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Full-Text Articles in Mechanical Engineering
A Lagrangian Stochastic Model For Dispersion In Stratified Turbulence, S. K. Das, Paul A. Durbin
A Lagrangian Stochastic Model For Dispersion In Stratified Turbulence, S. K. Das, Paul A. Durbin
Paul A. Durbin
In this paper we discuss the development of a Lagrangian stochastic model (LSM) for turbulent dispersion of a scalar (species). Given any tensorally linear second-moment closure (SMC) turbulence model we show how to derive a mathematically equivalent set of stochastic differential equations (SDEs), i.e., the second-moment equations constructed from these SDEs are exactly the same (within a realizability constraint) as the given SMC. This set of equations forms the LSM. Both turbulence anisotropy and buoyancy effects are incorporated by this method. In order to achieve the correct critical Richardson number and to obtain the simplest Lagrangian formulation, a revised set …
On The Equilibrium States Predicted By Second Moment Models In Rotating, Stably Stratified Homogeneous Shear Flow, Minsuk Ji, Paul A. Durbin
On The Equilibrium States Predicted By Second Moment Models In Rotating, Stably Stratified Homogeneous Shear Flow, Minsuk Ji, Paul A. Durbin
Paul A. Durbin
The structural equilibrium behavior of the general linear second-moment closure model in a stably stratified, spanwise rotating homogeneous shear flow is considered with the aid of bifurcation analysis. A closed form equilibrium solution for the anisotropy tensor aij, dispersion tensor Kij, dimensionless scalar variance q2/k (S/Sθ)2, and the ratio of mean to turbulent time scale ε/Sk is found. The variable of particular interest to bifurcation analysis, ε/Sk is shown as a function of the parameters characterizing the body forces: Ω/S (the ratio of the rotation rate to the mean shear rate) for rotation and Rig (the gradient Richardson number) for …