Irreversible Statistical Mechanics and the Structure of Anisotropic Turbulent Stress Tensor

1969 ◽  
Vol 46 (1A) ◽  
pp. 109-109
Author(s):  
M. Yildiz
Keyword(s):  
Statistical Mechanics ◽  
Stress Tensor ◽  
Turbulent Stress

The stress tensor of a molecular system: An exercise in statistical mechanics

2006 ◽  
Vol 125 (3) ◽  
pp. 034101 ◽  
Author(s):  
S. Morante ◽  
G. C. Rossi ◽  
M. Testa
Keyword(s):  
Statistical Mechanics ◽  
Stress Tensor ◽  
Molecular System

Statistical mechanics of inhomogeneous fluids

1982 ◽  
Vol 379 (1776) ◽  
pp. 231-246 ◽  
Keyword(s):  
Surface Tension ◽  
Free Energy ◽  
Angular Momentum ◽  
Statistical Mechanics ◽  
Stress Tensor ◽  
Pressure Difference ◽  
Strain Tensor ◽  
Pressure Tensor ◽  
Conservation Of Momentum ◽  
Statistical Mechanical

The nature of the microscopic stress tensor in an inhomogeneous fluid is discussed, with emphasis on the statistical mechanics of drops. Changes in free energy for isothermal deformations of a fluid are expressible as volume integrals of the stress tensor ‘times’ a strain tensor. A particular radial distortion of a drop leads to statistical mechanical expressions for the pressure difference across the surface of the drop. We find that the stress tensor is not uniquely defined by the microscopic laws embodying the conservation of momentum and angular momentum and that the am­biguity remains in the ensemble average, or pressure tensor, in regions of inhomogeneity. This leads to difficulties in defining statistical mechanical expressions for the surface tension of a drop.

scholarly journals Realizability conditions for the turbulent stress tensor in large-eddy simulation

1994 ◽  
Vol 278 ◽  
pp. 351-362 ◽  
Author(s):  
Bert Vreman ◽  
Bernard Geurts ◽  
Hans Kuerten
Keyword(s):  
Kinetic Energy ◽  
Large Eddy Simulation ◽  
Stress Tensor ◽  
Turbulent Kinetic Energy ◽  
Point Of View ◽  
Theoretical Point ◽  
Turbulent Stress ◽  
Eddy Simulation ◽  
Subgrid Model ◽  
Large Eddy

The turbulent stress tensor in large-eddy simulation is examined from a theoretical point of view. Realizability conditions for the components of this tensor are derived, which hold if and only if the filter function is positive. The spectral cut-off, one of the filters frequently used in large-eddy simulation, is not positive. Consequently, the turbulent stress tensor based on spectrally filtered fields does not satisfy the realizability conditions, which leads to negative values of the generalized turbulent kinetic energy k. Positive filters, e. g. Gaussian or top-hat, always give rise to a positive k. For this reason, subgrid models which require positive values for k should be used in conjunction with e. g. the Gaussian or top-hat filter rather than with the spectral cutoff filter. If the turbulent stress tensor satisfies the realizability conditions, it is natural to require that the subgrid model for this tensor also satisfies these conditions. With respect to this point of view several subgrid models are discussed. For eddy-viscosity models a lower bound for the generalized turbulent kinetic energy follows as a necessary condition. This result provides an inequality for the model constants appearing in a ‘Smagorinsky-type’ subgrid model for compressible flows.

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