Open AccessProbability density of displacement and overturning length scales under diverse stratification
Author(s) -
Lorke Andreas,
Wüest Alfred
Publication year - 2002
Publication title -
journal of geophysical research: oceans
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.67
H-Index - 298
eISSN - 2156-2202
pISSN - 0148-0227
DOI - 10.1029/2001jc001154
Subject(s) - turbulence , length scale , dissipation , probability density function , stratification (seeds) , statistical physics , scale (ratio) , displacement (psychology) , physics , turbulence kinetic energy , scaling , mechanics , kinetic energy , mathematics , statistics , geometry , classical mechanics , thermodynamics , seed dormancy , psychology , germination , botany , quantum mechanics , psychotherapist , dormancy , biology
Vertical overturns, produced by turbulence in density‐stratified lakes and oceans, are often quantified by the Thorpe scale, L T . The correlation between L T and the Ozmidov (energy‐containing) scale can be used to estimate rates of turbulent dissipation and vertical diffusivities. Based on temperature microstructure measurements from several stratified lakes, the probability density functions (pdf's) of Thorpe displacements and overturning length scales are distinguished and discussed. The stratification was varying over five orders of magnitude between the different data sets, resulting in Thorpe scales between 1 cm and 100 m. It is shown that the analyzed pdf's follow a universal form that can be empirically described by an exponential function and parameterized by a single length scale. The functional form of the pdf of overturning length scales can be related to the inertial subrange, which is found in temperature, as well as in length‐scale fluctuation spectra. As a result, the ratio between the maximum displacement length scale, L max , and the Thorpe scale depends on the rate of turbulent kinetic energy dissipation. Based on the universal pdf of overturning length scales, we show with numerical simulations that L max is a more appropriate macroscopic length scale than L T for the estimation of turbulence based on displacements in temperature profiles.