dissipation equation 
The characteristic length scale of subgrid turbulence is no longer given by the spatial discretization step size, but by the use of a dissipation equation.


Fallacies include the mixinglength concept; the effect of pressure gradient on Reynolds shear stress; the separability of time and space derivatives; models of the dissipation equation; and chaos.


Fluctuationdissipation equation of asymmetric simple exclusion processes


We prove that the fluctuationdissipation equation w=Lu+D?η has a solution for some function u and some constant D identified to be the diffusion coefficient.


It is shown that this behavior is very much dependent on the gravitational production term in the turbulent dissipation equation, about which there is insufficient understanding in the literature.


An analytical discussion of the problems associated with the constants of the dissipation equation is presented.


It is shown here that the choice of the constants in the dissipation equation is quite crucial and the turbulence structure is very sensitive to these constants.


A direct numerical simulation of turbulent channel flow with an imposed mean scalar gradient is analyzed with a focus on passive scalar flux modelling and in particular the treatment of the passive scalar dissipation equation.


A modification based on the exact dissipation equation is found to significantly improve the model behaviour for this flow.


It was further shown that ad hoc modifications to the dissipation equation, such as those based on the ratio of the turbulent to mean strain time scale, can improve results at the expense of generality.


In this paper, the E  ε method is extended to the atmospheric boundary layer for which a modification of the dissipation equation is found to be necessary in order to give results comparable with observational data.


Fluctuation Dissipation Equation for Lattice Gas with Energy


In this paper we introduce a "lattice gas with energy," and obtain the "fluctuation dissipation equation" for it.


Once the "fluctuation dissipation equation" is established, the hydrodynamic limit is easily deduced from it by using the methods found in ref.


For curved or swirling flows, correction terms are invoked in the dissipation equation and eddy viscosity formulation.

