相关论文: One-dimensional model of freely decaying two-dimen…
Gathering together some existing results, we show that the solutions to the one-dimensional Burgers equation converge for long times towards the stationary solutions to the steady Burgers equation, whose Fourier spectrum is not integrable.…
We consider freely decaying two-dimensional isotropic turbulence. It is usually assumed that, in such turbulence, the energy spectrum at small wave number, takes the form, where is the two-dimensional version of Loitsyansky's integral. In…
We study the scaling properties of two-dimensional turbulence using dimensional analysis. In particular, we consider the energy spectrum both at large and small scales and in the "inertial ranges" for the cases of freely decaying and forced…
In this work we construct and analyze continuous hydrodynamic models in one space dimension, which are induced by shell models of turbulence. After Fourier transformation, such continuous models split into an infinite number of uncoupled…
We consider the generalised Burgers equation $$ \frac{\partial u}{\partial t} + f'(u)\frac{\partial u}{\partial x} - \nu \frac{\partial^2 u}{\partial x^2}=0,\ t \geq 0,\ x \in S^1, $$ where $f$ is strongly convex and $\nu$ is small and…
An energy-spectrum bottleneck, a bump in the turbulence spectrum between the inertial and dissipation ranges, is shown to occur in the non-turbulent, one-dimensional, hyperviscous Burgers equation and found to be the Fourier-space signature…
The randomly driven Burgers equation with pressure is considered as a 1D model of strong turbulence of compressible fluid. It is shown that infinitely small pressure provides a finite effect on the velocity and density statistics and this…
We propose a ballistic coalescence model (punctuated-Hamiltonian approach) mimicking the fusion of vortices in freely decaying two-dimensional turbulence. A temporal scaling behaviour is reached where the vortex density evolves like…
In this paper, we establish the existence and uniqueness of solutions to the two-dimensional Burgers equation using the framework of infinite-dimensional dynamical systems. The two-dimensional Burgers equation, which models the interplay…
Data-driven turbulence modeling is experiencing a surge in interest following algorithmic and hardware developments in the data sciences. We discuss an approach using the differentiable physics paradigm that combines known physics with…
We present an introductory overview of several challenging problems in the statistical characterisation of turbulence. We provide examples from fluid turbulence in three and two dimensions, from the turbulent advection of passive scalars,…
This work is devoted to the study of the decay of multiscale deterministic solutions of the unforced Burgers' equation in the limit of vanishing viscosity. A deterministic model of turbulence-like evolution is considered. We con- struct the…
An exact analysis is performed for the two-point correlation function C(r,t) in dissipative Burgers turbulence with bounded initial data, in arbitrary spatial dimension d. Contrary to the usual scaling hypothesis of a single dynamic length…
The last decades witnessed a renewal of interest in the Burgers equation. Much activities focused on extensions of the original one-dimensional pressureless model introduced in the thirties by the Dutch scientist J.M. Burgers, and more…
We present results for the 1 dimensional stochastically forced Burgers equation when the spatial range of the forcing varies. As the range of forcing moves from small scales to large scales, the system goes from a chaotic, structureless…
Applying a modified version of the Gledzer-Ohkitani-Yamada (GOY) shell model, the signatures of so-called two-dimensionalization effect of three-dimensional incompressible, homogeneous, isotropic fully developed unforced turbulence have…
Two-dimensional turbulence self-organizes through a process of energy accumulation at large scales, forming a coherent flow termed a condensate. We study the condensate in a model with local dynamics, the large-scale quasi-geostrophic…
Talk presented at the International Conference on Mathematical Physics (Brisbane 1997). This is an introduction to recent work on the scaling and intermittency in forced Burgers turbulence. The mapping between Burgers' equation and the…
We analyze the stochastic scaling laws arising in the invicid limit of the decaying solutions of the Burgers equation. The linear scaling of the velocity structure functions is shown to reflect the domination by shocks of the long-time…
This work is devoted to the decay ofrandom solutions of the unforced Burgers equation in one dimension in the limit of vanishing viscosity. The initial velocity is homogeneous and Gaussian with a spectrum proportional to $k^n$ at small…