Research

Self-organization of turbulent flows

Turbulence is usually viewed as the breaking up of a large scale flow into ever smaller chaotic motions. A quantitative manifestation of this picture is the energy cascade, with energy flowing from large scales to increasingly smaller ones, where it is eventually dissipated by viscosity.
On the contrary, when most of the energy is concetrated in 2d modes, energy is transferred to progressively larger scales–in an inverse cascade. This process can then terminate in the self-organization of the turbulence into a large scale mean flow, a so-called condensate, on top of small scale fluctuations.

Although such 2d turbulence may seem like an abstract concept, many natural flows are effectively restricted to two dimensions: planetary-scale flows in the ocean and atmosphere are an example, and they are often made up of coherent currents or vortices in combination with chaotic fluctuations.

Our work is centered around the following questions: What are the rules of self-organization for the condensate? Which of its features are universal? What happens when the range of fluid-element interactions is below the energy injection scale? Recently, we have also started to explore condensates that have both 2d-like and 3d-like interactions.

Subcritical transition to turbulence

Fluid flow generically becomes turbulent when the Reynolds number, which is the relevant control parameter, is sufficiently increased. In flows where the base state is linearly stable, termed subcritical flows, this transition occurs directly to a turbulent state, with turbulence appearing intermittently in space and time. With increasing Reynolds number, the system transitions between several different phases until finally reaching the homogeneous turbulent state.

Building on recent progress in the field, our work aims to understand the different possible phases and under which conditions they occur; the role of fluctuations and the mechanisms leading to transitions between phases and the generallity of the subcritical transition scenario.

Universality in the breakup of a fluid bridge

The breakup of a fluid object is a singular and dramatic process. We explore how a cylindrical soap film bridge breaks when stretched, and find that it always forms one large central satellite bubble. We show that the size of this bubble is extremely reproducible, and grows with the stretching rate and with the initial bridge aspect ratio. We trace the robustness of the size to an underlying universal dynamical solution.

Lagrangian time irreversibility of turbulence

Turbulence is an out-of-equilibrium phenomena as evidenced by the flux of energy through scales. But how could you see that irreversibility if you are only watching particles in the flow? What is the manifestation of the energy flux, which is a property of the velocity field, for particles? What changes if the flow is compressible?

Lagrangian conservation laws

Conservation laws and symmetries play a central role in physics. Relatively recently, it was discovered that Lagrangian statistical conservation laws, related to the dynamics of particles, play a crucial role in the field theoretic description of turbulence. Their influence was demonstrated for the statistics of a field advected by the flow, and their form could be computed in simplified models for the velocity field. It remains unclear how to obtain such laws for a real turbulent velocity field, and what their influence could be on the field’s statistics. We have made some attempts in that direction.