245 citations · 388 across the 12 of their papers we have counts for
24 papers
Inertial Range Scaling, Karman-Howarth Theorem and Intermittency for Forced and Decaying Lagrangian Averaged MHD in 2D
J. Pietarila Graham, D. D. Holm, P. Mininni +1
We present an extension of the Karman-Howarth theorem to the Lagrangian averaged magnetohydrodynamic (LAMHD-alpha) equations. The scaling laws resulting as a corollary of this theo…
Elliptic instability in the Lagrangian-averaged Euler-Boussinesq-alpha equations
Bruce R. Fabijonas, Darryl D. Holm
We examine the effects of turbulence on elliptic instability of rotating stratified incompressible flows, in the context of the Lagragian-averaged Euler-Boussinesq-alpha, or \laeba…
Hasimoto Transformation and Vortex Soliton Motion Driven by Fluid Helicity
Darryl D. Holm, Samuel N. Stechmann
Vorticity filament motions with respect to the Dirac bracket of Rasetti and Regge [1975] are known to be related to the nonlinear Schrödinger equation by the Hasimoto transformatio…
Euler-Poincare formulation and elliptic instability for nth-gradient fluids
Bruce R. Fabijonas, Darryl D. Holm
The energy of an gradient fluid depends on its Eulerian velocity gradients of order . A variational principle is introduced for the dynamics of gradient fluids…
Reduced Singular Solutions of EPDiff Equations on Manifolds with Symmetry
Darryl D. Holm, Jonathan Munn, Samuel N. Stechmann
The EPDiff equation governs geodesic flow on the diffeomorphisms with respect to a chosen metric, which is typically a Sobolev norm on the tangent space of vector fields. EPDiff ad…
Momentum Maps and Measure-valued Solutions (Peakons, Filaments and Sheets) for the EPDiff Equation
Darryl D. Holm, Jerrold E. Marsden
We study the dynamics of measure-valued solutions of what we call the EPDiff equations, standing for the {\it Euler-Poincaré equations associated with the diffeomorphism group (of…