Open+Questions

= = LIST OF OPEN QUESTIONS 2011 Everyone is invited to edit and add! This includes also researchers not here at KITP! Each person that is interested in the topics should add his or her name in the link provided!


 * pictures of meetings are [|here]**



**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.

D efinitions - 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}