Reinterpretation of the Thorpe Length Scale

Lakshmi Kantha aEmeritus Professor, University of Colorado, Boulder, CO, USA

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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 σK, which allows Thorpe sorting technique to be applied to all turbulent flows, including those generated by convection.

© 2024 American Meteorological Society. This is an Author Accepted Manuscript distributed under the terms of the default AMS reuse license. For information regarding reuse and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: kantha@colorado.edu

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 σK, which allows Thorpe sorting technique to be applied to all turbulent flows, including those generated by convection.

© 2024 American Meteorological Society. This is an Author Accepted Manuscript distributed under the terms of the default AMS reuse license. For information regarding reuse and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: kantha@colorado.edu
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