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Abstract: A simple k–ε turbulence closure is introduced which has no stability functions but instead a Richardson number-dependent turbulent Prandtl number. Its free parameters are determined in a comparison with microstructure observations from a stratified and sheared tidal estuary and laboratory measurements. The closure is able to simulate observed turbulent dissipation rates (ε) and turbulent length scales (l th) in regions of strong mean shear and small gradient Richardson number (R g) to within factors of 2–3. It fails in regions of small shear and large R g, presumably because of the dominance of internal wave-driven mixing. Additional simulations with a k–ε closure with stability functions taken from Canuto et al. [Canuto, V.M., Howard, A., Cheng, Y., Dubovikov, M.S., 2001. Ocean turbulence I: one-point closure model. Momentum and heat vertical diffusivities. J. Phys. Oceanogr. 31, 1413–1426] and with the closure of Baumert and Peters [Baumert, H., Peters, H., 2004. Turbulence closure, steady state, and collapse into waves. J. Phys. Oceanogr. 34, 505–512] show poor performance. Establishing a valid 1:1 comparison of simulated and observed ε and l th requires nudging the model velocity and density toward observed values because free model integrations quickly diverge from the observations. Steady state gradient Richardson numbers are constrained to a range of 0.18–0.25, while flux Richardson numbers are constrained to the range of 0.1–0.22. The closure output is rather insensitive to such parameter variations. The simulations are sensitive, however, to the treatment of the observed velocity and density used to nudge the model. Good closure performance requires averaging the measured tidal flow over about an hour, a time scale for which conventional numerical models of estuarine circulations should be able to match observed shears. In the closure simulations the TKE balance stays close to a production–dissipation balance. The time rate of change and vertical diffusion of TKE are small, of the same order of magnitude, and vary in magnitude relative to each other systematically across the water column. [Copyright &y& Elsevier]

Turbulence in the Red Sea outflow plume in the western Gulf of Aden was observed with an upward-looking, five-beam, 600-kHz acoustic Doppler current profiler (ADCP). The “Bottom Lander” ADCP was deployed on the seafloor in two narrow, topographically confined outflow channels south of Bab el Mandeb for periods of 18–40 h at three locations at 376-, 496-, and 772-m depths. Two deployments were taken during the winter season of maximum outflow from the Red Sea and two in the summer season of minimum outflow. These short-term observations exhibit red velocity spectra with high-frequency fluctuations of typically a few centimeters per second RMS velocity during strong plume flow as well as strong subtidal variations. In one winter season event, the plume flow was reduced by a factor of 4 over an 18-h time span. In variance-preserving form, velocity spectra show a separation at frequencies of 0.3–3 cycles per hour between low-frequency and high-frequency signals. The latter show significant coherence between horizontal and vertical velocity components; hence they carried turbulent stress. Based on a comparison with velocity spectra from atmospheric mixed-layer observations, the authors argue that large variance at frequencies of the order of 1 cph was possibly associated with bottom-generated, upward-propagating internal waves. One coherent feature that matched such waves was observed directly. Higher frequencies correspond to turbulent motions of energy-carrying scales. The turbulent Reynolds stress at heights above the bottom between 4 and 30–40 m was computed for most of the ADCP observations. Near the bottom, the streamwise turbulent stress and the streamwise velocity followed a quadratic drag law with drag coefficients ranging from 0.002 to 0.008. There was also significant spanwise stress, hinting at the three-dimensional nature of the boundary layer flow. The time–height variations of the stress and its spectrum proved to be complex, one of its most striking features being angles of up to ∼40° between the direction of the stress and that of the low-frequency flow. The turbulent shear production and eddy viscosity were also examined. On the technical side, the paper discusses the role of the fifth, center-beam velocity measurements in correcting for instrument tilt along with the effect of beam spreading in the 30° Janus configuration of the “regular” four ADCP beams. Instrumental noise and detection limits for the stress are also established. [ABSTRACT FROM AUTHOR]

