Ilya Staroselsky

The effect of small-scale forcing on large-scale structures in two-dimensional flows

Abstract The effect of small-scale forcing on large-scale structures in β-plane two-dimensional (2D) turbulence is studied using long-term direct numerical simulations (DNS). We find that nonlinear effects remain strong at all times and for all scales and establish an inverse energy cascade that extends to the largest scales available in the system. The large-scale flow develops strong spectral anisotropy: k − 5 3 Kolmogorov scaling holds for almost all φ, φ = arctan ( k y k x ) except in the small vicinity of kx = 0, where Rhiness k−5 scaling prevails. Due to the k−5 scaling, the spectral evolution of β-plane turbulence becomes extremely slow which, perhaps, explains why this scaling law has never before been observed in DNS. Simulations with different values of β indicate that the β-effect diminishes at small scales where the flow is nearly isotropic. Thus, for simulations of β-plane turbulence forced at small scales sufficiently removed from the scales where β-effect is strong, large eddy simulation (LES) can be used. A subgrid scale (SGS) parameterization for such LES must account for the small-scale forcing that is not explicitly resolved and correctly accommodate two inviscid conservation laws, viz. energy and enstrophy. This requirement gives rise to a new anisotropic stabilized negative viscosity (SNV) SGS representation which is discussed in the context of LES of isotropic 2D turbulence.

Interaction of surface waves with turbulence: direct numerical simulations of turbulent open-channel flow

We report direct numerical simulations of incompressible unsteady open-channel flow. Two mechanisms of turbulence production are considered: shear at the bottom and externally imposed stress at the free surface. We concentrate upon the effects of mutual interaction of small-amplitude gravity waves with in-depth turbulence and statistical properties of the near-free-surface region. Extensions of our approach can be used to study turbulent mixing in the upper ocean and wind–sea interaction, and to provide diagnostics of bulk turbulence.

A quasinormal scale elimination model of turbulent flows with stable stratification

A new spectral model for turbulent flows with stable stratification is presented. The model is based on a quasi-Gaussian mapping of the velocity and temperature fields using the Langevin equations and employs a recursive procedure of small-scale mode elimination that results in a coupled system of differential equations for effective, horizontal and vertical, viscosities and diffusivities. With increasing stratification, the vertical viscosity and diffusivity are suppressed while their horizontal counterparts are enhanced thus explicitly accounting for the anisotropy introduced by stable stratification. The new model is used to derive various spectral characteristics of stably stratified turbulent flows. It accounts for energy accumulation in the horizontal components at the expense of the energy reduction in the vertical component. The scale elimination algorithm explicitly accounts for the combined effect of turbulence and internal waves. A modified dispersion relation for internal waves, a relationship...

Nanoscale air bearing modeling via lattice Boltzmann method

As spacing between the two solid surfaces in operating condition becomes much smaller than the mean free path of the air, continuum-based Navier–Stokes equation is no longer valid and one has to use a modified Reynolds equation (MRE) in simulating high Knudsen number air bearing. This MRE, which stems from the linearized Boltzmann transport equation with Bhatnagar–Gross–Krook approximation via the appropriate choice of the boundary condition, has the advantages of calculating the pressure distribution in a nanoscale confined gaseous system. In this paper, we provide a methodology based on the lattice Boltzmann method (LBM), which could enhance the computational capability of nanoscale confined gaseous system by calculating both velocity and pressure fields simultaneously. The advantage of transient and parallel nature makes this LBM an attractive tool for the next generation air bearing design. Furthermore, LBM is suitable for hybridization with lubricant morphology as well as multiscale modeling includin...

