245 citations · 388 across the 12 of their papers we have counts for
6 papers · 1 filter
Variational Principles of Lagrangian Averaged Fluid Dynamics
Darryl D. Holm
The Lagrangian average (LA) of the ideal fluid equations preserves their fundamental transport structure. This transport structure is responsible for the Kelvin circulation theorem…
An Optimal Control Formulation for Inviscid Incompressible Ideal Fluid Flow
A. M. Bloch, P. E. Crouch, D. D. Holm +1
In this paper we consider the Hamiltonian formulation of the equations of incompressible ideal fluid flow from the point of view of optimal control theory. The equations are compar…
Euler-Poincaré Dynamics of Perfect Complex Fluids
Darryl D. Holm
Lagrangian reduction by stages is used to derive the Euler-Poincaré equations for the nondissipative coupled motion and micromotion of complex fluids. We mainly treat perfect compl…
Renormalized HVBK dynamics for Superfluid Helium Turbulence
Darryl D. Holm
We review the Hall-Vinen-Bekarevich-Khalatnikov (HVBK) equations for superfluid Helium turbulence and discuss their implications for recent measurements of superfluid turbulence de…
The Three Dimensional Viscous Camassa-Holm Equations, and Their Relation to the Navier-Stokes Equations and Turbulence Theory
C. Foias, D. D. Holm, E. S. Titi
We show here the global, in time, regularity of the three dimensional viscous Camassa-Holm (Lagrangian Averaged Navier-Stokes-alpha) equations. We also provide estimates, in terms…
Navier-Stokes-alpha model: LES equations with nonlinear dispersion
J. A. Domaradzki, Darryl D. Holm
We present a framework for discussing LES equations with nonlinear dispersion. In this framework, we discuss the properties of the nonlinearly dispersive Navier-Stokes-alpha model…