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Small-Scale Spectrum of a Scalar Field in Water: The Batchelor and Kraichnan Models

The theoretical models of Batchelor and Kraichnan, which account for the smallest scales of a scalar field passively advected by a turbulent fluid (Prandtl . 1), have been validated using shear and temperature profiles measured with a microstructure profiler in a lake. The value of the rate of dissipation of turbulent kinetic energy « has been computed by fitting the shear spectra to the Panchev and Kesich theoretical model and the one-dimensional spectra of the temperature gradient, once « is known, to the Batchelor and Kraichnan models and from it determining the value of the turbulent parameter q. The goodness of the fit between the spectra corresponding to these models and the measured data shows a very clear dependence on the degree of isotropy, which is estimated by the Cox number. The Kraichnan model adjusts better to themeasured data than the Batchelor model, and the values of the turbulent parameter that better fit the experimental data are qв 5 4.4 ± 0.8 and qK 5 7.9± 2.5 for Batchelor and Kraichnan, respectively, when Cox ≥ 50. Once the turbulent parameter is fixed, a comparison of the value of « determined from fitting the thermal gradient spectra to the value obtained after fitting the shear spectra shows that the Kraichnan model gives a very good estimate of the dissipation, which the Batchelor model underestimates

This research was developed under Spanish Government Project FIS2008-03608. We would also like to thank Francesc Nogue´ (University of Girona) for his electronic engineering support and Joan Corominas (Banyoles) for his sailing support

American Meteorological Society

Manager: Ministerio de Educación y Ciencia (Espanya)
Author: Sánchez Martín, Xavier
Roget, Elena
Planella Morató, Jesús
Forcat Torras, Francesc
Date: 2018 June 5
Abstract: The theoretical models of Batchelor and Kraichnan, which account for the smallest scales of a scalar field passively advected by a turbulent fluid (Prandtl . 1), have been validated using shear and temperature profiles measured with a microstructure profiler in a lake. The value of the rate of dissipation of turbulent kinetic energy « has been computed by fitting the shear spectra to the Panchev and Kesich theoretical model and the one-dimensional spectra of the temperature gradient, once « is known, to the Batchelor and Kraichnan models and from it determining the value of the turbulent parameter q. The goodness of the fit between the spectra corresponding to these models and the measured data shows a very clear dependence on the degree of isotropy, which is estimated by the Cox number. The Kraichnan model adjusts better to themeasured data than the Batchelor model, and the values of the turbulent parameter that better fit the experimental data are qв 5 4.4 ± 0.8 and qK 5 7.9± 2.5 for Batchelor and Kraichnan, respectively, when Cox ≥ 50. Once the turbulent parameter is fixed, a comparison of the value of « determined from fitting the thermal gradient spectra to the value obtained after fitting the shear spectra shows that the Kraichnan model gives a very good estimate of the dissipation, which the Batchelor model underestimates
This research was developed under Spanish Government Project FIS2008-03608. We would also like to thank Francesc Nogue´ (University of Girona) for his electronic engineering support and Joan Corominas (Banyoles) for his sailing support
Document access: http://hdl.handle.net/2072/320406
Language: eng
Publisher: American Meteorological Society
Rights: Tots els drets reservats
Subject: Turbulència
Turbulence
Dinàmica de fluids
Fluid dynamics
Title: Small-Scale Spectrum of a Scalar Field in Water: The Batchelor and Kraichnan Models
Type: info:eu-repo/semantics/article
Repository: Recercat

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