On the existence and scaling of structure functions in turbulence according to the data

We sample a velocity field that has an inertial spectrum and a skewness that matches experimental data. In particular, we compute a self-consistent correction to the Kolmogorov exponent and find that for our model it is zero. We find that the higher order structure functions diverge for orders larger than a certain threshold, as theorized in some recent work. The significance of the results for the statistical theory of homogeneous turbulence is reviewed.Comment: 15 pages, 5 figures, to appear in PNA

Numerical Modeling of Turbulent Combustion

The work in numerical modeling is focused on the use of the random vortex method to treat turbulent flow fields associated with combustion while flame fronts are considered as interfaces between reactants and products, propagating with the flow and at the same time advancing in the direction normal to themselves at a prescribed burning speed. The latter is associated with the generation of specific volume (the flame front acting, in effect, as the locus of volumetric sources) to account for the expansion of the flow field due to the exothermicity of the combustion process. The model was applied to the flow in a channel equipped with a rearward facing step. The results obtained revealed the mechanism of the formation of large scale turbulent structure in the wake of the step, while it showed the flame to stabilize on the outer edges of these eddies

The Characteristic Length Scale of the Intermediate Structure in Zero-Pressure-Gradient Boundary Layer Flow

In a turbulent boundary layer over a smooth flat plate with zero pressure gradient, the intermediate structure between the viscous sublayer and the free stream consists of two layers: one adjacent to the viscous sublayer and one adjacent to the free stream. When the level of turbulence in the free stream is low, the boundary between the two layers is sharp and both have a self-similar structure described by Reynolds-number-dependent scaling (power) laws. This structure introduces two length scales: one --- the wall region thickness --- determined by the sharp boundary between the two intermediate layers, the second determined by the condition that the velocity distribution in the first intermediate layer be the one common to all wall-bounded flows, and in particular coincide with the scaling law previously determined for pipe flows. Using recent experimental data we determine both these length scales and show that they are close. Our results disagree with the classical model of the "wake region".Comment: 11 pages, includes 2 tables and 3 figure

A Model of a Turbulent Boundary Layer With a Non-Zero Pressure Gradient

According to a model of the turbulent boundary layer proposed by the authors, in the absence of external turbulence the intermediate region between the viscous sublayer and the external flow consists of two sharply separated self-similar structures. The velocity distribution in these structures is described by two different scaling laws. The mean velocity u in the region adjacent to the viscous sublayer is described by the previously obtained Reynolds-number-dependent scaling law $\phi = u/u_*=A\eta^{\alpha}$, $A=\frac{1}{\sqrt{3}} \ln Re_{\Lambda}+ \frac 52$, $\alpha=\frac{3}{2\ln Re_{\Lambda}}$, $\eta = u_* y/\nu$. (Here $u_*$ is the dynamic or friction velocity, y is the distance from the wall, $\nu$ the kinematic viscosity of the fluid, and the Reynolds number $Re_{\Lambda}$ is well defined by the data) In the region adjacent to the external flow the scaling law is different: $\phi= B\eta^{\beta}$. The power $\beta$ for zero-pressure-gradient boundary layers was found by processing various experimental data and is close (with some scatter) to 0.2. We show here that for non-zero-pressure-gradient boundary layers, the power $\beta$ is larger than 0.2 in the case of adverse pressure gradient and less than 0.2 for favourable pressure gradient. Similarity analysis suggests that both the coefficient B and the power $\beta$ depend on $Re_{\Lambda}$ and on a new dimensionless parameter P proportional to the pressure gradient. Recent experimental data of Perry, Maru\v{s}i\'c and Jones (1)-(4) were analyzed and the results are in agreement with the model we propose.Comment: 10 pages, 9 figure

Renormalization group and perfect operators for stochastic differential equations

We develop renormalization group methods for solving partial and stochastic differential equations on coarse meshes. Renormalization group transformations are used to calculate the precise effect of small scale dynamics on the dynamics at the mesh size. The fixed point of these transformations yields a perfect operator: an exact representation of physical observables on the mesh scale with minimal lattice artifacts. We apply the formalism to simple nonlinear models of critical dynamics, and show how the method leads to an improvement in the computational performance of Monte Carlo methods.Comment: 35 pages, 16 figure