“…As it turns out, the phenomenon stems from the Euler equations and has omnipresence beyond geophysical flows. Sun (2008) derived the PIF model from the stratified-turbulence equations of Riley et al (1981) by taking the limit of vanishing vertical velocity under low Froude number. For a steady pseudo-plane flow u = [u(x, y, z), v(x, y, z), 0], the Euler equations under Boussinesq approximation also reduce to the PIF model…”