Recently, the development of machine learning (ML) potentials has made it possible to perform large-scale and long-time molecular simulations with the accuracy of quantum mechanical (QM) models. However, for different...
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We present a new formulation of the incompressible Navier-Stokes equation in terms of an auxiliary field that differs from the velocity by a gauge transformation. The gauge freedom allows us to assign simple and speci...
The Kolmogorov relation for the third-order moments of the velocity differences is generalized for the case of statistically steady turbulence and applied to the Bénard convection problem. The predicted temperatu...
The Kolmogorov relation for the third-order moments of the velocity differences is generalized for the case of statistically steady turbulence and applied to the Bénard convection problem. The predicted temperature and velocity spectra are ET≊k−7/5 and E≊k−11/5, respectively. At the smaller scales, in the dissipation range of the temperature fluctuations, the Kolmogorov range where most of the energy is dissipated is predicted. The new set of scaling exponents, which can be observed in the experiments in the small-aspect-ratio convection cells, is derived.
We report numerical simulations of Bénard convection in infinite Prandtl number fluids driven by thermocapillary forces. At high Marangoni numbers a spectrum E(k)∼k−3 of surface temperature fluctuations is estab...
We report numerical simulations of Bénard convection in infinite Prandtl number fluids driven by thermocapillary forces. At high Marangoni numbers a spectrum E(k)∼k−3 of surface temperature fluctuations is established due to the formation of discontinuities of the temperature gradient in the form of thermal ripples between contiguous convective cells. The results support the applicability of Sivashinsky's model equation beyond its mathematical limit of validity.
Fast numerical methods are used to solve the equations for periodically rotating spiral waves in excitable media, and the associated eigenvalue problem for the stability of these waves. Both equally and singly diffusi...
Fast numerical methods are used to solve the equations for periodically rotating spiral waves in excitable media, and the associated eigenvalue problem for the stability of these waves. Both equally and singly diffusive media are treated. Rotating-wave solutions are found to be discretely selected by the system and an isolated, complex-conjugate pair of eigenmodes is shown to cause instability of these waves. The instability arises at the point of zero curvature on the spiral interface and results in wavelike disturbances which propagate from this point along the interface.
We consider a few cases of homogeneous and isotropic turbulence differing by the mechanisms of turbulence generation. The advective terms in the Navier-Stokes and Burgers equations are similar. It is proposed that the...
We consider a few cases of homogeneous and isotropic turbulence differing by the mechanisms of turbulence generation. The advective terms in the Navier-Stokes and Burgers equations are similar. It is proposed that the longitudinal structure functions Sn(r) in homogeneous and isotropic three-dimensional turbulence are governed by a one-dimensional (1D) equation of motion, resembling the 1D Burgers equation, with the strongly nonlocal pressure contributions accounted for by Galilean invariance-breaking terms. The resulting equations, not involving parameters taken from experimental data, give both scaling exponents and amplitudes of the structure functions in an excellent agreement with experimental data. The derived probability density function P(Δu,r)≠P(−Δu,r), but P(Δu,r)=P(−Δu,−r), in accord with the symmetry properties of the Navier-Stokes equations. With decrease of the displacement r, the probability density, which cannot be represented in a scale-invariant form, shows smooth variation from the Gaussian at the large scales to close-to-exponential function, thus demonstrating onset of small-scale intermittency. It is shown that accounting for the subdominant contributions to the structure functions Sn(r)∝rξn is crucial for a derivation of the amplitudes of the moments of the velocity difference.
We present a physical model constructed from the Navier-Stokes equation to describe the evolution of the probability distribution function of transverse velocity gradients in 3D isotropic turbulence. Quanitative agree...
We present a physical model constructed from the Navier-Stokes equation to describe the evolution of the probability distribution function of transverse velocity gradients in 3D isotropic turbulence. Quanitative agreement with data from direct numerical simulations of isotropic turbulence for a wide range of Reynolds number is obtained. The model is based on a concrete physical picture of self-distortion of structures and interaction between random eddies and structures; the dynamical balance explains the non-Gaussian equilibrium probability distributions.
A simple fluctuation argument A la Landau suggests why probability density functions of velocity gradients of turbulent velocity fields are often found to have a close to exponential tail. The detailed functional form...
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A simple fluctuation argument A la Landau suggests why probability density functions of velocity gradients of turbulent velocity fields are often found to have a close to exponential tail. The detailed functional form depends on the assumptions made concerning the intermittency.
Intermittency effects in turbulence are discussed from a dynamical point of view. A two-fluid model is developed to describe quantitatively the non-gaussian statistics of turbulence at small scales. With a self-simila...
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Intermittency effects in turbulence are discussed from a dynamical point of view. A two-fluid model is developed to describe quantitatively the non-gaussian statistics of turbulence at small scales. With a self-similarity argument, the model gives rise to the entire set of inertial range scaling exponents for normalized velocity structure functions. The results are in excellent agreement with experimental and numerical measurements. The model suggests a physical mechanism of intermittency, namely the self-interaction of turbulence structures.
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