Related papers: Anomalous dissipation in a stochastic inviscid dya…
When the intensity of turbulence is increased (by increasing the Reynolds number, e.g. by reducing the viscosity of the fluid), the rate of the dissipation of kinetic energy decreases but does not tend asymptotically to zero: it levels off…
We report the experimental evidence of the existence of a random attractor in a fully developed turbulent swirling flow. By defining a global observable which tracks the asymmetry in the flux of angular momentum imparted to the flow, we can…
We consider the variational wave equation in one-dimensional space with stochastic forcing by an additive noise. Blow-up of local smooth solutions is established, and global existence is proved in the class of weak martingale solutions.
Due to the chaotic nature of turbulence, statistical quantities are often more informative than pointwise characterizations. In this work, we consider the stochastic Ladyzhenskaya-Smagorinsky equation driven by space-time Gaussian noise on…
Following Abbatiello et al. [ DCCDS-A (41), 2020], we introduce dissipative turbulent solutions to a simple model of a mixture of two non interacting compressible fluids {\tc filling a bounded domain with general non zero inflow/outflow…
We consider a system-reservoir model where the reservoir is modulated by an external noise. Both the internal noise of the reservoir and the external noise are stationary, Gaussian and are characterized by arbitrary decaying correlation…
The kinetic energy of supersonic turbulence within interstellar clouds is subject to cooling by dissipation in shocks and subsequent line radiation. The clouds are therefore susceptible to a condensation process controlled by the specific…
In this study we investigate shallow turbidity density currents and underflows from mechanical point of view. We propose a simple hyperbolic model for such flows. On one hand, our model is based on very basic conservation principles. On the…
We address the experimentally observed non-Gaussian fluctuations for the energy injected into a closed turbulent flow at fixed Reynolds number. We propose that the power fluctuations mirror the internal kinetic energy fluctuations. Using a…
In the dynamics of driven impurity models, there is a fundamental asymmetry between the processes of emission and absorption of environment excitations: most of the emitted excitations are rapidly and irreversibly scattered away, and only a…
Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…
The inviscid limit of the stochastic Burgers equation is discussed in terms of the level surfaces of the minimising Hamilton-Jacobi function, the classical mechanical caustic and the Maxwell set and their algebraic pre-images under the…
The Smagorinsky model, unmodified, is often reported to severely overdiffuse flows. Previous estimates of the energy dissipation rate of the Smagorinsky model for shear flows reflect a blow up of model energy dissipation as Re increases.…
We study the development of mean structures in a nonlinear model of large scale ocean dynamics with bottom topography and dissipation, and forced with a noise term. We show that the presence of noise in this nonlinear model leads to…
Intermittency is an essential property of astrophysical fluids, which demonstrate an extended inertial range. As intermittency violates self-similarity of motions, it gets impossible to naively extrapolate the properties of fluid obtained…
As a minimal mathematical model generating cascade analogous to that of the Navier-Stokes turbulence in the inertial range, we propose a one-dimensional partial-differential-equation model that conserves the integral of the squared…
When complex systems are driven to extinction by some external factor, their non-stationary dynamics can present an intermittent behaviour between relative tranquility and burst of activity whose consequences are often catastrophic. To…
This article introduces, and reviews recent work using, a simple optimisation technique for analysing the nonlinear stability of a state in a dynamical system. The technique can be used to identify the most efficient way to disturb a system…
Consider a chaotic dynamical system generating Brownian motion-like diffusion. Consider a second, non-chaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in…
The Buridan's ass paradox is characterized by perpetual indecision between two states, which are never attained. When this problem is formulated as a dynamical system, indecision is modeled by a discrete-state Markov process determined by…