# Analysis Seminar

#### How similar are quantum and classical turbulence? Some answers from the velocity circulation

**Speaker:**
Giorgio Krstulovic, Université Côte d'Azur, Observatoire de la Côte d'Azur

**Location:**
Warren Weaver Hall 1302

**Date:**
Thursday, May 25, 2023, 11 a.m.

**Synopsis:**

The velocity circulation, the line integral of the velocity field along a closed path, is a fundamental observable in classical and quantum flows. It provides a measure of fluid rotation within a closed path. It is a Lagrangian invariant in inviscid classical fluids described by the incompressible Euler equations. In quantum fluids, which can be described by the defocusing nonlinear Schrodinger equation, circulation is quantized, taking discrete values related to the number and the orientation of thin vortex filaments enclosed by the path. By varying the size of such closed loops, the circulation provides a measure of the dependence of the flow structure at the considered scale. In turbulent flows, by varying the scale of the loops, one might expect the emergence of power laws reflecting the complexity of turbulence.

In this talk, I will present some results on the circulation statistics in classical and quantum turbulent fluids, described by the 3D Navier-Stokes and 3D defocusing nonlinear Schrodinger equation (NLS), respectively. We produce high-resolution numerical simulations of these two models and compare the circulation statistics. We show that statistics of velocity circulation in the NLS equation exhibit the same behavior that the one previously observed in classical fluids using the incompressible Navier-Stokes equations [Iyer et al. Phys. Rev. X 9, 041006 (2019).]. This finding includes the emergence of the power-law scalings predicted from Kolmogorov's 1941 theory of turbulence and intermittency deviations for high-order moments. These results strongly reinforce the resemblance between classical and quantum turbulence. It highlights the universality of the inertial range dynamics, including intermittency, across these two a priori very different systems (incompressible Navier-Stokes equations and NLS).