Related papers: Applicability of Boussinesq approximation in a tur…
A Rayleigh B\'enard instability study using the energy conserving dissipative particle dynamics method is presented here for the first time. The simulation is performed on an ideal dissipative particle dynamics fluid in a three dimensional…
In this article we consider the asymptotic stability of the two-dimensional Boussinesq equations with partial dissipation near a combination of Couette flow and temperature profiles $T(y)$. As a first main result we show that if $T'$ is of…
A new mechanism of double-component convection is discovered. It emerges in a horizontal layer of Boussinesq fluid as a stable stratification due to flux boundary conditions is added to an unstable gradient specified by fixed boundary…
Large-scale patterns, which are well-known from the spiral defect chaos regime of thermal convection at Rayleigh numbers $Ra < 10^4$, continue to exist in three-dimensional numerical simulations of turbulent Rayleigh-B\'{e}nard convection…
The Oberbeck-Boussinesq approximation is the most widely employed theoretical scheme for the study of natural or mixed convection flows. However, the misunderstanding of this approximated framework is a possibility that may cause the…
Near the thermodynamic critical point, the physical properties of binary fluids exhibit large variations in response to small temperature and concentration differences, whose effects on the onset of double-diffusive convection are reported…
Starting from the linearized fluctuating Boussinesq equations we derive an expression for the structure factor of fluids in stationary convection-free thermal nonequilibrium states, taking into account both gravity and finite-size effects.…
We present an extensive study of Boussinesq thermal convection including a temperature-dependent internal heating source, based on numerical three-dimensional simulations. The temperature dependence mimics triple-$\alpha$ nuclear reactions…
We consider the two-dimensional Rayeigh-B\'enard convection problem between Navier-slip fixed-temperature boundary conditions and present a new upper bound for the Nusselt number. The result, based on a localization principle for the…
In the quest to understand the basic universal features of compressible convection, one would like to disentangle genuine consequences of compression from spatial variations of transport properties. In the present work, we consider a very…
Throughout the history of the study of turbulence in fluid dynamics, there has yet to arise a unique definition or theoretical criterion for this important phenomenon. There have been interesting conjectures made by Ruelle [2], Muriel [3],…
We derive an improved rigorous bound on the space and time averaged temperature $<T>$ of an infinite Prandtl number Boussinesq fluid contained between isothermal no-slip boundaries thermally driven by uniform internal heating. A novel…
The Rayleigh number $Ra$ dependence of the Nusselt number $Nu$ in turbulent Rayleigh--B\'enard convection is numerically investigated for a moderate and low Prandtl number, $Pr=0.7$ and $0.021$, respectively. Here we specifically address…
A novel phase field method is proposed to model the continuous transition of binary fluids exhibiting temperature sensitive miscibility gap, from immiscible state to miscible state via partially miscible states. The model is employed to…
We investigate here the interactions of waves governed by a Boussinesq system with a partially immersed body allowed to move freely in the vertical direction. We show that the whole system of equations can be reduced to a transmission…
In this paper, we first revisit the celebrated Boussinesq approximation in stratified flows. Using scaling arguments we show that when the background shear is weak, the Boussinesq approximation yields either (i) $A_t\ll \mathcal{O}(1)$ or…
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…
We study the problem of gravity surface waves for the ideal fluid model in (2+1)-dimensional case. We apply a systematic procedure for deriving the Boussinesq equations for a prescribed relationship between the orders of four expansion…
Numerical simulations of convection in a layer filled with ideal gas are presented. The control parameters are chosen such that there is a significant variation of density of the gas in going from the bottom to the top of the layer. The…
As shown in earlier work (Ahlers et al., J. Fluid Mech. 569, p.409 (2006)), non-Oberbeck Boussinesq (NOB) corrections to the center temperature in turbulent Rayleigh-Benard convection in water and also in glycerol are governed by the…