Second Moments Of Fluctuations Research Articles

Formula omitted]-[formula omitted]-[formula omitted] model in turbulent superfluid helium

We generalize the K−ϵ model of classical turbulence to superfluid helium. In a classical viscous fluid the phenomenological eddy viscosity characterizing the effects of turbulence depends on the turbulent kinetic energy K and the dissipation function ϵ, which are mainly related to the fluctuations of the velocity field and of its gradient. In superfluid helium, instead, we consider the necessary coefficients for describing the effects of classical and quantum turbulence, involving fluctuations of the velocity, the heat flux, and the vortex line density of the quantized vortex lines. By splitting the several fields into a time-average part and a fluctuating part, some expressions involving the second moments of the turbulent fluctuations appear in the evolution equations for the average quantities. As in the K−ϵ model, a practical way of closing such equations is to tentatively express such fluctuating terms as a function of the average quantities. In this context we propose how the turbulent coefficients so introduced could depend on the second moments of the fluctuations of v, q and L (respectively denoted as K, Kq and KL), and on their respective dissipation functions (related to the second moments of their gradients) ϵ, ϵq and ϵL.

Simulation of Second Moments of Fluctuations of the Velocity and Temperature of Particles in Equilibrium Turbulent Flows

An analysis is performed of equilibrium solutions of equations for the second moments of fluctuations of the velocity and temperature of particles in a homogeneous shear flow, in a homogeneous flow subjected to tensile or compressive strain, and in a wall layer. The stability of equilibrium solutions to small perturbations is investigated. Algebraic models are given for turbulent stresses in the dispersed phase.

Fluctuations of the field of a wave beam on reflection in a turbulent atmosphere

The approximation of smooth perturbations is used to obtain an expression for the second moments of fluctuations of the field of a wave beam reflected in a turbulent atmosphere. It is shown that the enhancement of fluctuations of the amplitude depends on the diffraction size of the beam, whereas the phase fluctuations do not have such dependence. The variance and spatial correlation of the amplitude and phase fluctuations are considered.