Related papers: Note on Forced Burgers Turbulence
Travelling-wave solutions of the inviscid Burgers equation having smooth initial wave profiles of suitable shapes are known to develop shocks (infinite gradients) in finite times. Such singular solutions are characterized by energy spectra…
Numerical simulations of particle acceleration in magnetized turbulence have recently observed powerlaw spectra where pile-up distributions are rather expected. We interpret this as evidence for particle segregation based on acceleration…
A uniform bounded variation estimate for finite volume approximations of the nonlinear scalar conservation law $\partial_t \alpha + \mathrm{div}(\boldsymbol{u}f(\alpha)) = 0$ in two and three spatial dimensions with an initial data of…
Following the idea that dissipation in turbulence at high Reynolds number is by events singular in space-time and described by solutions of the inviscid Euler equations, we draw the conclusion that in such flows scaling laws should depend…
We are interested in the tail behavior of the pdf of mass density within the one and $d$-dimensional Burgers/adhesion model used, e.g., to model the formation of large-scale structures in the Universe after baryon-photon decoupling. We show…
For Burgers equations with real data and complex forcing terms, Lerner, Morimoto and Xu [{\it Instability of the Cauchy-Kovalevskaya solution for a class of non-linear systems}, Amer.~J.~Math.~2010] proved that only analytical data generate…
In this paper, we find a new large scale instability displayed by a rotating flow in forced turbulence. The turbulence is generated by a small scale external force at low Reynolds number. The theory is built on the rigorous asymptotic…
We analyze the field theory of fully developed Burgers turbulence. Its key elements are shock fields, which characterize the singularity statistics of the velocity field. The shock fields enter an operator product expansion describing…
The supernova-driven interstellar medium in star-forming galaxies has Reynolds numbers of the order of $10^{6}$ or even larger. We study, by means of adaptive mesh refinement hydro- and magnetohydrodynamical simulations that cover the full…
We consider a planar viscous shock of moderate strength for a scalar viscous conservation law in multi-D. We consider a strictly convex flux, as a small perturbation of the Burgers flux, along the normal direction to the shock front.…
The effect of introducing a mass dependent diffusion rate ~ m^{-alpha} in a model of coagulation with single-particle break up is studied both analytically and numerically. The model with alpha=0 is known to undergo a nonequilibrium phase…
Inertial-range features of turbulence are investigated using data from experimental measurements of grid turbulence and direct numerical simulations of isotropic turbulence simulated in a periodic box, both at the Taylor-scale Reynolds…
Motivated by theoretical studies of gravitational clustering in the Universe, we compute propagators (response functions) in the adhesion model. This model, which is able to reproduce the skeleton of the cosmic web and includes nonlinear…
The normalized turbulent dissipation rate $C_\epsilon$ is studied in decaying and forced turbulence by direct numerical simulations, large-eddy simulations, and closure calculations. A large difference in the values of $C_\epsilon$ is…
We propose a model for the density statistics in supersonic turbulence, which play a crucial role in star-formation and the physics of the interstellar medium (ISM). Motivated by [Hopkins, MNRAS, 430, 1880 (2013)], the model considers the…
We analyze the data stemming from a forced incompressible hydrodynamic simulation on a grid of 2048^3 regularly spaced points, with a Taylor Reynolds number of Re~1300. The forcing is given by the Taylor-Green flow, which shares…
We consider the time-dependence of a hierarchy of scaled $L^{2m}$-norms $D_{m,\omega}$ and $D_{m,\theta}$ of the vorticity $\boldsymbol {\omega} = \boldsymbol{\nabla} \times {\mathbf u}$ and the density gradient $\boldsymbol{\nabla}…
A systematic analysis of large scale fluctuations in the low temperature pinned phase of a directed polymer in a random potential is described. These fluctuations come from rare regions with nearly degenerate ``ground states''. The…
Atmospheric gusts expose wall-bounded turbulence to severe unsteady forcing, triggering complex non-equilibrium dynamics and extreme aerodynamic loads. In this study, direct numerical simulations (DNS) are performed to investigate the…
We investigate the statistical properties, based on numerical simulations and analytical calculations, of a recently proposed stochastic model for the velocity field of an incompressible, homogeneous, isotropic and fully developed turbulent…