Rayleigh-B\`enard convection in the generalized Oberbeck-Boussinesq system
Abstract
The original Oberbeck-Boussinesq (OB) equations which are the coupled two dimensional Navier-Stokes(NS) and heat conduction equations have been investigated by E.N. Lorenz half a century ago with Fourier series and opened the way to the paradigm of chaos. In our former study-Chaos, Solitons and Fractals78, 249 (2015)-we presented fully analytic solutions for the velocity, pressure and temperature fields with the aim of the self-similar Ansatz and gave a possible explanation of the Rayleigh--B\`enard convection cells. Now we generalize the Oberbeck-Boussinesq hydrodynamical system, going beyond the first order Boussinesq approximation and consider a non-linear temperature coupling. We investigate more general, power law dependent fluid viscosity or heat conduction material equations as well. Our analytic results obtained via the self-similar Ansatz may attract the interest of various fields like meteorology, oceanography or climate studies.
Keywords
Cite
@article{arxiv.1701.01647,
title = {Rayleigh-B\`enard convection in the generalized Oberbeck-Boussinesq system},
author = {Imre Feren Barna and Mihály András Pocsai and Sándor Lökös and László Mátyás},
journal= {arXiv preprint arXiv:1701.01647},
year = {2017}
}
Comments
7 pages, 5 figures