surface boundary layer.

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Daniel B. Whitt and John R. Taylor

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Atmospheric storms are an important driver of changes in upper-ocean stratification and small-scale (1–100 m) turbulence. Yet, the modifying effects of submesoscale (0.1–10 km) motions in the ocean mixed layer on stratification and small-scale turbulence during a storm are not well understood. Here, large-eddy simulations are used to study the coupled response of submesoscale and small-scale turbulence to the passage of an idealized autumn storm, with a wind stress representative of a storm observed in the North Atlantic above the Porcupine Abyssal Plain. Because of a relatively shallow mixed layer and a strong downfront wind, existing scaling theory predicts that submesoscales should be unable to restratify the mixed layer during the storm. In contrast, the simulations reveal a persistent and strong mean stratification in the mixed layer both during and after the storm. In addition, the mean dissipation rate remains elevated throughout the mixed layer during the storm, despite the strong mean stratification. These results are attributed to strong spatial variability in stratification and small-scale turbulence at the submesoscale and have important implications for sampling and modeling submesoscales and their effects on stratification and turbulence in the upper ocean.

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Matthew N. Crowe and John R. Taylor

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Here, we examine baroclinic instability in the presence of vertical mixing in an idealized setting. Specifically, we use a simple model for vertical mixing of momentum and buoyancy and expand the buoyancy and vorticity in a series for small Rossby numbers. A flow in subinertial mixed layer (SML) balance (see the study by Young in 1994) exhibits a normal mode linear instability, which is studied here using linear stability analysis and numerical simulations. The most unstable modes grow by converting potential energy associated with the basic state into kinetic energy of the growing perturbations. However, unlike the inviscid Eady problem, the dominant energy balance is between the buoyancy flux and the energy dissipated by vertical mixing. Vertical mixing reduces the growth rate and changes the orientation of the most unstable modes with respect to the front. By comparing with numerical simulations, we find that the predicted scale of the most unstable mode matches the simulations for small Rossby numbers while the growth rate and orientation agree for a broader range of parameters. A stability analysis of a basic state in SML balance using the inviscid QG equations shows that the angle of the unstable modes is controlled by the orientation of the SML flow, while stratification associated with an advection/diffusion balance controls the size of growing perturbations for small Ekman numbers and/or large Rossby numbers. These results imply that baroclinic instability can be inhibited by small-scale turbulence when the Ekman number is sufficiently large and might explain the lack of submesoscale eddies in observations and numerical models of the ocean surface mixed layer during summer.

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Daniel B. Whitt and John R. Taylor
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Catherine A. Vreugdenhil and John R. Taylor

Abstract

Ocean turbulence contributes to the basal melting and dissolution of ice shelves by transporting heat and salt toward the ice. The meltwater causes a stable salinity stratification to form beneath the ice that suppresses turbulence. Here we use large-eddy simulations motivated by the ice shelf–ocean boundary layer (ISOBL) to examine the inherently linked processes of turbulence and stratification, and their influence on the melt rate. Our rectangular domain is bounded from above by the ice base where a dynamic melt condition is imposed. By varying the speed of the flow and the ambient temperature, we identify a fully turbulent, well-mixed regime and an intermittently turbulent, strongly stratified regime. The transition between regimes can be characterized by comparing the Obukhov length, which provides a measure of the distance away from the ice base where stratification begins to dominate the flow, to the viscous length scale of the interfacial sublayer. Upper limits on simulated turbulent transfer coefficients are used to predict the transition from fully to intermittently turbulent flow. The predicted melt rate is sensitive to the choice of the heat and salt transfer coefficients and the drag coefficient. For example, when coefficients characteristic of fully developed turbulence are applied to intermittent flow, the parameterized three-equation model overestimates the basal melt rate by almost a factor of 10. These insights may help to guide when existing parameterizations of ice melt are appropriate for use in regional or large-scale ocean models, and may also have implications for other ice–ocean interactions such as fast ice or drifting ice.

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Scott D. Bachman and John R. Taylor

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Submesoscale dynamics are hypothesized to play a leading-order role in setting the stratification of the mixed layer via the interaction of submesoscale eddies and surface forcing. Previous studies of such interactions have generally focused on the time-evolving characteristics of submesoscale turbulence, such as the spindown of a baroclinically unstable front. This paper focuses instead on the equilibrium dynamics of the oceanic mixed layer, where forcing and dissipation are in balance, through a combination of scaling analysis and numerical simulations. The steady dynamics are well described by a turbulent thermal wind balance, with external forcing parameterized by a strong vertical diffusivity κ. Scaling laws are developed for the characteristic vertical length scale L υ, ageostrophic velocity scales U and V, buoyancy frequency N 2, and eddy buoyancy flux , which are appropriate for a turbulent mixed layer whose stratification is equilibrated against strong vertical mixing. A suite of numerical simulations is developed to test these scalings for different values of κ and lateral buoyancy gradient. The scaling relations are shown to be very robust across all simulations, and this allows the new scaling for to be directly compared against an extant parameterization in the forcing scenarios explored here.

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Callum J. Shakespeare and John R. Taylor

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A simple analytical model is presented describing the spontaneous generation of inertia–gravity waves at density fronts subjected to strong horizontal strain rates. The model considers fronts of arbitrary horizontal and vertical structure in a semi-infinite domain, with a single boundary at the ocean surface. Waves are generated because of the acceleration of the steady uniform strain flow around the density front, analogous to the generation of lee waves via flow over a topographic ridge. Significant wave generation only occurs for sufficiently strong strain rates α > 0.2f and sharp fronts H/L > 0.5f/N, where f is the Coriolis parameter, N is the stratification, and H and L are the height and width scales of the front, respectively. The frequencies of the generated waves are entirely determined by the strain rate. The lowest-frequency wave predicted to be generated via this mechanism has a Lagrangian frequency ω = 1.93f as measured in a reference frame moving with the background strain flow. The model is intended as a first-order description of wave generation at submesoscale (1 to 10 km wide) fronts where large strain rates are commonplace. The analytical model compares well with fully nonlinear numerical simulations of the submesoscale regime.

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