Memory effects in turbulence

Experimental investigations of the wake flow of a hemisphere and cylinder show that such memory effects can be substantial and have a significant influence on momentum transport. Memory effects are described in terms of suitable memory functions

Skin friction in zero-pressure-gradient boundary layers

A global approach leading to a self-consistent solution to the Navier-Stokes-Prandtl equations for zero-pressure-gradient boundary layers is presented. It is shown that as $Re_{\delta}\rightarrow \infty$, the dynamically defined boundary layer thickness $\delta(x)\propto x/\ln^{2}Re_{x}$ and the skin friction $\lambda=\frac{2\tau_{w}}{\rho U_{0}^{2}}\propto 1/\ln^{2}\delta(x)$. Here $\tau_{w}$ and $U_{0}$ are the wall shear stress and free stream velocity, respectively. The theory is formulated as an expansion in powers of a small dimensionless parameter $\frac{d\delta(x)}{dx}\rightarrow 0$ in the limit $x\rightarrow \infty$

Is turbulent mixing a self convolution process ?

Experimental results for the evolution of the probability distribution function (PDF) of a scalar mixed by a turbulence flow in a channel are presented. The sequence of PDF from an initial skewed distribution to a sharp Gaussian is found to be non universal. The route toward homogeneization depends on the ratio between the cross sections of the dye injector and the channel. In link with this observation, advantages, shortcomings and applicability of models for the PDF evolution based on a self-convolution mechanisms are discussed.Comment: 4 page

Simulation of a particle-laden turbulent channel flow using an improved stochastic Lagrangian model

The purpose of this paper is to examine the Lagrangian stochastic modeling of the fluid velocity seen by inertial particles in a nonhomogeneous turbulent flow. A new Langevin-type model, compatible with the transport equation of the drift velocity in the limits of low and high particle inertia, is derived. It is also shown that some previously proposed stochastic models are not compatible with this transport equation in the limit of high particle inertia. The drift and diffusion parameters of these stochastic differential equations are then estimated using direct numerical simulation (DNS) data. It is observed that, contrary to the conventional modeling, they are highly space dependent and anisotropic. To investigate the performance of the present stochastic model, a comparison is made with DNS data as well as with two different stochastic models. A good prediction of the first and second order statistical moments of the particle and fluid seen velocities is obtained with the three models considered. Even for some components of the triple particle velocity correlations, an acceptable accordance is noticed. The performance of the three different models mainly diverges for the particle concentration and the drift velocity. The proposed model is seen to be the only one which succeeds in predicting the good evolution of these latter statistical quantities for the range of particle inertia studied

Gravitational waves from stochastic relativistic sources: primordial turbulence and magnetic fields

The power spectrum of a homogeneous and isotropic stochastic variable, characterized by a finite correlation length, does in general not vanish on scales larger than the correlation scale. If the variable is a divergence free vector field, we demonstrate that its power spectrum is blue on large scales. Accounting for this fact, we compute the gravitational waves induced by an incompressible turbulent fluid and by a causal magnetic field present in the early universe. The gravitational wave power spectra show common features: they are both blue on large scales, and peak at the correlation scale. However, the magnetic field can be treated as a coherent source and it is active for a long time. This results in a very effective conversion of magnetic energy in gravitational wave energy at horizon crossing. Turbulence instead acts as a source for gravitational waves over a time interval much shorter than a Hubble time, and the conversion into gravitational wave energy is much less effective. We also derive a strong constraint on the amplitude of a primordial magnetic field when the correlation length is much smaller than the horizon.Comment: Replaced with revised version accepted for publication in Phys Rev

On the Nature of Incompressible Magnetohydrodynamic Turbulence

A novel model of incompressible magnetohydrodynamic turbulence in the presence of a strong external magnetic field is proposed for explanation of recent numerical results. According to the proposed model, in the presence of the strong external magnetic field, incompressible magnetohydrodynamic turbulence becomes nonlocal in the sense that low frequency modes cause decorrelation of interacting high frequency modes from the inertial interval. It is shown that the obtained nonlocal spectrum of the inertial range of incompressible magnetohydrodynamic turbulence represents an anisotropic analogue of Kraichnan's nonlocal spectrum of hydrodynamic turbulence. Based on the analysis performed in the framework of the weak coupling approximation, which represents one of the equivalent formulations of the direct interaction approximation, it is shown that incompressible magnetohydrodynamic turbulence could be both local and nonlocal and therefore anisotropic analogues of both the Kolmogorov and Kraichnan spectra are realizable in incompressible magnetohydrodynamic turbulence.Comment: Physics of Plasmas (Accepted). A small chapter added about 2D MHD turbulenc

