The technique of semidefinite programming is used to replace direct numerical simulations and time integrations turbulent flows with an optimization problem which easier solve but returns only upper bounds the averages simulation would have produced. This idea applied rotating Rayleigh-B\'enard convection at infinite Prandtl number. obtained are not sharp they reproduce qualitative behavior res...

We offer a unifying theory for turbulent purely internally heated convection, generalizing the theories of Grossmann and Lohse (2000, 2001) Rayleigh--B\'enard turbulence Shishkina, (2016) horizontal which are both based on splitting kinetic thermal dissipation rates in respective boundary bulk contributions. obtain mean temperature system Reynolds number (which response parameters) as function ...

The paper considers the moderately turbulent natural convection flow of a stably stratified fluid along an infinite vertical plate (wall). Attention is restricted to statistically stationary flow driven by constant surface forcing (heating), with Prandtl number of unity. The flow is controlled by the surface energy production rate Fs , molecular viscosity/diffusivity ν and ambient stratificatio...

The figures on the left show effect of Prandtl number (Pr) Rayleigh-B\'enard problem with Boussinesq conditions, for same Grashof ${10}^{9}$. Top: Pr = 12.73; bottom, ${10}^{\ensuremath{-}4}$. plot right shows that low molecular yields an inversely varying turbulent number; is, flow behaves effectively as a high fluid. data are non-Boussinesq conditions. qualitative is case well, but dependence...

The problems with explaining the Small Ionized and Neutral Structures (SINS) appealing to turbulence stem from inefficiency of the Kol-mogorov cascade in creating large fluctuations at sufficiently small scales. However , other types of cascades are possible. When magnetic turbulence in a fluid with viscosity that is much larger than resistivity gets to a viscous damping scale, the turbulence d...

The validity of the anelastic approximation has recently been questioned in the regime of rapidly-rotating compressible convection in low Prandtl number fluids (Calkins, Julien and Marti, Proc. R. Soc. A, 2015, vol. 471, 20140689). Given the broad usage and the high computational efficiency of sound-proof approaches in this astrophysically relevant regime, this paper clarifies the conditions fo...