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H. J. S. Fernando

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Whither the Stable Boundary Layer?

A Shift in the Research Agenda

H. J. S. Fernando and J. C. Weil
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E. J. Strang and H. J. S. Fernando

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A stratified shear layer was generated in the laboratory by driving a turbulent mixed layer of depth D over a quiescent, deep dense layer. As a result, a density interface of thickness δ b across which the buoyancy jump is Δb was formed between the upper and lower layers. This density interface was embedded in a velocity shear layer of thickness δ s across which the velocity jump was ΔU. Detailed velocity, density, and average local Richardson number (Ri g) measurements were made through the stratified shear layer, from which the fluxes of momentum and density through the interface as well as energetics of the stratified shear layer were evaluated as a function of Ri g. The quantities measured included the flux Richardson number (Ri f), the dissipation flux coefficient (Γ), and the eddy diffusivities of momentum and density (K m and K ρ), averaged across the shear layer. The results were compared with various deep and coastal oceanic data as well as common oceanic eddy diffusivity and flux parameterization schemes.

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H. J. S. Fernando and C. Y. Ching

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Polar ice cap cracks open sporadically to form thin, long, narrow channels of open water, which are referred to as “leads.” When the open water is exposed to ambient air in the winter, surface freezing occurs, thus rejecting dense salty water into the ocean interior. Using a laboratory experiment that models leads as line buoyant plumes, it is demonstrated that the lead-induced motions are affected by the background rotation after descending to a depth of 3.2 (q 03)1/3, where q 0 is the surface buoyancy flux per unit length and Ω is the rate of background rotation. The width of the plume at this point is 1.1 (q 03)1/3. After some time, the plume becomes unstable at its transverse edges and deflects sideways, thereby producing a strongly three-dimensional cyclonic spiraling flow pattern.

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I. D. Lozovatsky and H. J. S. Fernando

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Microstructure measurements were carried out on the shallow shelf of the Black Sea, from the sea surface to the bottom, using a free-falling BAKLAN-S profiler released from an anchored ship. A northeast to southwest transect consisting of eight measurement stations, with several casts made at each station, enabled the evaluation of microstructure statistics across the shelf. The eddy and scalar diffusivities as well as the mixing efficiencies were evaluated for distinct layers that were identified based on mean stratification and the “state” of turbulence. These include five main layers with persistent features (upper and bottom boundary layers, diurnal and main pycnoclines, and a stratified weakly turbulent inner layer) and several transient (patchy) features embedded within such layers (quasi-homogeneous, active turbulent, stratified dissipative, and microstructure displacement patches). The Thorpe displacement scale L Th measurements of this study, together with those reported in Dillon and Gibson et al. indicated that the normalized (by the patch thickness h p) Thorpe scale L Th/h p is a function of the mixing Reynolds number R m and the patch Richardson number Rip, but approaches a constant value for high R m. Layer-averaged diffusivities, which are of direct utility in computing vertical transports at various depths in shelf waters, were evaluated and from which the weighted column-averaged diffusivity 〈K〉 ≈ 10−4 m2 s−1 in the Black Sea shallow shelf waters under moderate winds in the beginning of the autumn transition season was estimated. This latter value, however, may be an underestimation given the neglect of near-surface (<3 m) turbulent mixing in the calculations.

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Y. Noh and H. J. S. Fernando

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The effects of background turbulence on gravity currents produced by lock exchange are investigated using a numerical model with the aim of understanding the fluid motions associated with coastal fronts. It is shown that, at high turbulence intensities, the mutual intrusion of gravity currents is inhibited and the horizontal mass transport is dominated by the turbulent diffusion. The propagation of the front, the horizontal density flux, and the potential energy anomaly are calculated and are compared with available experimental data. The model is extended to include the effects of background rotation. It is found that, in the presence of background turbulence, the geostrophic equilibrium cannot be achieved, and the cross-frontal velocity persists indefinitely. The effects of rotation on the fluid motions were found to be impaired by the background turbulence.

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S. I. Voropayev, H. J. S. Fernando, and L. A. Mitchell

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The purpose of this paper is to present the results of a series of laboratory experiments aimed at understanding the frazil ice growth in polar regions during the summer whence a freshwater layer at temperature 0°C spreads between an old ice sheet and underlying salty seawater that is at its freezing point. The aim of the experiments was to study the influence of external turbulence on the rate of new frazil ice formation. The experiments were conducted in a large walk-in freezer at a temperature near 0°C. To produce controlled turbulence, two oscillating grids were installed in a tank filled with two layers of water: fresh water at temperature 0°C in the upper layer and salty (35 psu) cold water at temperature −1.9°C in the bottom layer. During the experiments, the bottom layer was cooled from below, using Peltie elements, and its temperature was near the freezing point. The turbulence induced in both layers facilitates the transport of heat across the density interface between layers, and as the time progresses the lower boundary of the upper layer becomes overcooled, and small crystals of frazil ice intensively form in this overcooled zone. These buoyant crystals rise to the surface, and with time a sheet of frazil ice is formed at the surface of the fresh water. It is found that the rate of frazil ice formation in the presence of turbulence is a function of the interfacial Richardson number and is much higher (30–100 times) than the case where there is no turbulence. A theoretical explanation is given to explain thew observed high ice formation rates.

