Reinterpretation of the Thorpe Length Scale

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 L T 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 L O , 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 conductivity–temperature–depth (CTD) 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, the 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 L T is proportional to L O . 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 the Thorpe sorting technique to be applied to all turbulent flows, including those generated by convection. Significance Statement Routine monitoring of the turbulence structure in the global atmosphere is of societal importance and practical utility. Remote sensing by wind profiler radars provides routine information at only a few stations around the globe. Monitoring by sensors deployed on commercial aircraft provides data only along flight routes and mostly at flight altitudes. However, high-vertical-resolution radiosondes that are now being routinely deployed at over 900 stations around the globe provide a means for routine probing and monitoring of turbulence in the global atmosphere, by using the Thorpe sorting technique to extract the dissipation rate of turbulence kinetic energy. Reinterpretation of the technique in this study extends its application to all turbulent flows in the atmospheric column, including convective turbulence.