Self-similarity of strongly stratified inviscid flows

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Stratified turbulence dominated by vortical motion (2004, methodology): “Billant & Chomaz (2001) showed that in the limit of strong stratification, the inviscid Boussinesq equations are selfsimilar with respect to the variable zN/U, suggesting a characteristic vertical length scale of U/N ,w hereU is a horizontal velocity scale and z is the vertical coordinate.”
The energy cascade in a strongly stratified fluid (2006, methodology): “They also present evidence that the layer thickness scales as lv ∼ u/N , confirming the scaling suggested by Billant & Chomaz (2001).”
Stratified Turbulence: A Possible Interpretation of Some Geophysical Turbulence Measurements (2007, background): “…shear will develop in the layers and become so strong that the local Froude number based upon this vertical scale, F (cid:6) (cid:2) u / N (cid:1) (cid:6) , will become of order 1, and hence the local Richardson number Ri will also become order 1, as pointed out by Billant and Chomaz (2001).”
Scaling analysis and simulation of strongly stratified turbulent flows (2007, methodology): “Another consequence of this scaling is that the potential energy is of the same order as the kinetic energy ( Billant & Chomaz 2001 ).”