Transverse Velocity Difference Research Articles

How to impose stick boundary conditions in coarse-grained hydrodynamics of Brownian colloids and semi-flexible fiber rheology

Long-range hydrodynamics between colloidal particles or fibers is modelled by the fluid particle model. Two methods are considered to impose the fluid boundary conditions at colloidal surfaces. In the first method radial and transverse friction forces between particle and solvent are applied such that the correct friction and torque follows for moving or rotating particles. The force coefficients are calculated analytically and checked by numerical simulation. In the second method a collision rule is used between colloidal particle and solvent particle that imposes the stick boundary conditions exactly. The collision rule comprises a generalisation of the Lowe-Anderson thermostat to radial and transverse velocity differences.

The statistical properties of two-dimensional turbulent wake of a heated cylinder

By analyzing the experimental data, the statistical properties of 2D turbulent wake of a heated cylinder are studied. The coherent structures may have the stronger effect upon the transverse velocity and temperature than the longitudinal velocity. In the near wake, the transverse velocity v and the temperature T have the bimodal distribution and the χ 2 distribution, respectively. But the distribution of the longitudinal velocity u is near the Gaussian even in the near wake. The statistical distributions for the velocity differences and the temperature differences are studied. In the near wake, the pdfs of the transverse velocity differences are concave functions only for the time separations n Δt : n c 1 <n<n c 2 . Otherwise, they will be the convex functions. The pdf of the temperature difference will change from the nearly exponential distribution to the Gaussian distribution as the time separation nΔ t increasing in the near wake. Using the detrended fluctuation analysis, it is found out that the longitudinal velocity and temperature have the long-range correlation with the exponent α≈0.7 in the near and intermediate wake and the transverse velocity has the weakly anti-correlation with the exponent α≈0.44 in the intermediate wake.

Mean-field approximation and a small parameter in turbulence theory

Numerical and physical experiments on two-dimensional (2D) turbulence show that the differences of transverse components of velocity field are well described by Gaussian statistics and Kolmogorov scaling exponents. In this case the dissipation fluctuations are irrelevant in the limit of small viscosity. In general, one can assume the existence of a critical space dimensionality d=d(c), at which the energy flux and all odd-order moments of velocity difference change sign and the dissipation fluctuations become dynamically unimportant. At d<d(c) the flow can be described by the "mean-field theory," leading to the observed Gaussian statistics and Kolmogorov scaling of transverse velocity differences. It is shown that in the vicinity of d=d(c) the ratio of the relaxation and translation characteristic times decreases to zero, thus giving rise to a small parameter of the theory. The expressions for pressure and dissipation contributions to the exact equation for the generating function of transverse velocity differences are derived in the vicinity of d=d(c). The resulting equation describes experimental data on two-dimensional turbulence and demonstrates the onset of intermittency as d-d(c)>0 and r/L-->0 in three-dimensional flows in close agreement with experimental data. In addition, some exact relations between correlation functions of velocity differences are derived. It is also predicted that the single-point probability density function of transverse velocity components in developing as well as in the large-scale stabilized two-dimensional turbulence is a Gaussian.

Two-dimensional turbulence in the inverse cascade range.

Numerical and physical experiments on forced two-dimensional Navier-Stokes equations show that transverse velocity differences are described by "normal" Kolmogorov scaling <(deltav)(2n)> proportional r(2n/3) and obey Gaussian statistics. Since nontrivial scaling is a sign of the strong nonlinearity of the problem, these two results seem to contradict each other. A theory explaining these observations is presented in this paper. The derived self-consistent expression for the pressure gradient contributions leads to the conclusion that small-scale transverse velocity differences are governed by a linear Langevin-like equation, stirred by a nonlocal, universal, solution-dependent Gaussian random force. This explains the experimentally observed Gaussian statistics of transverse velocity differences and their Kolmogorov scaling. The solution for the PDF of longitudinal velocity differences is based on the numerical smallness of the energy flux in two-dimensional turbulence. The theory makes a few quantitative predictions that can be tested experimentally.

Statistical study of anisotropic anomalous behavior of a cylinder wake

An experimental investigation of the statistical properties of the velocity difference in an anisotropic turbulent cylinder wake at moderate Reλ is conducted by a triple hot-wire anemometer (HWA) probe. The energy spectra show a clear large scale anisotropy due to the presence of the Von Karman vortices. In spite of the low Reλ and the large scale anisotropy, the extended-self-similarity (ESS) allows location of broad scaling ranges and the calculation of the scaling exponents of the three velocity structure function components in order to examine the intermittency anomalies. More intermittent behavior of the transverse velocity components with respect to the longitudinal one is found both by ESS and by comparison of the longitudinal and transverse velocity difference probability distribution functions (PDF).

Experimental analysis of transverse intermittency in a turbulent jet flow

The statistical properties of the velocity differences are experimentally investigated in a turbulent jet-flow at moderate Reλ by X-probe hot wire anemometry measurements. It is found that the traverse velocity components show a more intermittent behavior with respect to the longitudinal ones. This result is obtained by the analysis of the longitudinal and transverse intermittency exponents measured by the Extended Self-Similarity form of scaling, and by the comparison of the longitudinal and transverse velocity difference Probability Distribution Functions.