In this paper, using hydrodynamic entropy, we quantify multiscale disorder in Euler and
hydrodynamic turbulence. These examples illustrate that the hydrodynamic entropy is not …

For the steady state of Burgers turbulence, Saffman [in Topics in Nonlinear Physics
(Springer, Berlin, 1968), pp. 485–614] derived analytical expressions for the second-order …

In this work, we examine the classical Burgers equation and investigate the effects of a
random force on the wave field. Two scenarios are considered: the impact of a random force …

We construct a formally time-reversible, one-dimensional forced Burgers equation by
imposing a global constraint of energy conservation, wherein the constant viscosity is …

Using numerical simulations, we show that the asymptotic states of two-dimensional (2D)
Euler turbulence exhibit large-scale flow structures due to nonzero energy transfers among …

In this article, we report the equilibrium and nonequilibrium features of two-dimensional (2D)
and three-dimensional (3D) Euler turbulence. To obtain a full range of equilibrium spectra …

We have two basic observations: mathematically, the variational principle and Hamiltonian
formulation of some models, such as the Korteweg-de Vries (KdV) equation, are …

We propose and demonstrate, with the one-dimensional Korteweg-de Vries-Burgers model,
the scenarios of transfer loop and\textit {all-scale} statistical equilibrium, the former being …