Decay of scalar variance in isotropic turbulence in a bounded domain

The decay of scalar variance in isotropic turbulence in a bounded domain is investigated. Extending the study of Touil, Bertoglio and Shao (2002; Journal of Turbulence, 03, 49) to the case of a passive scalar, the effect of the finite size of the domain on the lengthscales of turbulent eddies and scalar structures is studied by truncating the infrared range of the wavenumber spectra. Analytical arguments based on a simple model for the spectral distributions show that the decay exponent for the variance of scalar fluctuations is proportional to the ratio of the Kolmogorov constant to the Corrsin-Obukhov constant. This result is verified by closure calculations in which the Corrsin-Obukhov constant is artificially varied. Large-eddy simulations provide support to the results and give an estimation of the value of the decay exponent and of the scalar to velocity time scale ratio

Inertial range scaling in numerical turbulence with hyperviscosity

Numerical turbulence with hyperviscosity is studied and compared with direct simulations using ordinary viscosity and data from wind tunnel experiments. It is shown that the inertial range scaling is similar in all three cases. Furthermore, the bottleneck effect is approximately equally broad (about one order of magnitude) in these cases and only its height is increased in the hyperviscous case--presumably as a consequence of the steeper decent of the spectrum in the hyperviscous subrange. The mean normalized dissipation rate is found to be in agreement with both wind tunnel experiments and direct simulations. The structure function exponents agree with the She-Leveque model. Decaying turbulence with hyperviscosity still gives the usual t^{-1.25} decay law for the kinetic energy, and also the bottleneck effect is still present and about equally strong.Comment: Final version (7 pages

Dissipation equals production in the log layer of wall-induced turbulence

Asymptotic analysis is presented of the energy balance equations derived from statistically averagedNavier-Stokes equations pertinent to wall-induced turbulence. Attention is focused on the inertialsublayer, the region outside the viscous sublayer, and the buffer layer where the log-law for meanflow holds. Production and dissipation of turbulence are shown to be equal with a relative error of order(x2 /L), where x2 is the distance from the wall and L is the external length (pipe radius, channelhalf-height, boundary layer thickness). Diffusion of pressure and kinetic energy together are only ofrelative magnitude order (x2 /L). Pressure gradient terms are shown to redistribute longitudinalturbulence production in equal portions dissipated in the three orthogonal directions

Effects of Forcing Time Scale on the Simulated Turbulent Flows and Turbulent Collision Statistics of Inertial Particles

In this paper, we study systematically the effects of forcing time scale in the large-scale stochastic forcing scheme of Eswaran and Pope [ An examination of forcing in direct numerical simulations of turbulence, Comput. Fluids 16, 257 (1988)] on the simulated flow structures and statistics of forced turbulence. Using direct numerical simulations, we find that the forcing time scale affects the flow dissipation rate and flow Reynolds number. Other flow statistics can be predicted using the altered flow dissipation rate and flow Reynolds number, except when the forcing time scale is made unrealistically large to yield a Taylor microscale flow Reynolds number of 30 and less. We then study the effects of forcing time scale on the kinematic collision statistics of inertial particles. We show that the radial distribution function and the radial relative velocity may depend on the forcing time scale when it becomes comparable to the eddy turnover time. This dependence, however, can be largely explained in terms of altered flow Reynolds number and the changing range of flow length scales present in the turbulent flow. We argue that removing this dependence is important when studying the Reynolds number dependence of the turbulent collision statistics. The results are also compared to those based on a deterministic forcing scheme to better understand the role of large-scale forcing, relative to that of the small-scale turbulence, on turbulent collision of inertial particles. To further elucidate the correlation between the altered flow structures and dynamics of inertial particles, a conditional analysis has been performed, showing that the regions of higher collision rate of inertial particles are well correlated with the regions of lower vorticity. Regions of higher concentration of pairs at contact are found to be highly correlated with the region of high energy dissipation rate. © 2015 AIP Publishing LLC