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Lakshmi Kantha

Abstract

In 1977, S. A. Thorpe proposed a method to estimate the dissipation rate ε of turbulence kinetic energy (TKE) in an overturning turbulent layer in a lake, by sorting the observed (unstable) density profile to render it stable and thus deriving a length scale LT named after him, from the resulting vertical displacements of water parcels. By further proposing that this purely empirical scale (with no a priori physical basis, unlike many other turbulence length scales) is proportional to the Ozmidov scale LO , definable only for stably (not unstably or neutrally) stratified flows, he was able to extract ε. The simplicity of the approach that requires nothing but CTD (Conductivity, Temperature and Depth) casts in water bodies, including lakes and oceans, made it attractive, until microstructure profilers were developed and perfected in later decades to actually make in-situ measurements of ε. Since equivalent microstructure devices are not available for the atmosphere, Thorpe technique has been resurrected in recent years for application to the atmosphere, using potential temperature profiles obtained from high vertical resolution radiosondes. Its popularity and utility have increased lately, in spite of unresolved issues related to the validity of assuming LT is proportional to LO . In this study, we touch upon these issues and offer an alternative interpretation of the Thorpe length scale as indicative of the turbulence velocity scale σ K , which allows Thorpe sorting technique to be applied to all turbulent flows, including those generated by convection.

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Lakshmi Kantha
and
Sandro Carniel

Abstract

In a recent paper, Canuto et al. made a crucial contribution to modeling mixing in stably stratified flows by discovering that a modification to one of the closure constants can push the critical gradient Richardson number RiCR, beyond which turbulence is extinguished, to infinity. In this note, following their approach, the Kantha model is modified to yield a value of infinity for RiCR. The results are in good agreement with both the Canuto et al. results and the data presented in their paper.

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Lakshmi H. Kantha
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Lakshmi H. Kantha

Abstract

Cheng, Canuto, and Howard have presented a second-moment closure PBL model that appears to overcome some of the shortcomings of the existing Mellor and Yamada–type closure models. This note demonstrates that with a slight readjustment in the closure constants of the latter, more specifically the Kantha and Clayson closure model, they can be made to yield results very much similar to that of the Cheng et al. model.

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Lakshmi H. Kantha

Abstract

No abstract available.

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Lakshmi H. Kantha

Abstract

Two-equation models are being increasingly used to model turbulence in geophysical flows. A salient aspect of these flows is the stable gravitational stratification, which implies that turbulent fluctuations can generate internal waves that drain energy from turbulent eddies. This energy is not available for mixing, and therefore this transfer of energy from turbulence to internal waves has strong implications to mixing in the atmospheric boundary layer and the oceanic mixed layer. How to parameterize energy leakage to internal waves in turbulence models has been the subject of many studies, most recently by Baumert and Peters. This comment is an attempt to critique their work and to explore alternative options.

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Lakshmi H. Kantha
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Lakshmi Kantha
and
Hubert Luce

Abstract

Turbulent mixing in the interior of the oceans is not as well understood as mixing in the oceanic boundary layers. Mixing in the generally stably stratified interior is primarily, although not exclusively, due to intermittent shear instabilities. Part of the energy extracted by the Reynolds stresses acting on the mean shear is expended in increasing the potential energy of the fluid column through a buoyancy flux, while most of it is dissipated. The mixing coefficient χ m , the ratio of the buoyancy flux to the dissipation rate of turbulence kinetic energy ε, is an important parameter, since knowledge of χ m enables turbulent diffusivities to be inferred. Theory indicates that χ m must be a function of the gradient Richardson number. Yet, oceanic studies suggest that a value of around 0.2 for χ m gives turbulent diffusivities that are in good agreement with those inferred from tracer studies. Studies by scientists working with atmospheric radars tend to reinforce these findings but are seldom referenced in oceanographic literature. The goal of this paper is to bring together oceanographic, atmospheric, and laboratory observations related to χ m and to report on the values deduced from in situ data collected in the lower troposphere by unmanned aerial vehicles, equipped with turbulence sensors and flown in the vicinity of the Middle and Upper Atmosphere (MU) radar in Japan. These observations are consistent with past studies in the oceans, in that a value of around 0.16 for χ m yields good agreement between ε derived from turbulent temperature fluctuations using this value and ε obtained directly from turbulence velocity fluctuations.

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Carol Anne Clayson
and
Lakshmi Kantha

Abstract

Mixing in the free atmosphere above the planetary boundary layer is of great importance to the fate of trace gases and pollutants. However, direct measurements of the turbulent dissipation rate by in situ probes are very scarce and radar measurements are fraught with uncertainties. In this paper, turbulence scaling concepts, developed over the past decades for application to oceanic mixing, are used to suggest an alternative technique for retrieving turbulence properties in the free atmosphere from high-resolution soundings. This technique enables high-resolution radiosondes, which have become quite standard in the past few years, to be used not only to monitor turbulence in the free atmosphere in near–real time, but also to study its spatiotemporal characteristics from the abundant archives of high-resolution soundings from around the world. Examples from several locations are shown, as well as comparisons with radar-based estimations and a typical Richardson number–based parameterization.

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Joseph W. Lopez
and
Lakshmi H. Kantha

Abstract

A primitive equation, three-dimensional, baroclinic circulation model has been configured for use in the North Indian Ocean. After having been spun up by climatological winds, the model was used to generate a hindcast for 1993–95 under synoptic forcing, both with and without assimilation of multichannel sea surface temperature (MCSST) and altimetric sea surface height (SSH) anomaly data. Without data constraints, the model captures many of the salient oceanographic features in this region including equatorial surface and subsurface currents, the Laccadive High Eddy, the Great Whirl, and the reversing Somali Current. However, assimilation of altimetric data enables it to depict these features more accurately. MCSST data enable the near-surface layers to be simulated more accurately.

The National Aeronautics and Space Administration TOPEX precision altimeter has provided oceanographers with an important tool to study the variability in the circulation of the world’s oceans. The availability of SSH data from this altimeter provides a unique opportunity to assess the skill of a numerical model. More important, the assimilation of TOPEX altimetric observations, along with satellite-observed sea surface temperatures, greatly enhances the model’s ability to estimate the dynamical and thermodynamic state of the North Indian Ocean. The data-assimilative model provides therefore an additional tool for improving our understanding of the dynamical and thermodynamic processes in this region, through accurate hindcasts of the oceanic state. With the availability of real-time data streams, it also enables estimates of the oceanic state to be made in real-time nowcast/forecast mode.

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