Large data analysis for Kolmogorov's two-equation model of turbulence

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10401799" target="_blank" >RIV/00216208:11320/19:10401799 - isvavai.cz</a>

Result on the web

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=pmfE99QZX" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=pmfE99QZX</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.nonrwa.2019.04.008" target="_blank" >10.1016/j.nonrwa.2019.04.008</a>

Result language

angličtina

Original language name

Large data analysis for Kolmogorov's two-equation model of turbulence

Original language description

Kolmogorov seems to have been the first to recognize that a two-equation model of turbulence might be used as the basis of turbulent flow prediction. Nowadays, a whole hierarchy of phenomenological two-equation models of turbulence is in place. The structure of their governing equations is similar to the Navier-Stokes equations for incompressible fluids, the difference is that the viscosity is not constant but depends on two scalar quantities that measure the effect of turbulence: the average of the kinetic energy of velocity fluctuations (i.e. the turbulent energy) and the measure related to the length scales of turbulence. For these two scalar quantities two additional evolutionary convection-diffusion equations are added to the generalized Navier-Stokes system. Although Kolmogorov&apos;s model has so far been almost unnoticed, it exhibits interesting features. First of all, in contrast to other two-equation models of turbulence, there is no source term in the equation for the frequency. Consequently, nonhomogeneous Dirichlet boundary conditions for the quantities measuring the effect of turbulence are assigned to a part of the boundary. Second, the structure of the governing equations is such that one can find an &quot;equivalent&quot; reformulation of the equation for turbulent energy that eliminates the presence of the energy dissipation acting as the source in the original equation for turbulent energy and which is merely an L-1 quantity. Third, the material coefficients such as the viscosity and turbulent diffusivities may degenerate, and thus the a priori control of the derivatives of the quantities involved is unclear. We establish long-time and large-data existence of a suitable weak solution to three-dimensional internal unsteady flows described by Kolmogorov&apos;s two-equation model of turbulence. The governing system of equations is completed by initial and boundary conditions; concerning the velocity we consider generalized stick-slip boundary conditions. The fact that the admissible class of boundary conditions includes various types of slipping mechanisms on the boundary makes the result robust from the point of view of possible applications. (C) 2019 Elsevier Ltd. All rights reserved.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GA18-12719S" target="_blank" >GA18-12719S: Thermodynamical and mathematical analysis of flows of complex fluids</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2019

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Nonlinear Analysis: Real World Applications

ISSN

1468-1218

e-ISSN

—

Volume of the periodical

50

Issue of the periodical within the volume

December

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

40

Pages from-to

104-143

UT code for WoS article

000477783900008

EID of the result in the Scopus database

2-s2.0-85065230859