Large eddy simulation of two-dimensional isotropic turbulence

Large eddy simulation (LES) of forced, homogeneous, isotropic two-dimensional (2D) turbulence in the energy transfer subrange is the subject of this paper. A difficulty specific to this LES and its subgrid scale (SGS) representation is in that the energy source resides in high wave number modes excluded in simulations. Therefore, the SGS scheme in this case should assume the function of the energy source. In addition, the controversial requirements to ensure direct enstrophy transfer and inverse energy transfer make the conventional scheme of positive and dissipative eddy viscosity inapplicable to 2D turbulence. It is shown that these requirements can be reconciled by utilizing a two-parametric viscosity introduced by Kraichnan (1976) that accounts for the energy and enstrophy exchange between the resolved and subgrid scale modes in a way consistent with the dynamics of 2D turbulence; it is negative on large scales, positive on small scales and complies with the basic conservation laws for energy and enstrophy. Different implementations of the two-parametric viscosity for LES of 2D turbulence were considered. It was found that if kept constant, this viscosity results in unstable numerical scheme. Therefore, another scheme was advanced in which the two-parametric viscosity depends on the flow field. In addition, to extend simulations beyond the limits imposed by the finiteness of computational domain, a large scale drag was introduced. The resulting LES exhibited remarkable and fast convergence to the solution obtained in the preceding direct numerical simulations (DNS) by Chekhlovet al. (1994) while the flow parameters were in good agreement with their DNS counterparts. Also, good agreement with the Kolmogorov theory was found. This LES could be continued virtually indefinitely. Then, a simplified SGS representation was designed, referred to as the stabilized negative viscosity (SNV) representation, which was based on two algebraic terms only, negative Laplacian and positive biharmonic ones. It was found that the SNV scheme performed in a fashion very similar to the full equation and it was argued that this scheme and its derivatives should be applied for SGS representation in LES of quasi-2D flows.

CFD: Progress and problems

We give a brief review of the state-of-the-art in computational fluid dynamics. Most of this paper concerns several flow examples that emphasize the physics, mathematics, and numerics of the flows being simulated.

Direct numerical simulation tests of eddy viscosity in two dimensions

Two‐parametric eddy viscosity (TPEV) and other spectral characteristics of two‐dimensional (2‐D) turbulence in the energy transfer subrange are calculated from direct numerical simulation (DNS) with 5122 resolution. The DNS‐based TPEV is compared with those calculated from the test field model (TFM) and from the renormalization group (RG) theory. Very good agreement between all three results is observed.

Macroscopic description of arbitrary Knudsen number flow using Boltzmann–BGK kinetic theory

We extend our previous analysis of closed-form equations for finite Knudsen number flow and scalar transport that result from the Boltzmann-Bhatnagar-Gross-Krook (BGK) kinetic theory with constant relaxation time. Without approximation, we obtain closed-form equations for arbitrary spatial dimension and flow directionality which are local differential equations in space and integral equations in time. These equations are further simplified for incompressible flow and scalars. The particular case of no-flow scalar transport admits analytical solutions that exhibit ballistic behaviour at short times while behaving diffusively at long times. It is noteworthy that, even with constant relaxation time BGK microphysics, quite complex macroscopic descriptions result that would be difficult to obtain using classical constitutive models or continuum averaging.

Propagating high-frequency shear waves in simple fluids

A complex dynamics of a shear wave decay, defined as an initial value problem u(y,0)=U sin(ky)i, where i is a unit vector in the x-direction, is investigated in the entire range of the Weissenberg–Knudsen number (Wi=τνk2=τ2c2k2) variation 0≤Wi≤∞, where τ and c are the fluid relaxation time and speed of sound in the vicinity of thermodynamic equilibrium, respectively. It is shown that in the limit Wi⪡1, the shear wave decay is a purely viscous process obeying a parabolic diffusion equation. When Wi⪢1, a completely new regime emerges, the flow behaves as a dissipative transverse traveling wave. This transition is theoretically predicted as a solution to the Boltzmann–Bhatnagar–Gross–Krook equation and confirmed by the lattice Boltzmann numerical simulations. In the limit Wi=τνk2⪢1 the observed slowing down of the shear wave decay can be interpreted as a high-frequency drag reduction.

Studies of accurate multi-component lattice Boltzmann models on benchmark cases required for engineering applications

Abstract We present recent developments in lattice Boltzmann modeling for multi-component flows, implemented on the platform of a general purpose, arbitrary geometry solver PowerFLOW. Presented benchmark cases demonstrate the methods accuracy and robustness necessary for handling real world engineering applications at practical resolution and computational cost. The key requirements for such approach are that the relevant physical properties and flow characteristics do not strongly depend on numerics. In particular, the strength of surface tension obtained using our new approach is independent of viscosity and resolution, while the spurious currents are significantly suppressed. Using a much improved surface wetting model, undesirable numerical artifacts including thin film and artificial droplet movement on inclined wall are significantly reduced.