arXiv subjects

John Wanderer

Publications and source records attributed to John Wanderer.

4 recordsLinked to original sources

arXiv2011

Anomalous scaling of structure functions and sub-grid models for large eddy simulations of strong turbulence

The original goal of Large Eddy Simulations of fully developed turbulent flows was to accurately describe large-scale flow features ${\bf u}(Δ)$ at the scales $r\geq Δ$ where $Δ$ is a size of computational mesh. The effect of small-scale velocity fluctuations ($r<Δ$) was to be accounted for by effective transport coefficients (subgrid models) in the coarse-grained Navier-Stokes equations. It is shown in this paper that, due to anomalous inertial range scaling (intermittency) of the moments of velocity difference, the existing subgrid models are intrinsically incapable of quantitatively describing flow features at the scales $r<NΔ$ with $N\approx 10$. This increases computational work approximately by a factor $10^{3}-10^{4}$. The breakdown of the widely used Smagorinsky relation for the subgrid viscosity on the scales $Δ/L<1$ is demonstrated and a modification accounting for intermittency of the filtered out small-scale fluctuations is proposed.

physics.flu-dyn↗

arXiv2004

Generalized Boltzmann Equation: Slip-No -Slip Dynamic Transition in Flows of Strongly Non-Linear Fluids

The Navier-Stokes equations, are understood as the result of the low-order expansion in powers of dimensionless rate of strain $η_{ij}=τ_{0}S_{ij}$, where $τ_{0}$ is the microscopic relaxation time of a close-to- thermodynamic equilibrium fluid. In strongly sheared non-equilibrium fluids where $|η_{ij}|\geq 1$, the hydrodynamic description breaks down. According to Bogolubov's conjecture, strongly non-equlibrium systems are characterized by an hierarchy of relaxation times corresponding to various stages of the relaxation process. A "hydro-kinetic" equation with the relaxation time involving both molecular and hydrodynamic components proposed in this paper, reflects qualitative aspects of Bogolubov's hierarchy. It is shown that, applied to wall flows, this equation leads to qualitatively correct results in an extremely wide range of parameter $η$-variation. Among other features, it predicts the onset of slip velocity at the wall as an instability of the corresponding hydrodynamic approximation.

physics.flu-dyn↗

arXiv2004

Large-Scale Coherence and Law of Decay of Two-Dimensional Turbulence

At the short times, the enstrophy $Ω$ of a two-dimensional flow, generated by a random Gaussian initial condition decays as $Ω(t)\propto t^{-γ}$ with $γ\approx 0.7$. After that, the flow undergoes transition to a different state characterized by the magnitude of the decay exponent $γ\approx 0.4$ (Yakhot, Wanderer, Phys.Rev.Lett.{\bf 93}, 154502 \~(2004)). It is shown that the very existence of this transition and various characteristics of evolving flow crucially depend upon phase correlation between the large-scale modes containing only a few percent of total enstrophy.

nlin.CD↗

arXiv2004

A Cross-Over in the Enstrophy Decay in Two-Dimensional Turbulence in a Finite Box

The numerical simulation of two-dimensional decaying turbulence in a large but finite box presented in this paper uncovered two physically different regimes of enstrophy decay. During the initial stage, the enstrophy, generated by a random Gaussian initial condition, decays as t^{-gamma} with gamma approximately 0.7-0.8. After that, the flow undergoes a transition to a gas or fluid composed of distinct vortices. Simultaneously, the magnitude of the decay exponent crosses over to gamma approximately 0.4. An exact relation for the total number of vortices, N(t), in terms of the mean circulation of an individual vortex is derived. A theory predicting that N(t) is proportional to t^{-xi} and the magnitudes of exponents gamma=2/5 and xi=4/5 is presented and the possibility of an additional very late-time cross-over to gamma=1/3 and xi=2/3 is also discussed.

nlin.CD↗