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Turbulence and coherent flows

  • Can one derive exact flux relations for strong wave turbulence?
  • How turbulence interacts with a coherent flow? 2d turbulence suggests a simple picture: inverse turbulence cascade feeds the coherent flow, which suppresses the turbulence. In quantum turbulence, is the interaction of condensate and turbulence similar?
  • Can one analytically describe turbulence at infinite space dimensionality, starting from Burgers-like zeroth order?
  • Can one describe turbulence in fluid layers as being intermediate between 2d and 3d? Does inverse cascade exists for however thick layer (see the recent work)?
  • How to measure and interpret turbulent properties of Accretion Disks, e.g. a shallow, rotating, shearing 3D system with strong density gradients and subsonic (partly geostrophic) flows.

Boundary Layers

  • Similarity and differences b/w channel and turbulent boundary layer: effect of symmetry
  • Power-law and log-law: anisotropy, finite size, shear
  • Rescaling in turbulence and critical phenomena
  • Can one actually derive exact relations on the turbulence moments in BL (like 4/5-law)?
  • High Re wall flows: can the velocity/vorticity field close to the wall be really viewed as turbulent?

Rayleigh-Benard Convection

  • Scaling of Nu with Ra and Pr in the large Ra regime: ultimate regime
  • Nature of large scale structures
  • Effect of the finite size of a container
  • Phase transition b/w turbulent states
  • What can we learn from R-B convection for the subcritical Baroclinic Instability under rotation and shear?
  • Are there different (coexisting) states of thermal convection?

Tracers and Particles

  • St-Ku phase diagram
  • Singularities in Jacobian of the flow
  • Inertial particles
  • Non-spherical particles
  • Large particles: connection to boundary layers
  • Mean free path and particle size
  • Lines in turbulence
  • Lagrangian dynamics of the velocity gradients
  • Collision velocities of ballistic particles St > 1
  • Turbulent concentration for particles St > 1

Mixing, Reactive and Passive-Reactive flows

  • Compressible reactive flows
  • Fluctuations in passive advection
  • Coarse-graining

Quantum turbulence

  • A cascade from interactive vortices (where does the small scale kinetic energy go?)
  • Lack of evidence for cascades of waves in turbulence
  • Relation to Euler equation
  • Vortex tangle, vortex dynamics, vortex motion
  • How to solve Hall-Vinen equation?
  • Finite temperature effects

Turbulence in Field Theory

  • Relation of strong turbulence and Kolmogorov scaling.
  • (Quantum) turbulence as a non-equilibrium critical phenomenon.
  • Dynamics of the approach of the quantum critical point and critical slowing down.
  • Relation of this dynamics and the propagation of vortices and vortex lines in a superfluid.
  • Vortices (or other topological defects) in general O(N) field theories.
  • Measure the cascade in a simulation.

Reduced Models

  • Can one construct a numerical dynamic subgrid model based on detailed triad interactions?
  • What role does inviscid statistical equipartition play in forced-dissipative turbulence?
  • What can we learn about intermittency and dissipation from shell models?
  • Can one generalize K41 to handle anisotropy, finite Reynolds number, and bounded domains?
  • Same question about particle densities when, moreover, they have inertia and change phase? (think clouds)
  • What can we learn from statistical closures and the fluctuation-dissipation theorem?
  • In 2D, do global integrals of arbitrary C^1 functions of the vorticity field play a role in the turbulent cascade?
  • What can we learn from perturbative and non-perturbative renormalization group methods?

Lagrangian, Eulerian statistics

  • How can Lagrangian statisitcs filter out part of the physics seen instead by Eulerian statistics? For instance, spots of high intermittency.

Definitions - for discussion
  • Turbulence: a spatially extended field with a large, continuous range of aperiodic spatial and temporal non-equilibrium dynamics
  • Turbulence is a state of a system with many degrees of freedom deviated far from thermal equilibrium, see review
  • Quantum Turbulence: a turbulent complex field or interacting set of complex fields
  • Newtonian fluid turbulence: Turbulence in a classical, Newtonian viscous fluid
  • Kolmogorov turbulence: Turbulence exhibiting spatial power spectra with E(k) = k^{-5/3}