My understanding so far: given a small flow moving forward within a larger stationary body of water, the water ahead would pile up, creating hydrostatic pressure in all 2d directions (and thus acceleration), including to the sides. Wouldn't this side acceleration result in rotation, i.e. eddies or 2d vorticity?

But in my simulation code, no vorticity arises. (Of course, my code might be buggy.)

My understanding of the Shallow Water Equations and algorithm come from chapter 12 "Shallow Water" in Bridson's Fluid Simulation for Computer Graphics (whole chapter is available in the free preview)

Ideally, I'd like both a physical intuition and a mathematical understanding of this.

  • $\begingroup$ If I recall, the fluid motion we call vorticity requires a 3 dimensional framework $\endgroup$ – docscience Apr 28 '17 at 13:14
  • $\begingroup$ Perhaps because of vector cross products, Coriolis acceleration $\endgroup$ – docscience Apr 28 '17 at 13:15
  • $\begingroup$ @docscience Yes, I think maybe "proper" vorticity is 3d only, but 2d vortices are produced by 2d Navier Stokes equation simulations (e.g. those swirling 2d smoke toys, or try wong's online webgl fluid simulation). To make them 3d, the 2d vortices can be thought of as having an axis along the 3rd dimension. $\endgroup$ – hyperpallium Apr 28 '17 at 14:14
  • $\begingroup$ I would tend to call the 2D rotation an 'eddy'. $\endgroup$ – docscience Apr 28 '17 at 17:14
  • $\begingroup$ @docscience I agree, i actually almost wrote "eddies", I'll edit - title reads more cleanly now. Thanks. $\endgroup$ – hyperpallium Apr 29 '17 at 2:12

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