Related papers: A stationary solution for the mixed turbulence she…
This paper provides two results that are useful in the study of the existence and the stability properties of a periodic solution for a given dynamical system. The first result deals with scalar time-periodic systems and establishes the…
In this paper, we study the stability and instability of plane wave solutions to semilinear systems of wave equations satisfying the null condition. We identify a condition which allows us to prove the global nonlinear asymptotic stability…
Shell model turbulence is a simplified mathematical framework that captures essential features of incompressible fluid turbulence such as the energy cascade, intermittency and anomalous scaling of the fluid observables. We perform a…
We develop a methodology for proving well-posedness in optimal regularity spaces for a wide class of nonlinear parabolic initial-boundary value systems, where the standard monotone operator theory fails. A motivational example of a problem…
We present an extended version of an invited talk given on the International Conference "Turbulent Mixing and Beyond". The dynamical and statistical description of stably stratified turbulent boundary layers with the important example of…
The three--dimensional incompressible viscous Boussinesq equations, under the assumption of hydrostatic balance, govern the large scale dynamics of atmospheric and oceanic motion, and are commonly called the primitive equations. To overcome…
We perform a unique direct numerical simulation of Euler turbulence using delta-correlated velocity field as an initial condition, and report a full range of $k^2$ and $k$ energy spectra for 3D and 2D flows respectively, zero energy flux,…
The `local scaling' hypothesis, first introduced by Nieuwstadt two decades ago, describes the turbulence structure of stable boundary layers in a very succinct way and is an integral part of numerous local closure-based numerical weather…
We consider the dynamics of timelike spherical thin matter shells in vacuum. A general formalism for thin shells matching two arbitrary spherical spacetimes is derived, and subsequently specialized to the vacuum case. We first examine the…
Understanding under what conditions it is possible to construct equivalent ensembles is key to advancing our ability to connect microscopic and macroscopic properties of non-equilibrium statistical mechanics. In the case of fluid dynamical…
In this paper we study analytically the viscous `sabra' shell model of energy turbulent cascade. We prove the global regularity of solutions and show that the shell model has finitely many asymptotic degrees of freedom, specifically: a…
For a one-dimensional wave equation, we consider a mixed problem in a curvilinear half-strip. The initial conditions have a first-kind discontinuity at one point. The mixed problem models the problem of a longitudinal impact on a finite…
We introduce a shell model of turbulence featuring intermittent behaviour with anomalous power-law scaling of structure functions. This model is solved analytically with the explicit derivation of anomalous exponents. The solution…
A model of the thin shell expanding into a uniform ambient medium is developed. Density perturbations are described using equations with linear and quadratic terms, and the linear and the nonlinear solutions are compared. We follow the time…
A semi-empirical three-dimensional model of turbulence in the approximation of the far turbulent wake behind a body of revolution in a passive stratified medium is considered. The sought quantities are the kinetic turbulent energy, kinetic…
This paper presents a rigorous theoretical extension of the Smagorinsky model for turbulence simulations. The author builds on its fundamental framework, addressing known limitations, and making new mathematical advances. Specifically, this…
Modelling fluid turbulence using a `skeleton' of coherent structures has traditionally progressed by focusing on a few canonical laboratory experiments such as pipe flow and Taylor-Couette flow. We here consider the stratified inclined…
Convergence to stationary solutions in fully nonlinear parabolic systems with general nonlinear boundary conditions is shown in situations where the set of stationary solutions creates a $C^2$-manifold of finite dimension which is normally…
We discuss the effects of finite perturbations in fully developed turbulence by introducing a measure of the chaoticity degree associated to a given scale of the velocity field. This allows one to determine the predictability time for…
We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence. We achieve this by constructing, for any given nonlinear model, a linear model of passive advection of an…