Numerical and analytical studies of decaying, two-dimensional (2D) Navier-Stokes (NS) turbulence at high Reynolds numbers are reported. The effort is to determine computable distinctions between two different formulations of maximum entropy predictions for the decayed, late-time state. Though these predictions may be thought to apply only to the ideal Euler equations, there have been surprising and imperfectly-understood correspondences between the long-time computations of decaying states of NS flows and the results of the maximum-entropy analyses. Both formulations define an entropy through a somewhat ad hoc discretization of vorticity to the "particles" of which statistical mechanical methods are employed to define an entropy, before passing to a mean-field limit. In one case, the particles are delta-function parallel "line" vortices ("points" in two dimensions), and in the other, they are finite-area, mutually-exclusive convected "patches" of vorticity which in the limit of zero area become "points." The former are taken to obey Boltzmann statistics and the latter, Lynden-Bell statistics. Clearly, there is no unique way to reach a continuous differentiable vorticity distribution as a mean-field limit by either method. The simplest method of taking equal-strength points and equal-strength, equal-area patches is chosen here, no reason being apparent for attempting anything more complicated. In both cases, a non-linear partial differential equation results for the stream function of the "most probable" or maximum-entropy state, compatible with conserved total energy and positive and negative vorticity fluxes. These amount to generalizations of the "sinh-Poisson" equation which has become familiar from the "point" formulation. They have many solutions, which must be obtained numerically, and only one of which maximizes the entropy on the basis of which it was derived. These predictions can differ for the point and patch discretizations. The intent here is to use time-dependent, spectral-method direct numerical simulation of the Navier-Stokes equations to see if initial conditions which should relax to different late-time states under the two formulations actually do so.

The current work puts forth an implementation of a dynamic procedure to locally compute the value of the model constant CDES , as used in the eddy simulation branch of Delayed Detached Eddy Simulation (DDES). Former DDES formulations [P. R. Spalart et al., "A new version of detached-eddy simulation, resistant to ambiguous grid densities," Theor. Comput. Fluid Dyn. 20, 181 (2006) The current work puts forth an implementation of a dynamic procedure to locally compute the value of the model constant C DES , as used in the eddy simulation branch of Delayed Detached Eddy Simulation (DDES

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Numerical and analytical studies of final states of two-dimensional (2D) decaying turbulence are carried out. The first part of this work is trying to give a definition for final states of 2D decaying turbulence. The functional relation of -, which is frequently adopted as the characterization of those final states, is merely a sufficient but not necessary condition; moreover, it is not proper to use it as the definition. It is found that the method through the value of the effective area S covered by the scatter -plot, initially suggested by Read, Rhines, and White ["Geostrophic scatter diagrams and potential vorticity dynamics," J. Atmos. Sci. 43, 3226 (1986)] is more general and suitable for the definition. Based on this concept, a definition is presented, which covers all existing results in late states of decaying 2D flows (including some previous unexplainable weird double-valued -scatter plots). The remaining part of the paper is trying to further study 2D decaying turbulence with the assistance of this definition. Some numerical results, leading to "bar" final states and further verifying the predictive ability of statistical mechanics [Yin, Montgomery, and Clercx, "Alternative statistical-mechanical descriptions of decaying two-dimensional turbulence in terms of patches and points," Phys. Fluids 15, 1937 (2003)], are reported. It is realized that some simulations with narrow-band energy spectral initial conditions result in some final states that cannot be very well interpreted by the statistical theory (meanwhile, those final states are still in the scope of the definition).

A transport model for hybrid RANS/LES simulation of passive scalars is proposed. It invokes a dynamically computed subgrid Prandtl number. The method is based on computing test-filter fluxes. The formulation proves to be especially effective on coarse grids, as occur in DES. After testing it in a wall resolved LES, the present formulation is applied to the Adaptive DDES model of Yin et al. (Phys. Fluids 27, 025105 2015). It is validated by turbulent channel flow and turbulent boundary layer computations. Abstract A transport model for hybrid RANS/LES simulation of passive scalars is proposed. It invokes a dynamically computed subgrid Prandtl number. The method is based on computing test-filter fluxes. The formulation proves to be especially effective on coarse grids, as occur in DES. After testing it in a wall resolved LES, the present formulation is applied to the Adaptive DDES model of Yin et al. (2015). It is validated by turbulent channel flow and turbulent boundary layer computations.