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J. C. R. Hunt, H. J. S. Fernando, and M. Princevac

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The theoretical and laboratory studies on mean velocity and temperature fields of an unsteady atmospheric boundary layer on sloping surfaces reported here were motivated by recent field observations on thermally driven circulation in very wide valleys in the presence of negligible synoptic winds. The upslope (anabatic) flow on a long, shallow, heated (with a buoyancy flux F bs) slope of inclination α located adjoining a level plane and the effects of cooling of the slope on this flow during the evening transition are studied for the case of a gentle slope for which the length of the sloping plane far exceeds the thickness h of the convective boundary layer. First, a theoretical analysis is presented for the mean upslope flow velocity U M, noting that the turbulence but not the mean flow structure therein is similar to that on a level terrain. The analysis, which is based on mean momentum and heat equations as well as closure involving level-terrain turbulence parameterizations, shows that U M is proportional to α 1/3 w∗, where w∗ = (F bs h)1/3. Second, new physical effects associated with evening transition are elicited by considering the idealized case of (specified) cooling the upslope flow on a simple slope. Theory and available field data show that, because of their inertia and although the heating ceases, upslope winds decay only slowly over a period of about 10(h/U M), which is tantamount to several hours on gentle slopes, whereupon flow reversal occurs from upslope to downslope. During this stage, because the air is cooling as it rises up the slope, its potential energy increases, resulting in momentary stagnation of the airflow at a location within a few meters above the surface (in the form of a transition front) followed by local overturning due to convective instabilities; this scenario is consistent with some field observations but has not been observed in mesoscale model simulations because of insufficient resolution to capture the front. A laboratory experiment conducted by subjecting an upslope flow to a rapidly changing surface flux confirmed the theoretical result that flow reversal occurs at a finite distance along the slope with the appearance of a front, which quickly migrates down the slope as the first front of the ensuing katabatic current.

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M. Princevac, J. C. R. Hunt, and H. J. S. Fernando

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Theoretical and field observational studies on mean velocity and temperature fields of quasi-steady nocturnal downslope (katabatic) flows on sloping surfaces are reported for the case of very wide valleys in the presence of weak synoptic winds. Because of the lateral constraints on the flow, Coriolis effects are considered negligible. The layer-averaged equations of Manins and Sawford were used for the analysis. It is shown that (i) in the absence of significant turbulent entrainment into the current (i.e., at large Richardson numbers Ri = Δh cosα/U 2) the downslope flow velocity U is related to the slope length (LH), slope angle (α), and the buoyancy jump between the current and the background atmosphere (Δ) as U = λuLH sinα)1/2, where λu is a constant and h is the flow depth; (ii) on very long slopes h is proportional to Lh(tanα)1/2; and (iii) under highly stable conditions (i.e., Ri > 1) the katabatic flow exhibits pulsations with period T 0 = 2π/N sinα, where N is the buoyancy frequency of the background atmosphere. These predictions are verified principally using observations made during the Vertical Transport and Mixing Experiment (VTMX) conducted in Salt Lake City, Utah, in October 2000. By assuming the flow follows a straight line trajectory to the nearest ridgeline a good agreement was found between the predictions and observations over appropriate Richardson number ranges. For Ri > 1.5, λu ≈ 0.2, although λu was a decreasing function of Ri at lesser stabilities. Oscillations with period T 0 are simply alongslope (critical) internal-wave oscillations with a slope-normal wavenumber, which are liable for degeneration into turbulence during their reflection. These critical internal waves may be responsible, at least partly, for weak sustained turbulence often observed in complex-terrain nocturnal boundary layer flows.

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E. Kit, A. Cherkassky, T. Sant, and H. J. S. Fernando

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Although the integral quantities of atmospheric turbulence are conveniently measured using sonic anemometers, obtaining relevant finescale variables such as the kinetic energy dissipation using conventional hot-film/wire techniques remains a challenge because of two main difficulties. The first difficulty is the mean wind variability, which causes violation of the requirement that mean winds have a specific alignment with the hot-film/wire probe. To circumvent this problem, a combination of collocated sonic and hot-film anemometers, with the former measuring mean winds and aligning the latter in the appropriate wind direction via an automated platform, is successfully designed and implemented. The second difficulty is the necessity of frequent and onerous calibrations akin to hot-film anemometry that lead to logistical difficulties during outdoor (field) measurements. This is addressed by employing sonic measurements to calibrate the hot films in the same combination, with the output (velocity) to input (voltage) transfer function for the hot film derived using a neural network (NN) model. The NN is trained using low-pass-filtered hot-film and sonic data taken in situ. This new hot-film calibration procedure is compared with the standard calibration method based on an external calibrator. It is inferred that the sonic-based NN method offers great potential as an alternative to laborious standard calibration techniques, particularly in the laboratory and in stable atmospheric boundary layer settings. The NN approximation technique is found to be superior to the conventionally used polynomial fitting methods when used in conjunction with unevenly spaced calibration velocity data generated by sonic anemometers.

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