Following the ideas of operator product expansion, the velocity v, kinetic energy K=1/2v2, and dissipation rate ε=ν0(∂vi/∂xj)2 are treated as independent dynamical variables, each obeying its own equation of motion....
Following the ideas of operator product expansion, the velocity v, kinetic energy K=1/2v2, and dissipation rate ε=ν0(∂vi/∂xj)2 are treated as independent dynamical variables, each obeying its own equation of motion. The relations Δu(ΔK)2 ∝ r, Δu(Δε)2 ∝ r0, and (Δu)5≊rΔεΔK are derived. If velocity scales as (Δv)rms∝ r(γ/3)−1, then simple power counting gives (ΔK)rms ∝ r1−(γ/6) and (Δε)rms ∝ 1/√(Δv)rms ∝ r(1/2)−(γ/6). In the Kolmogorov turbulence (γ=4) the intermittency exponent μ=(γ/3)-1=1/3 and (Δε)2=O(Re1/4). The scaling relation for the ε fluctuations is a consequence of cancellation of ultraviolet divergences in the equation of motion for the dissipation rate.
Statistical properties of solutions of the random-force–driven Burgers equation are investigated by use of the dynamic renormalization group and direct numerical simulations. The agreement between computed and analyt...
Statistical properties of solutions of the random-force–driven Burgers equation are investigated by use of the dynamic renormalization group and direct numerical simulations. The agreement between computed and analytical results on both exponents and amplitudes of the correlation functions is good. It is shown that a small-scale noise dominates large-scale, long-time (k→0,ω→0) behavior of the system and, as a consequence, no microscopic system of interacting particles described by Burgers equation in the hydrodynamic limit (k→0,ω→0) exists.
We introduce a lattice Boltzmann model for simulating immiscible binary fluids in two dimensions. The model, based on the Boltzmann equation of lattice-gas hydrodynamics, incorporates features of a previously introduc...
We introduce a lattice Boltzmann model for simulating immiscible binary fluids in two dimensions. The model, based on the Boltzmann equation of lattice-gas hydrodynamics, incorporates features of a previously introduced discrete immiscible lattice-gas model. A theoretical value of the surface-tension coefficient is derived and found to be in excellent agreement with values obtained from simulations. The model serves as a numerical method for the simulation of immiscible two-phase flow; a preliminary application illustrates a simulation of flow in a two-dimensional microscopic model of a porous medium. Extension of the model to three dimensions appears straightforward.
The quantitative interpretation of the recent experiments on turbulent diffusivity in high‐Reynolds‐number Couette–Taylor flow by Tam and Swinney [Phys. Rev. A 36, 1374 (1987)], is presented.
The quantitative interpretation of the recent experiments on turbulent diffusivity in high‐Reynolds‐number Couette–Taylor flow by Tam and Swinney [Phys. Rev. A 36, 1374 (1987)], is presented.
For the iterative solution of saddle point problems, a nonsymmetric preconditioner is studied which, with respect to the upper-left block of the system matrix, can be seen as a variant of SSOR. An idealized situation ...
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Stealthy hyperuniform (SHU) many-particle systems are distinguished by a structure factor that vanishes not only at zero wavenumber (as in "standard" hyperuniform systems) but also across an extended range o...
