Projektbeschreibung
Eine bessere probabilistische Fluiddynamik zur Erforschung von Rauschen
Komplexe Fluide können zufälligen Mustern folgen, deren Wahrscheinlichkeit sich anhand von komplexen Gleichungen vorhersagen lässt. Das vom Europäischen Forschungsrat finanzierte Projekt NoisyFluid beabsichtigt, diese Gleichungen durch Modifizierungen weiterzuentwickeln, sodass das Vorliegen von zufälligen Elementen wie einem Additiv- oder Transportrauschen berücksichtigt werden kann. Die Forschenden werden Rauschen in Randnähe durch Vortex-Erzeugung, erhöhte Dissipation, erhöhte Koaleszenz sowie die Ausbreitung von Additivrauschen auf verschiedenen Skalen beschreiben. Unter anderem wird es dabei das Transportrauschen auf einer großen Skala und seine Auswirkungen auf die turbulente Scheinzähigkeit („eddy viscosity“) einbeziehen. Ein Ziel des Projekts besteht darin, ein besseres Verständnis davon zu gewinnen, ob Rauschen die dreidimensionalen Navier-Stokes-Gleichungen regularisiert.
Ziel
Fluids, in complex regimes, show random features. The aim of this project is approaching several questions around the randomness of fluids by means of a theory that could be called “Stochastic Fluid Mechanics”. The distinctive feature of this theory, opposite to others that investigated the stochastic features of fluids, is that it is based on the usual continuum mechanics equations, in particular the Navier-Stokes and Euler equations, but suitably modified by the presence of random elements, like an additive or a transport type noise.
Stochastic equations of fluid dynamics have been studied already for three decades and the number of foundational results is very large. However, two basic directions have been explored only partially:
a) the origin and the form of noise in fluids
b) the consequences of the presence of noise.
This project will make progresses in these two directions, describing the noise near boundary due to vortex productions, including the question of intrinsic stochasticity at the boundary, the propagation of additive noise at small scales to a transport-stretching noise at large scales, the consequences of transport noise on eddy viscosity, enhanced dissipation, enhanced coalescence, and other applications in turbulence and Geophysics.
The most ambitious core of the project is putting together these pieces in a picture that explains the mechanism of regularization by noise for the 3D Navier-Stokes equations. The additive noise at small scales is responsible for a transport-stretching noise at larger scales which could prevent blow-up of high intensity vortex structures. We have already proved recently that a noise, of transport type only, has this regularization effect, but stretching amplifies vorticity and new progresses are needed to cope with both processes. We aim to use the experimentally observed fact that small scale velocity should be approximately orthogonal to vorticity in high intensity regions.
Wissenschaftliches Gebiet
Programm/Programme
- HORIZON.1.1 - European Research Council (ERC) Main Programme
Thema/Themen
Finanzierungsplan
HORIZON-AG - HORIZON Action Grant Budget-BasedGastgebende Einrichtung
56126 Pisa
Italien