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

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): Miroslav Bulíček, Josef MálekAbstractKolmogorov 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’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 “equivalent” reformulation of the equation for turbulent energy that eliminates the presence of the energy dissip...

Source: Nonlinear Analysis: Real World Applications - May 10, 2019 Category: Research Source Type: research