Barotropic FRW cosmologies with Chiellini damping in comoving time

For nonzero cosmological constant Λ, we show that the barotropic FRW cosmologies as worked out in the comoving time lead in the radiation-dominated case to scale factors of identical form as for the Chiellini dissipative scale factors in conformal time obtained recently by us in Phys. Lett. A 379, 882 (2015). This is due to the Ermakov equation which is obtained in this case. For zero cosmological constant, several textbook solutions are easily obtained as particular cases of our formulas and hypergeometric solutions are also reminded.

An Energy-Based Similarity Subgrid-Scale Model in Two-Dimensional Planar Shear Flow

A new type of similarity subgrid-scale (SGS) model which based on energy and dissipative scale isotropy assumption is presented. This model combines the advantages of traditional Smagorinsky SGS model with similarity SGS model. And a two-dimensional shear layer flow is simulated using refined grid result as a standard and comparing witch LES method including multiple SGS models. The results indicate that the result of SIM model much approximates to refined grid result than other SGS models.

Acceleration statistics of finite-sized particles in turbulent flow: the role of Faxén forces

The dynamics of particles in turbulence when the particle size is larger than the dissipative scale of the carrier flow are studied. Recent experiments have highlighted signatures of particles' finiteness on their statistical properties, namely a decrease of their acceleration variance, an increase of correlation times (at increasing the particles size) and an independence of the probability density function of the acceleration once normalized to their variance. These effects are not captured by point-particle models. By means of a detailed comparison between numerical simulations and experimental data, we show that a more accurate description is obtained once Faxén corrections are included.

Small-Scale Mixing, Large-Scale Advection, and Stratospheric Tracer Distributions

The vertical mixing of tracers in the stratosphere is mainly due to patches of three-dimensional turbulence, which are highly intermittent in time and space. A simple heuristic model of this form of mixing is developed and employed to examine the effect of small-scale mixing on passive stratospheric tracers. The model is based on random-walk ideas, and it leads to an analog of the usual advection–diffusion equation in which the diffusion operator is replaced by a convolution operator taking the intermittency of the mixing into account. In its simplest form, this operator is defined by two parameters; these are estimated from midlatitude lower-stratospheric balloon data using a stochastic model of turbulent patches. The behavior of tracer distributions in some idealized flows shows how intermittency makes mixing less effective in damping the small-scale tracer fluctuations that arise through differential advection. This has consequences for stratospheric tracer distributions, which are demonstrated using numerical simulations based on observed stratospheric winds. Specifically, the new model of mixing leads to a horizontal tracer spectrum that is shallower, and closer to a k−2 power law, than the spectrum obtained with a diffusive parameterization of mixing. The horizontal scale below which intermittent mixing differs significantly from diffusion is estimated to be 15 km or so; remarkably, this coincides with the dissipative scale below which dissipation by small-scale mixing is crucial for tracer evolution.