What sets the thickness of spontaneous layers in stirred stratified fluid?
In plain words
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.
Precise statement
Stirring a linearly stratified fluid can produce a staircase of well-mixed layers separated by thin interfaces, through the Phillips (1972) mechanism in which the buoyancy flux decreases with increasing local gradient over some range. Predict the layer thickness $h$ as a function of $\mathrm{Re}_{b}$, horizontal Froude number and Pr, and the rate of layer merging at long times.
What would settle it
A theory predicting h and merger rates verified by forced stratified DNS and tank experiments over a decade of stirring strength.
Status in the literature
Unverified note
2025 simulations track layer and interface evolution over long times (arXiv:2512.08714); no theory predicts h.