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arXiv · 1701.01647

Rayleigh-B\`enard convection in the generalized Oberbeck-Boussinesq system

Imre Feren Barna·Mihály András Pocsai·Sándor Lökös·László Mátyás
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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.

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Imre Feren Barna, Mihály András Pocsai, Sándor Lökös, László Mátyás. 2017-01-06. Rayleigh-B\`enard convection in the generalized Oberbeck-Boussinesq system. https://arxiv.org/abs/1701.01647

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