Statut  Confirmé 
Série  COLLOQUIUMENS 
Domaines  physics 
Date  Mercredi 7 Fevrier 2024 
Heure  13:30 
Institut  DPTPHYSENS 
Salle  ConfIV (E244)  Dépt de Physique de l'ENS  24 rue Lhomond 75005 PARIS 
Nom de l'orateur  Nazarenco 
Prenom de l'orateur  Sergey 
Addresse email de l'orateur  
Institution de l'orateur  
Titre  Universal scalings in evolving and stationary wave turbulence 
Résumé  Using the NonlinearSchrodinger (NLS) equation as a master model, I will present analytical and numerical results concerning several types of universal scaling regimes in wave turbulence. In stationary turbulence, these will be concerned with a revised theory of the famous KolmogorovZakharov (KZ) spectra, both the direct and the inverse cascades. In evolving wave turbulence, the universal scalings manifest themselves in selfsimilar asymptotics (referred to as "nonthermal fixed points" in some recent papers). The latter behaviour comes in three flavours: selfsimilarity of the first, second and third kinds respectively. The selfsimilarity of the first kind appears as a large time asymptotic of the spectrum propagating toward high frequencies. Its scaling is fully determined by energy conservation. The selfsimilarity of the second kind appears as a finite time blowup of the wavekinetic equation (WKE) at the zero frequency: it is related to a physical phenomenon of the BoseEinstein condensation. The scaling of this selfsimilarity is nontrivial: it cannot be found from conservation laws, and it is determined by solving a "nonlinear eigenvalue problem". The selfsimilarity of the third kind appears in the forceddissipated settings as a final stage of transition to the KZ spectrum and it takes the form of a frequencyspace wave reflected from the lowfrequency dissipative range. Its scaling is inherited from the previous (blowup) selfsimilar stage. I will present numerical results testing the analytical predictions arising from simulations of both the WKE and the 3D NLS equation. 
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