South of the Strait of Bab el Mandeb, saline Red Sea Water flows downslope into the Gulf of Aden mainly along the narrow 130-km-long “Northern Channel” (NC) and the shorter and wider “Southern Channel” (SC). In the NC, the Red Sea plume simultaneously exhibited weak entrainment into a 35–120-m-thick, weakly stratified bottom layer while a 35–285-m-thick interfacial layer above showed signs of vigorous mixing, overturns up to 30 m thick, and extensive zones of gradient Richardson numbers below 1/4. Turbulent overturning scales, or Thorpe scales, are extracted from regular CTD profiles and equated to Ozmidov scales. On this basis, interfacial mixing is quantified in terms of estimated turbulent dissipation rates, vertical turbulent salt flux, and interfacial stress. Even though these estimates are subject to significant uncertainty, they demonstrate the intensity of mixing during strong winter outflow in terms of eddy diffusivities Kρ on the order of 10-2 m2 s-1. The large Kρ occur in strong stratification such that vertical turbulent salt fluxes are also large. Along the NC, relative maxima of Kρ correspond to maxima in the bulk Froude number. Direct short-term measurements of the Reynolds stress just above the seafloor at two locations, one in the NC and one in the SC, allow comparisons of the bottom stress τb with the interfacial turbulent stress τi. The ratio τi/τb shows large scatter in a small sample, with maximum values on the order of 1. Anoutlines procedures of making and reducing lowered acoustic Doppler current profiler measurements optimized for observing descending plumes. [ABSTRACT FROM AUTHOR]

Presents a simple, two-equation turbulence closure. Extra energy sink in the turbulent kinetic energy equation; Transfer of energy from turbulent kinetic energy to internal waves and other nonturbulent motions; Turbulent time scale; Turbulent dissipation rate; Buoyancy period; Onset of the collapse of turbulence into nonturbulence.

Spatial variations of vertical turbulent mixing along a stretch of the Hudson River estuary are examined with focus on the vicinity of a “hydraulic control point” at the George Washington Bridge at which the cross section narrows and the thalweg takes a bend. Richardson numbers are lowered and mixing is enhanced downstream of this “modest” morphological feature, qualitatively following predictions based on hydraulic theory by Chant and Wilson. The enhancement in the viscous dissipation rate ℇ is only a modest factor of 2–3, however, extending over 2 km along the river. Upon averaging over tidal and fortnightly cycles and multiple cruises, streamwise variations of ℇ along the probed 15-km stretch of the estuary are surprisingly small, given that individual depth averages of ℇ across the halocline vary by over three orders of magnitude. The principal result is that the observed part of the Hudson River showed strong broadly distributed mixing everywhere, with little local concentration. [ABSTRACT FROM AUTHOR]

ABSTRACT Turbulent mixing in the water column was observed with a microstructure profiler in the Hudson River estuary during two cruises in summer and fall 1995. The focus is on the estimation of turbulent salt flux and turbulent stress from measured viscous dissipation rates (e), and on the tidal and fortnightly variability of these fluxes. In estimating eddy viscosity (K[sub m]) and eddy diffusivity (K[sub p]), the authors follow measurement/modeling techniques of Busch and Osborn, while prescribing a variable flux Richardson number (R[sub j]) dependent upon the gradient Richardson number (Ri). It is argued that a steady-state production-dissipation balance holds in the turbulent kinetic energy budget. All turbulence characteristics varied strongly over semidiurnal tidal cycles and over the fortnightly cycle. Subject to complications arising from nontidal flows, the "strongest" mixing occurred during flood on neap tides, and during ebb on spring tides. In the lower part of the water column during floods and spring ebb K[sub m] and K[sub p] reached maxima of 1-5 (x 10[sup -2] m[sup 2] s[sup -1]) and decreased roughly exponentially with increasing height by 1-3 decades. The smallest eddy coefficients occurred in the halocline during neap tide with K[sub m] Is equivalent to 10[sup 4] m[sup 2] s[sup -1] and K[sub p] Is approximately equal to 10[sup -5] m[sup 2] s[sup -1]. Mostly, the internal turbulent stress (tau[sub y]) was close to 0 in the upper third of the water column and approached the bottom shear stress with decreasing height. Neap ebb had small |tau[sub y]| even close to... [ABSTRACT FROM AUTHOR]

The article informs that the author claims of a better fit to laboratory data of turbulent length scales than that found in BPO4. It can be achieved either with a traditional model or with a modification of the BPO4 closure, and he finally argues that there is no need for BPO4's explicit term of energy transfer from turbulence to internal waves. The notation herein is that of K05 and BPO4 and needs no specific definitions. BPO4 deliberately refrained from tuning and optimizing parameters. This closure is not tunable; its body and its parameter values form a unity.

