We study homogenization of the G-equation with a flow straining term (or the strain G-equation) in two dimensional periodic cellular flow. The strain G-equation is a highly non-coercive and non-convex level set HamiltonJacobi equation. The main objective is to investigate how the flow induced straining (the nonconvex term) influences front propagation as the flow intensity <i>A</i> increases. Three distinct regimes are identified. When <i>A</i> is below the critical level, homogenization holds and the turbulent flame speed <i>s</i> _T (effective Hamiltonian) is well-defined for any periodic flow with small divergence and is enhanced by the cellular flow as <i>s</i> _T <i>O</i>(<i>A</i>/log <i>A</i>). In the second regime where <i>A</i> is slightly above the critical value, homogenization breaks down, and <i>s</i> _T is not well-defined along any direction. Solutions become a mixture of a fast moving part and a stagnant part. When <i>A</i> is

This paper presents a numerical study of the Rayleigh-Benard convection (RBC) in two-dimensional cells with asymmetric (ratchet) roughness distributed on the top and bottom surfaces. We consider two aspect ratios of roughness gamma = 1, 2 and the range of the Rayleigh number 1.0 x 10(6) <= Ra <= 2.0 x 10(10) with the Prandtl number Pr = 4. The influences of the roughness on the heat transfer and the flow structure are found to be strongly dependent on both Ra and the roughness geometry. We find that the roughness can have a significant influence on the organization of the secondary corner rolls, and the corner rolls are evidently suppressed by the roughness for intermediate values of Ra. In the presence of the roughness, a sharp jump of the Nu values is identified as the Ra value is slightly increased, accompanied with the dramatic changes of the large-scale flow structure and the plume dynamics. The influences of the ratchet orientation on the heat transfer and the flow structure are discussed and analyzed.

We study the two-point correlation function of a freely decaying scalar in Kraichnan's model of advection by a Gaussian random velocity field that is stationary and white noise in time, but fractional Brownian in space with roughness exponent 0&lt;<i></i>&lt;2, appropriate to the inertial-convective range of the scalar. We find all self-similar solutions by transforming the scaling equation to Kummer's equation. It is shown that only those scaling solutions with scalar energy decay exponent <i>a</i>(<i>d</i>/<i></i>)+1 are statistically realizable, where <i>d</i> is space dimension and <i></i>=2<i></i>. An infinite sequence of invariants <i>J</i> _p, <i>p</i>=0,1,2,..., is pointed out, where <i>J</i> ₀ is Corrsin's integral invariant but the higher invariants appear to be new. We show that at least one of the invariants <i>J</i> ₀ or <i>J</i> ₁ must be nonzero (possibly infinite) for realizable initial data. Initial datum with a finite, nonzero invariantthe first being <i>J</i> _pconverges at long times to a scaling

In this numerical study on Rayleigh-Benard convection, we seek to improve the heat transfer by passive means. To this end we introduce a single tilted conductive barrier centered in an aspect ratio one cell, breaking the symmetry of the geometry and to channel the ascending hot and descending cold plumes. We study the global and local heat transfer and the flow organization for Rayleigh numbers 10(5) <= Ra <= 10(9) for a fixed Prandtl number of Pr = 4.3. We find that the global heat transfer can be enhanced up to 18%, and locally around 800%. The averaged Reynolds number is always decreased when a barrier is introduced, even for those cases where the global heat transfer is increased. We map the entire parameter space spanned by the orientation and the size of a single barrier for Ra = 10(8).

The bifurcations of penetrative Rayleigh-Benard convection in cylindrical containers are studied by the linear stability analysis (LSA) combined with the direct numerical simulation (DNS) method. The working fluid is cold water near 4 degrees C, where the Prandtl number Pr is 11.57, and the aspect ratio (radius/height) of the cylinder ranges from 0.66 to 2. It is found that the critical Rayleigh number increases with the increase in the density inversion parameter (m). The relationship between the normalized critical Rayleigh number (Ra-c((m))/Ra-c(0)) and (m) is formulated, which is in good agreement with the stability results within a large range of (m). The aspect ratio has a minor effect on Ra-c((m))/Ra-c(0). The bifurcation processes based on the axisymmetric solutions are also investigated. The results show that the onset of axisymmetric convection occurs through a trans-critical bifurcation due to the top-bottom symmetry breaking of the present system. Moreover, two kinds of qualitatively different steady axisymmetric solutions are identified.