Fluid-Dynamics Day in Trieste

Wednesday, 30^th March 2022

Seminar Room, Third Floor of the H2-Bis building (DMG) and Online

The workshop takes place in a hybrid version (in presence and online) at the Department of Mathematics and Geosciences of the University of Trieste (Italy) and aims at presenting recent advances in fluid-dynamics.

Timetable (Central European Time)

Time	Speaker
10.00 - 11.00 CET	Šárka Nečasová
11.15 - 12.15 CET	Massimiliano Berti
14.30 - 15.30 CET	Francesco Fanelli
15.45 - 16.45 CET	Stefano Scrobogna

Speakers and abstracts

• Šárka Nečasová (Institut of Mathematics, Academy of Sciences of the Czech Republic): "A bi-fluid model for a mixture of two compressible non interacting fluids with general boundary data"
  
  

  Abstract: We deal with the global existence of weak solutions for a version of one velocity Baer-Nunziato system with dissipation describing a mixture of two non interacting viscous compressible fluids in a piecewise regular Lipschitz domain with general inflow/outflow boundary conditions. The geometrical setting is general enough to comply with most current domains important for applications as, for example, (curved) pipes of picewise regular and axis-dependent cross sections. Moreover, we introduce dissipative turbulent solutions and prove an existence of such solutions for all adiabatic coefficients γ > 1, their compatibility with classical solutions, the relative energy inequality, and the weak strong uniqueness principle in this class. The class of dissipative turbulent solutions is so far the largest class of generalized solutions which still enjoys the weak strong uniqueness property. It is a joint work with S. Kračmar, B. J. Jin, Y. Kwon and A. Novotný.



• Massimiliano Berti (SISSA): "Benjamin-Feir instability of Stokes waves"
  
  

  Abstract: A classical subject in fluid dynamics regards the spectral instability of Stokes waves -traveling periodic water waves-, pioneered by Stokes in 1847. Benjamin-Feir (1967) and Zhakarov, through experiments and formal arguments, discovered that Stokes waves in deep water are unstable. More precisely, they found unstable eigenvalues near the origin of the complex plane, corresponding to small Floquet exponents μ or equivalently to long-wave perturbations. The first local rigorous mathematical proofs have been given by Bridges-Mielke (1995) in finite depth and by Nguyen-Strauss (2020) in infinite depth. On the other hand, it has been found numerically that when the Floquet number μ varies, the above two eigenvalues trace an entire figure-eight with a cross at the origin. I will present a novel approach to prove this conjecture. The proof exploits the Hamiltonian and reversibility properties of the water waves, a symplectic version of Kato’s theory of similarity transformations, and a block diagonalization idea, inspired by KAM theory. This is joint work with A. Maspero and P. Ventura.



• Francesco Fanelli (Université Claude Bernard Lyon 1): "Well- and ill-posedness issues for some turbulence model"
  
  

  Abstract: In this talk, we review some recent results about the so-called Kolmogorov two-equation model of turbulence. This is a coupling of three degenerate parabolic equations for the mean velocity field u of the fluid, the mean frequency ω of the turbulent fluctuations and the average turbulent kinetic energy k. We focus in particular on the case when the initial turbulent kinetic energy k₀ is allowed to vanish, in space dimension d = 1. We show that, in this case, smooth local solutions exist, but in general they must blow up in finite time. This is a joint work with R. Granero-Belinchón (Universidad de Cantabria – Santander, Spain).



• Stefano Scrobogna (Università Degli Studi di Trieste): "On the effect of viscosity in surface waves"
  
  

  Abstract: The motion of water waves is a classical research topic that has attracted a lot of attention from many different researchers in Mathematics, Physics and Engineering and it is classically modeled by the free-boudary irrotational Euler equations. Usually, these assumptions are enough to describe the main part of the dynamics of real water waves, however, discrepancies between experimental experiences and computer simulations show that sometimes viscosity needs to be taken into account. In this setting the Euler equations should be replaced by the Navier-Stokes equations and the irrotationality hypothesis has to be dropped. It is known however, since the works of Boussinesq (1895) and Lamb (1932) that the vorticity plays a role only close to the free boundary, thus, it would be desirable to add dissipative effects to the water waves equations without going all the way to the Navier-Stokes equations and the subsequent removal of the irrotationality assumption. This problem has been addressed by a number of people starting with Boussinesq and Lamb, in this talk we will investigate a a model proposed by Dias, Dyachenko & Zakharov (Physics Letters A 2008), and we will

  1. Construct global solutions for the full Dias, Dyachenko & Zakharov system stemming from small data which become instantaneously analytic,
  2. Construct an asymptotic model in small amplitude regime which captures up to quadratic interactions of the full model,
  3. Prove that the asymptotic model is well posed.
  
  This is a joint work with R. Granero-Belinchón (U. Cantabria).

Organizers

• Daniele Del Santo (Università Degli Studi di Trieste)
• Gabriele Sbaiz (Università Degli Studi di Trieste and Université Claude Bernard Lyon 1)

For any further information, please write to gabriele.sbaiz[AT]phd.units.it (replace [AT] with @)

Covid-19 rules

It is mandatory to have the Green Pass certificate, to keep the mask on and to follow the Covid-19 rules:

• Emergency Covid-19 UniTs