Stealthy hyperuniform (SHU) many-particle systems are distinguished by a structure factor that vanishes not only at zero wavenumber (as in "standard" hyperuniform systems) but also across an extended range of wavenumbers near the origin. We generate disordered SHU packings of identical and ‘nonoverlapping’ spheres in d-dimensional Euclidean space using a modified collective-coordinate optimization algorithm that incorporates a soft-core repulsive potential between particles in addition to the standard stealthy pair potential. Compared to SHU packings without soft-core repulsions, these SHU packings are ultradense with packing fractions ranging from 0.67-0.86 for d = 2 and 0.47-0.63 for d = 3, spanning a broad spectrum of structures depending on the stealthiness parameter χ. We consider two-phase media composed of hard particles derived from ultradense SHU packings (phase 2) embedded in a matrix phase (phase 1), with varying stealthiness parameter χ and packing fractions . Our main objective is the estimation of the dynamical physical properties of such two-phase media, namely, the effective dynamic dielectric constant and the time-dependent diffusion spreadability, which is directly related to nuclear magnetic relaxation in fluid-saturated porous media. We show through spreadability that two-phase media derived from ultradense SHU packings exhibit faster interphase diffusion due to the higher packing fractions achievable compared to media obtained without soft-core repulsion. The imaginary part of the effective dynamic dielectric constant of SHU packings vanishes at a small wavenumber, implying perfect transparency for the corresponding wavevectors. While a larger packing fraction yields a smaller transparency interval, we show that it also displays a reduced height of the attenuation peak. We also obtain cross-property relations between transparency characteristics and long-time behavior of the spreadability for such two-phase media, showing that one leads to infor
The Kolmogorov relation for the third order structure function is used to derive the energy spectrum in the far dissipation range (k→∞). This contains no unspecified constants. Using methods from matched asymptotic ...
The Kolmogorov relation for the third order structure function is used to derive the energy spectrum in the far dissipation range (k→∞). This contains no unspecified constants. Using methods from matched asymptotic expansions and mild analyticity assumptions, a uniformly valid form for the inertial through the dissipative ranges is obtained. An analogous energy spectrum is presented. This is compared with the results of physical and numerical experiments on the energy spectra E(k). The theoretical predictions are found to deviate by not more than a few percent from the measured data in the entire range of wave numbers where the energy spectrum E(k) varies by more than 30 orders of magnitude.
A two-species reaction-diffusion model is used to study bifurcations in one-dimensional excitable media. Numerical continuation is used to compute branches of traveling waves and periodic steady states, and linear sta...
A two-species reaction-diffusion model is used to study bifurcations in one-dimensional excitable media. Numerical continuation is used to compute branches of traveling waves and periodic steady states, and linear stability analysis is used to determine bifurcations of these solutions. It is shown that the sequence of symmetry-breaking bifurcations which lead from the homogeneous excitable state to stable traveling waves can be understood in terms of an O(2)-symmetric normal form.
High-resolution numerical experiments, described in this work, show that velocity fluctuations governed by the one-dimensional Burgers equation driven by a white-in-time random noise with the spectrum ‖f(k)‖2¯...
High-resolution numerical experiments, described in this work, show that velocity fluctuations governed by the one-dimensional Burgers equation driven by a white-in-time random noise with the spectrum ‖f(k)‖2¯∝k−1 exhibit a biscaling behavior: All moments of velocity differences Sn≤3(r)=‖u(x+r)-u(x)‖n¯≡‖Δu‖n¯ ∝rn/3, while Sn>3(r)∝rnξ with ξn≊1 for real n>0 [Chekhlov and Yakhot, Phys. Rev. E 51, R2739 (1995)]. The probability density function, which is dominated by coherent shocks in the interval Δu<0, is scrP(Δu,r)∝(Δu)−q with q≊4. A phenomenological theory describing the experimental findings is presented.
By direct numerical simulations of the plane Couette flow (PCF) in a large computational domain, it is shown that an isolated turbulent band decays monotonically at low Reynolds numbers but experiences transient growt...
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By direct numerical simulations of the plane Couette flow (PCF) in a large computational domain, it is shown that an isolated turbulent band decays monotonically at low Reynolds numbers but experiences transient growth before the eventual relaminarization at moderate Reynolds numbers. The lower bound Reynolds number of the transient-growth regime is determined as 286. The width, length, and tilt angle of the iso- lated band structure are defined based on the disturbance kinetic energy in the mid-plane, and the geometric characteristics of the band can be described with a tilted rectangle. It is illustrated that before its eventual fragmentation, the isolated turbulent band decays in a style of longitudinal contraction, where the center, width, and tilt angle of the band keep almost constant but the band length contracts with a statistically constant velocity.
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