Abstract: Mixing of overflows released from polar and marginal seas is a key process shaping the structure of the meridional overturning circulation. Ocean general circulation models have difficulty in resolving the overflows, and therefore they must rely on parameterizations. In this study, the performance of a set of turbulence closures in reproducing mixing of an overflow is quantified. We simulate the Red Sea overflow by employing standard k–ε, k–ω and Mellor–Yamada schemes with various stability functions, as well as a modified k–ε model that relies on the prescription of the turbulent Prandtl number rather than on stability functions. The simpler KPP mixing scheme and experiments without turbulent fluxes serve as useful references. To our knowledge, this is the first time that the performance of two-equation turbulence models has been examined so closely using data from an overflow. It is found that without turbulence closures, the hydrodynamic model has difficulty in reproducing the correct three-dimensional pathway of the Red Sea overflow, consisting of a distinct bifurcation into two diverging channels. All turbulence models capture the vertical structure of this overflow consisting of an interfacial layer, characterized by the density gradient, and a well-mixed bottom layer. Mean eddy diffusivity values from most closures are comparable those from observations. But we find that KPP leads to eddy diffusivity values that are too small while those from Mellor–Yamada with Galperin [Galperin, B., Kantha, L.H., Hassid, S., Rosati, A., 1988. A quasi-equilibrium turbulent energy model for geophysical flows. J. Atmos. Sci. 45, 55–62] stability functions are too large. Such high diffusivities lead to excessive mixing in the bottom layer of the overflow, ultimately resulting in a salinity deficit of approximately 1psu in the product water mass. Salinity deviations between the models and observations are quantified using both data taken along the channels and two sections across the overflow. KPP and Mellor–Yamada with Galperin (1988) stability functions produce the largest deviations from the observations, while the modified k–ε exhibits the smallest deviations. The other four closures fall in between, showing results similar to one another. The performance of the Mellor–Yamada turbulence closure is improved considerably by using the stability functions by Kantha and Clayson [Kantha, L.H., Clayson, C.A., 1994. An improved mixed layer model for geophysical applications. J. Geophys. Res. 99 (December), 25235–25266], which allow for a stationary Richardson number of 0.21. In conclusion, we find that most turbulence closures lead to a satisfactory reproduction of the Red Sea overflow, within the temporal and spatial sampling uncertainties of the REDSOX data, provided that fairly high-resolution regional models are used. [Copyright &y& Elsevier]

Abstract: Mixing between overflows and ambient water masses is a critical problem of deep-water mass formation in the downwelling branch of the meridional overturning circulation of the ocean. Modeling approaches that have been tested so far rely either on algebraic parameterizations in hydrostatic ocean circulation models, or on large eddy simulations that resolve most of the mixing using nonhydrostatic models. In this study, we examine the performance of a set of turbulence closures, that have not been tested in comparison to observational data for overflows before. We employ the so-called very large eddy simulation (VLES) technique, which allows the use of models in nonhydrostatic models. This is done by applying a dynamic spatial filtering to the equations. To our knowledge, this is the first time that the VLES approach is adopted for an ocean modeling problem. The performance of and VLES models are evaluated by conducting numerical simulations of the Red Sea overflow and comparing them to observations from the Red Sea Outflow Experiment (REDSOX). The computations are constrained to one of the main channels transporting the overflow, which is narrow enough to permit the use of a two-dimensional (and nonhydrostatic) model. A large set of experiments are conducted using different closure models, Reynolds numbers and spatial resolutions. It is found that, when no turbulence closure is used, the basic structure of the overflow, consisting of a well-mixed bottom layer (BL) and entraining interfacial layer (IL), cannot be reproduced. The model leads to unrealistic thicknesses for both BL and IL, while VLES results in the most realistic reproduction of the REDSOX observations. [Copyright &y& Elsevier]