We show that the Pu(ω) ∝ ω −7/3 shear velocity power spectrum gives rise to a PΘ(ω) ∝ ω −4/3 power spectrum for a passively advected scalar, as measured in experiment [K. Sreenivasan, Proc. R. Soc. London A 434, 165 (1991)]. Applying our argument to high Rayleigh number Rayleigh Benard flow, we can account for the measured scaling exponents equally well as the Bolgiano Obukhov theory (BO59). Ye...

Linear stability analysis is performed for the onset of thermosolutal convection in a horizontal fluid layer with rigid-rigid boundaries. The temperature field between the walls of the fluid layer consists of two parts: a steady part and a time-dependent periodic part that oscillates with time. Only infinitesimal disturbances are considered. The effect of temperature modulation on the onset of ...

A general theory for the stability and coexistence of nonequilibrium phases is formulated. An integral formulation of the second entropy is given, the functional maximization of which yields nonlinear hydrodynamics. Rayleigh-Bénard convection is analyzed, and analytic approximations are obtained for the second entropy for conduction and for convection. Despite the simplicity of the model, coexi...

We investigate the early stages of mass convection in a colloidal suspension at high solutal Rayleigh number Ras. From the time evolution of shadowgraph images and by assuming a diffusive growth of the boundary layers we obtain an indirect measurement of the concentration boundary layer thickness delta* at the onset of convection. We show that the dimensionless boundary layer thickness delta=de...

This paper presents a physicist’s approach to Rayleigh-Bbnard convection widely illustrated with experimental results. The basis of the mechanism of the instability is simply presented with physical reasons for the existence of a critical threshold. A detailed examination of the spatial organization is made with discussion of ordered and disordered structures. Furthermore it is shown that the m...

Much effort has been expended in recent decades in addressing the problem of heat transfer in Rayleigh-Bénard (RB) thermal convection cells. There is increasing agreement that in general there are no clean scaling laws for Nu(Ra, Pr) and Re(Ra, Pr), apart from asymptotic cases. One of these asymptotic cases has been doped the ultimate state of thermal convection, i.e. Ra → ∞, where the heat flu...

We investigate the asymptotic relaxation of so-called pulled fronts propagating into an unstable state, and generalize the universal algebraic velocity relaxation of uniformly translating fronts to fronts that generate periodic or even chaotic states. A surprising feature is that such fronts also exhibit a universal algebraic phase relaxation. For fronts that generate a periodic state, like tho...

We consider the Boltzmann equation for a gas in a horizontal slab, subject to a gravitational force. The boundary conditions are of diffusive type, specifying the wall temperatures, so that the top temperature is lower than the bottom one (Benard setup). We consider a 2-dimensional convective stationary solution, which is close for small Knudsen number to the convective stationary solution of t...