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We develop first-principles theory of relativistic fluid turbulence at high Reynolds and P\'eclet numbers. We follow an exact approach pioneered by Onsager, which we explain as a non-perturbative application of the principle of…
The flow of a viscous fluid is perturbed by its internal friction which generates heat and leads to a small temperature change. This does not occur for an ideal fluid. We would like to resolve this picture as a function of the dynamical…
We study the holographic hydrodynamics in the Einstein-Gauss-Bonnet(EGB) gravity in the framework of the large $D$ expansion. We find that the large $D$ EGB equations can be interpreted as the hydrodynamic equations describing the conformal…
We use continuum elasticity theory to revise scaling laws for radial breathing-like and shear-like vibration modes in quasi-2D nanostructures including finite-width nanoribbons and finite-size thin circular discs. Such modes can be observed…
In previous papers I have argued that the \emph{fusion rules hypothesis}, which was originally introduced by L'vov and Procaccia in the context of the problem of three-dimensional turbulence, can be used to gain a deeper insight in…
We study conformal invariance of vorticity clusters in weakly compressible two-dimensional turbulence at low Mach numbers. On the basis of very high resolution direct numerical simulation we demonstrate the scaling invariance of the inverse…
The Navier-Stokes (NS) equations as a turbulence model have been widely applied in lots of fields. The NS equations contain such a fundamental assumption that all small physical/artificial disturbances could be neglected. Is this assumption…
Passive scalar mixing (metals, molecules, etc.) in the turbulent interstellar medium (ISM) is critical for abundance patterns of stars and clusters, galaxy and star formation, and cooling from the circumgalactic medium. However, the…
The understanding of fluid turbulence has considerably progressed in recent years. The application of the methods of statistical mechanics to the description of the motion of fluid particles, i.e. to the Lagrangian dynamics, has led to a…
This work presents Direct Numerical Simulations of capillary wave turbulence solving the full 3D Navier Stokes equations of a two-phase flow. When the interface is locally forced at large scales, a statistical stationary state appears after…
The Cahn-Hilliard-Navier-Stokes (CHNS) partial differential equations (PDEs) provide a powerful framework for the study of the statistical mechanics and fluid dynamics of multiphase fluids. We provide an introduction to the equilibrium and…
Phase separation in binary and ternary fluids is studied using a two dimensional Lattice Gas Automata. The lengths, given by the the first zero crossing point of the correlation function and the total interface length is shown to exhibit…
The inverse energy cascade in Charney-Hasegawa-Mima turbulence is investigated. Kolmogorov law for the third order velocity structure function is shown to be independent on the Rossby number, at variance with the energy spectrum, as shown…
We present a unified theoretical and numerical framework for self-similar multi-shock implosions achieving ultrahigh compression in a uniform solid spherical target. Extending the classical Guderley model to N stacked, spherically…
Understanding inhomogeneous and anisotropic fluid flows require mathematical and computational tools that are tailored to such flows and distinct from methods used to understand the canonical problem of homogeneous and isotropic turbulence.…
The statistical features of homogeneous, isotropic, two-dimensional stochastic turbulence are discussed. We derive some rigorous bounds for the mean value of the bulk energy dissipation rate $\mathbb{E} [\varepsilon ]$ and enstrophy…
We examine the dynamics of two coalescing liquid drops in the `inertial regime', where the effects of viscosity are negligible and the propagation of the bridge front connecting the drops can be considered as `local'. The solution fully…
Isotropic turbulence is typically studied numerically through the direct numerical simulations (DNS). The DNS flows are described by the Navier-Stokes equation in a 'box', defined through periodic boundary conditions. The DNS flows live in…
Polymeric turbulence, flows of fluids with dilute polymer additives at high Reynolds numbers, exhibits striking deviations from the Kolmogorovean behaviour of Newtonian turbulence. Recent experiments as well as simulations have uncovered a…
In Navier-Stokes turbulence, energy and helicity injected at large scales are subject to a joint direct cascade, with both quantities exhibiting a spectral scaling $\propto k^{-5/3}$. We demonstrate via direct numerical simulations that the…