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Geometry and curvature of diffeomorphism groups with $H^1$ metric and mean hydrodynamics

Abstract:

Recently, Holm, Marsden, and Ratiu [1998] have derived a new model for the mean motion of an ideal fluid in Euclidean space given by the equation $\dot{V}(t) + \nabla_{U(t)} V(t) - \alpha^2 [\nabla U(t)]^t \cdot \triangle U(t) = -\text{grad} p(t)$ where $\text{div} U=0$, and $V = (1- \alpha^2 \triangle)U$. In this model, the momentum $V$ is transported by the velocity $U$, with the effect that nonlinear interaction between modes corresponding to length scales smaller than $\alpha$ is negligib...

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Publication date:
1998-07-15
URN:
uuid:72cc1b7a-6981-449a-bdd7-40320d524a28
Source identifiers:
407491
Local pid:
pubs:407491

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