Turbulence on the Banks of the Arno

Contribution List

1. Registration

31/01/2024, 08:00

2. Coti Zelati - Lecture 1

31/01/2024, 09:00

3. Nualart Batalla

31/01/2024, 11:30

In this talk we consider the long-time behavior of solutions to the two dimensional non-homogeneous Euler equations under the Boussinesq approximation posed on a periodic channel. We prove inviscid damping for the linearized equations around the stably stratified Couette flow using stationary-phase methods of oscillatory integrals. We discuss how these oscillatory integrals arise, what are the...

4. Del Zotto

31/01/2024, 12:00

The Boussinesq equations are a fundamental tool for describing the behavior of stratified fluids. This model possesses an intrinsic oscillating structure, which can be viewed as a stabilizing mechanism. When we consider a stable linear stratification combined with a background Couette flow in a three-dimensional unbounded channel, we will demonstrate how this oscillating structure contributes...

5. Bec - Lecture 1

31/01/2024, 14:00

6. Boutros

31/01/2024, 16:30

Onsager's conjecture states that 1/3 is the critical (Hölder) regularity threshold for energy conservation by weak solutions of the incompressible Euler equations. We consider an analogue of Onsager's conjecture for the hydrostatic Euler equations (also known as the inviscid primitive equations of oceanic and atmospheric dynamics). The anisotropic nature of these equations allows us to...

7. Inversi

31/01/2024, 17:00

The incompressible Euler equations govern the evolution of an ideal fluid. It is well known that the total kinetic energy is preserved along the time evolution of a regular fluid flow. However, when the motion is very rough, there is theoretical and experimental evidence of formation of chaotic structures that support the dissipation of kinetic energy. Mathematically, this problem translates...

8. Abbate

31/01/2024, 17:30

The α-Euler equations feature remarkable relevance from a theoretical point of view, among Large Eddy Simulation approximating schemes. The analysis for the limit of the solutions as α goes to zero has been widely studied in literature. In our work, we employ Langrangian techniques on this system to examine the convergence of its solutions to solutions of the Euler equations on the...

9. Coti Zelati - Lecture 2

01/02/2024, 09:00

10. Johansson

01/02/2024, 11:30

We study dissipation enhancing properties of the advection-diffusion equation advected by a class of Hamiltonian flows with a non-degenerate elliptic point which are quantitatively close to radial flows. Namely, we aim at establishing a convergence towards the streamline average on sub-diffusive timescales. However, for our class of Hamiltonians, contrary to radial flows, the average along the...

11. Sorella

01/02/2024, 12:00

In this talk, we present a new result of a 2d autonomous divergence free velocity field in $C^\alpha$ (for alpha <1 arbitrary but fixed) for which solutions of the advection diffusion equation exhibit anomalous dissipation for some initial data. We will focus on the proof for a simplified version of the velocity field which is just bounded. The proof relies on proving spontaneous stochasticity...

15. Bec - Lecture 2

01/02/2024, 14:00

12. Bilotto

01/02/2024, 16:30

In the context of geostrophic models, the study of stationary features is of particular interest, as they characterize most of the oceanic and atmospheric currents responsible for major climate events. This work illustrates some numerical results on the stability and characteristics of stationary states of viscous flows over a topography, both in laminar and turbulent cases. Using a classical...

13. Bechtold

01/02/2024, 17:00

We study the surface quasi-geostrophic equation driven by a generic additive noise process W. By means of convex integration techniques, we establish existence of weak solutions whenever the stochastic convolution z associated with W is well defined and fulfills certain regularity constraints. Quintessentially, we show that the so constructed solutions to the non-linear equation are controlled...

14. Yaroslavtsev

01/02/2024, 17:30

Thanks to the work of Arnold, Crauel, and Wihstutz it is known that for any self-adjoint operator $T$ acting on a finite dimensional space with the negative trace the corresponding linear equation $dx_t=Tx_tdt$ can be stabilized by a noise, i.e. there exists operator-valued Brownian motion $W$ such that the solution of $dx_t + d Wx_t=Tx_tdt$ vanishes a.s. for any initial value $x_0=x$. The...

16. Coti Zelati - Lecture 3

02/02/2024, 09:00

17. Cocciaglia

02/02/2024, 11:30

The statistical properties of turbulent flows are fundamentally different from those of systems at equilibrium due to the presence of an energy flux from the scales of injection to those where energy is dissipated by the viscous forces: a scenario dubbed “direct energy cascade”. From a statistical mechanics point of view, the cascade picture prevents the existence of detailed balance, which...

18. Ertel

02/02/2024, 12:00

Random Vortex Methods are a class of Monte Carlo algorithms that aim to approximate the solution to the incompressible Navier-Stokes equation (NSE) using a system of interacting Stochastic Differential Equations. Such methods have originally been introduced and mathematically analyzed for homogenous 2D NSE on the full plane, however extensions to more pracically interesting regimes such as the...

19. Bec - Lecture 3

02/02/2024, 14:00

20. Poster session

02/02/2024, 16:30