Publications
335 results found
Fringer OB, Holm DD, 2001, Integrable vs. nonintegrable geodesic soliton behavior, PHYSICA D, Vol: 150, Pages: 237-263, ISSN: 0167-2789
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- Citations: 26
Holm DD, 2001, Renormalized HVBK dynamics for Superfluid Helium Turbulence
We review the Hall-Vinen-Bekarevich-Khalatnikov (HVBK) equations forsuperfluid Helium turbulence and discuss their implications for recentmeasurements of superfluid turbulence decay. A new Hamiltonian formulation of these equations renormalizes the vortex linevelocity to incorporate finite temperature effects. These effects alsorenormalize the coupling constant in the mutual friction force between thesuperfluid and normal fluid components by a factor of rho_s / \rho (thesuperfluid mass fraction) but they leave the vortex line tension unaffected.Thus, the original HVBK form is recovered at zero temperature and its mutualfriction coefficients are renormalized at nonzero temperature. The HVBKequations keep their form and no new parameters are added. However, atemperature dependent trade-off does arise between the mutual friction couplingand the vortex line tension. The renormalized HVBK equations obtained via this new Hamiltonian approachimply a dynamical equation for the space-integrated vortex tangle length, whichis the quantity measured by second sound attenuation experiments in superfluidturbulence. A Taylor-Proudman theorem also emerges for the superfluid vorticesthat shows the steady vortex line velocity becomes columnar under rapidrotation.
Domaradzki JA, Holm DD, 2001, Navier-stokes-alpha model: LES equations with nonlinear dispersion, Publisher: arXiv
We present a framework for discussing LES equations with nonlineardispersion. In this framework, we discuss the properties of the nonlinearlydispersive Navier-Stokes-alpha model of incompressible fluid turbulence ---also called the viscous Camassa-Holm equations and the LANS equations in theliterature --- in comparison with the corresponding properties of large eddysimulation (LES) equations obtained via the approximate-inverse approach. In this comparison, we identify the spatially filtered NS-alpha equationswith a class of generalized LES similarity models. Applying a certainapproximate inverse to this class of LES models restores the Kelvin circulationtheorem for the defiltered velocity and shows that the NS-alpha model describesthe dynamics of the defiltered velocity for this class of generalized LESsimilarity models. We also show that the subgrid scale forces in the NS-alphamodel transform covariantly under Galilean transformations and under a changeto a uniformly rotating reference frame. Finally, we discuss in the spectralformulation how the NS-alpha model retains the local interactions among thelarge scales, retains the nonlocal sweeping effects of large scales on smallscales, yet attenuates the local interactions of the small scales amongstthemselves.
Holm DD, 2001, Introduction to HVBK dynamics, Conference on Quantized Vortex Dynamics and Superfluid Turbulence, Publisher: SPRINGER-VERLAG BERLIN, Pages: 114-130, ISSN: 0075-8450
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- Citations: 17
Holm DD, 2001, Variational principles, geometry and topology of Lagrangian-Averaged fluid dynamics, London, Geometry and topology of fluid flows; an introduction to the geometry and topology of fluid flows, Cambridge, September 2000, Publisher: Kluwer Academic, Pages: 271-292
Holm DD, 2001, Introduction to HVBK dynamics, Quantized vortex dynamics and superfluid turbulence, Editors: Barenghi, Donnelly, Vinen, Berlin, Publisher: Springer, Pages: 114-130, ISBN: 9783540422266
Holm DD, 2001, Variational principles, geometry and topology of Lagrangian-averaged fluid dynamics, Pedagogical Workshop on Geometry and Topology of Fluid Flows, Publisher: SPRINGER, Pages: 271-291, ISSN: 1568-2609
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- Citations: 4
Bloch AM, Crouch PE, Holm DD, et al., 2000, An optimal control formulation for inviscid incompressible ideal fluid flow, 39th IEEE Conference on Decision and Control, Publisher: IEEE, Pages: 1273-1278, ISSN: 0743-1546
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- Citations: 13
Alber MS, Camassa R, Fedorov YN, et al., 1999, On billiard solutions of nonlinear PDEs, PHYSICS LETTERS A, Vol: 264, Pages: 171-178, ISSN: 0375-9601
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- Citations: 31
Chen S, Foias C, Holm DD, et al., 1999, The Camassa-Holm equations and turbulence, 18th Annual International Conference of the Center-for-Nonlinear-Studies, Publisher: ELSEVIER SCIENCE BV, Pages: 49-65, ISSN: 0167-2789
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- Citations: 175
Holm DD, 1999, Fluctuation effects on 3D Lagrangian mean and Eulerian mean fluid motion, 18th Annual International Conference of the Center-for-Nonlinear-Studies, Publisher: ELSEVIER SCIENCE BV, Pages: 215-269, ISSN: 0167-2789
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- Citations: 117
Chen SY, Holm DD, Margolin LG, et al., 1999, Direct numerical simulations of the Navier-Stokes alpha model, 18th Annual International Conference of the Center-for-Nonlinear-Studies, Publisher: ELSEVIER, Pages: 66-83, ISSN: 0167-2789
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- Citations: 150
Chen S, Foias C, Holm DD, et al., 1999, A connection between the Camassa-Holm equations and turbulent flows in channels and pipes, International Conference on Turbulence, Publisher: AMER INST PHYSICS, Pages: 2343-2353, ISSN: 1070-6631
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- Citations: 206
Cendra H, Holm DD, Marsden JE, et al., 1999, Lagrangian reduction, the Euler--Poincaré Equations, and semidirect products, Publisher: ArXiv
There is a well developed and useful theory of Hamiltonian reduction forsemidirect products, which applies to examples such as the heavy top,compressible fluids and MHD, which are governed by Lie-Poisson type equations.In this paper we study the Lagrangian analogue of this process and link it withthe general theory of Lagrangian reduction; that is the reduction ofvariational principles. These reduced variational principles are interesting intheir own right since they involve constraints on the allowed variations,analogous to what one finds in the theory of nonholonomic systems with theLagrange d'Alembert principle. In addition, the abstract theorems aboutcirculation, what we call the Kelvin-Noether theorem, are given.
