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 dissi...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2011 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10256/8466 |
| Acceso en línea: | http://hdl.handle.net/10256/8466 |
| Access Level: | acceso abierto |
| Palabra clave: | Turbulència Turbulence Dinàmica de fluids Fluid dynamics |
| Sumario: | 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 |
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