• Mathematics
  • Published 2005

Kähler Geometry and the Navier-Stokes Equations

@inproceedings{Roulstone2005KhlerGA,
  title={K{\"a}hler Geometry and the Navier-Stokes Equations},
  author={Ian Roulstone and Bertrand Banos and John D. Gibbon and Vladimir Roubtsov},
  year={2005}
}
We study the Navier-Stokes and Euler equations of incompressible hydrodynamics in two and three spatial dimensions and show how the constraint of incompressiblility leads to equations of Monge--Amp\ere type for the stream function, when the Laplacian of the pressure is known. In two dimensions a K\\ahler geometry is described, which is associated with the Monge--Amp\ere problem. This K\\ahler structure is then generalised to `two-and-a-half dimensional\' flows, of which Burgers\' vortex is one… CONTINUE READING
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SHOWING 1-10 OF 25 REFERENCES

Are there higheraccuracy analogues of semigeostrophic theory ?

M. E. McIntyre, I. Roulstone
  • Large - scale atmosphere — ocean dynamics , Vol . II : Geometric methods and models
  • 2002
VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL

Holomorphic structures in hydrodynamical models of nearly geostrophic flow

  • Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 2001
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

Evidence for a singularity of the three-dimensional incompressible Euler equations

R M.
  • formulation and solutions. J. Atmos. Sci.,
  • 1993
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

Local classifications of Monge – Ampère equations

V. V. Lychagin, V. N. Roubtsov
  • Dokl . Bielor . Acad . Sci .
  • 1983
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

Vorticity and scaling of collapsing Euler vortices

R. M. Kerr
  • Phys . Fluids
  • 2005
VIEW 1 EXCERPT