Duan JQ, Holm DD, Li KT, 1999, Variational methods and nonlinear quasigeostrophic waves, PHYSICS OF FLUIDS, Vol: 11, Pages: 875-879, ISSN: 1070-6631
Holm DD, Kouranbaeva S, Marsden JE, et al., 1999, A nonlinear analysis of the averaged euler equations
This paper develops the geometry and analysis of the averaged Euler equationsfor ideal incompressible flow in domains in Euclidean space and on Riemannianmanifolds, possibly with boundary. The averaged Euler equations involve aparameter $\alpha$; one interpretation is that they are obtained by ensembleaveraging the Euler equations in Lagrangian representation over rapidfluctuations whose amplitudes are of order $\alpha$. The particle flowsassociated with these equations are shown to be geodesics on a suitable groupof volume preserving diffeomorphisms, just as with the Euler equationsthemselves (according to Arnold's theorem), but with respect to a rightinvariant $H^1$ metric instead of the $L^2$ metric. The equations are alsoequivalent to those for a certain second grade fluid. Additional properties ofthe Euler equations, such as smoothness of the geodesic spray (the Ebin-Marsdentheorem) are also shown to hold. Using this nonlinear analysis framework, thelimit of zero viscosity for the corresponding viscous equations is shown to bea regular limit, {\it even in the presence of boundaries}.
Holm DD, 1999, Alpha models for 3D Eulerian mean fluid circulation, NUOVO CIMENTO DELLA SOCIETA ITALIANA DI FISICA C-GEOPHYSICS AND SPACE PHYSICS, Vol: 22, Pages: 857-866, ISSN: 0390-5551
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- Citations: 1
Chen S, Foias C, Holm DD, et al., 1998, Camassa-Holm equations as a closure model for turbulent channel and pipe flow, PHYSICAL REVIEW LETTERS, Vol: 81, Pages: 5338-5341, ISSN: 0031-9007
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- Citations: 265
Holm DD, Marsden JE, Ratiu TS, 1998, The Euler-Poincare equations and semidirect products with applications to continuum theories, ADVANCES IN MATHEMATICS, Vol: 137, Pages: 1-81, ISSN: 0001-8708
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- Citations: 647
Cendra H, Holm DD, Hoyle MJW, et al., 1998, The Maxwell-Vlasov equations in Euler-Poincare form, JOURNAL OF MATHEMATICAL PHYSICS, Vol: 39, Pages: 3138-3157, ISSN: 0022-2488
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- Citations: 59
Holm DD, Marsden JE, Ratiu TS, 1998, Euler-Poincare models of ideal fluids with nonlinear dispersion, PHYSICAL REVIEW LETTERS, Vol: 80, Pages: 4173-4176, ISSN: 0031-9007
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- Citations: 231
Holm DD, Zeitlin V, 1998, Hamilton's principle for quasigeostrophic motion, PHYSICS OF FLUIDS, Vol: 10, Pages: 800-806, ISSN: 1070-6631
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- Citations: 26
Duan JQ, Holm DD, 1998, Essential manifold reduction and nonlinear quasi-geostrophic waves, 3rd International Conference on Nonlinear Mechanics, Publisher: SHANGHAI UNIV, Pages: 622-625
Camassa R, Holm DD, Levermore CD, 1997, Long-time shallow-water equations with a varying bottom, JOURNAL OF FLUID MECHANICS, Vol: 349, Pages: 173-189, ISSN: 0022-1120
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- Citations: 32
Allen JS, Gent PR, Holm DD, 1997, On Kelvin waves in balance models, JOURNAL OF PHYSICAL OCEANOGRAPHY, Vol: 27, Pages: 2060-2063, ISSN: 0022-3670
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- Citations: 2
Aceves A, Holm DD, Kovacic G, et al., 1997, Homoclinic orbits and chaos in a second-harmonic generating optical cavity, PHYSICS LETTERS A, Vol: 233, Pages: 203-208, ISSN: 0375-9601
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- Citations: 2
Gabitov I, Holm DD, Luce BP, 1997, Low-noise picosecond soliton transmission by use of concatenated nonlinear amplifying loop mirrors, JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS, Vol: 14, Pages: 1850-1855, ISSN: 0740-3224
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- Citations: 12
Fabijonas B, Holm DD, Lifschitz A, 1997, Secondary instabilities of flows with elliptic streamlines, PHYSICAL REVIEW LETTERS, Vol: 78, Pages: 1900-1903, ISSN: 0031-9007
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- Citations: 14
Gjaja I, Holm DD, 1996, Self-consistent Hamiltonian dynamics of wave mean-flow interaction for a rotating stratified incompressible fluid, 15th Annual International Conference of the Center-for-Nonlinear-Studies on Nonlinear Phenomena in Ocean Dynamics, Publisher: ELSEVIER SCIENCE BV, Pages: 343-378, ISSN: 0167-2789
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- Citations: 39
Holm DD, 1996, Hamiltonian balance equations, Publisher: ELSEVIER SCIENCE BV, Pages: 379-414, ISSN: 0167-2789
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- Citations: 23
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