Stratified and rotating turbulence and mixing

5 problems

• Is the oceanic internal-wave spectrum a wave-turbulence steady state?

  Partially resolved

  The ocean interior is filled with internal waves, waves that travel inside a fluid layered by density, whose energy follows nearly the same frequency spectrum everywhere. Whether this universal shape is a steady state of wave-wave interactions moving energy to small scales is open, although the energy flow these interactions predict now matches observed ocean mixing.

• What sets the thickness of spontaneous layers in stirred stratified fluid?

  Open

  Stirring a fluid whose density increases smoothly with depth can produce a staircase of uniform layers separated by sharp steps. What sets the height of the steps and how they evolve is not understood.

• Is the flux coefficient of stratified turbulence a universal constant?

  Contested

  When turbulence stirs water layered by temperature or salt, part of its energy lifts heavy fluid and mixes the layers and the rest turns into heat. Ocean models assume that a fixed fraction (about one sixth) goes into mixing, but measurements scatter widely.

• Is the Rayleigh-Taylor mixing growth constant universal?

  Contested

  When heavy fluid rests on light fluid under gravity, the interface overturns and a turbulent mixing zone grows with the square of time. Simulations give a growth rate about half of what experiments measure, and whether a single universal value exists is unknown.

• Critical Rossby number for the inverse cascade in rotating turbulence

  Partially resolved

  Rapid rotation makes turbulence nearly two-dimensional and can reverse the direction of energy flow, sending energy to large scales. The rotation rate at which this switch happens, and whether it is sharp like a phase transition, are unsettled.