Imperial College London
Alternate

ProfessorDarrylHolm

Faculty of Natural Sciences, Department of Mathematics

Chair in Applied Mathematics
 
 
 
//

Contact

 

+44 (0)20 7594 8531d.holm Website

 
 
//

Location

 

6M27Huxley BuildingSouth Kensington Campus

//

Summary

 

Publications

Publication Type
Year
to

335 results found

Fringer OB, Holm DD, 2001, Integrable vs. nonintegrable geodesic soliton behavior, PHYSICA D, Vol: 150, Pages: 237-263, ISSN: 0167-2789

Journal article

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.

Conference paper

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.

Working paper

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

Conference paper

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

Conference paper

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

Book chapter

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

Conference paper

Bloch AM, Crouch PE, Holm DD, Marsden JEet 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

Conference paper

Alber MS, Camassa R, Fedorov YN, Holm DD, Marsden JEet al., 1999, On billiard solutions of nonlinear PDEs, PHYSICS LETTERS A, Vol: 264, Pages: 171-178, ISSN: 0375-9601

Journal article

Chen S, Foias C, Holm DD, Olson E, Titi ES, Wynne Set 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

Conference paper

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

Conference paper

Chen SY, Holm DD, Margolin LG, Zhang RYet 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

Conference paper

Chen S, Foias C, Holm DD, Olson E, Titi ES, Wynne Set 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

Conference paper

Cendra H, Holm DD, Marsden JE, Ratiu TSet 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.

Working paper

Duan JQ, Holm DD, Li KT, 1999, Variational methods and nonlinear quasigeostrophic waves, PHYSICS OF FLUIDS, Vol: 11, Pages: 875-879, ISSN: 1070-6631

Journal article

Holm DD, Kouranbaeva S, Marsden JE, Ratiu T, Shkoller Set 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}.

Working paper

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

Journal article

Chen S, Foias C, Holm DD, Olson E, Titi ES, Wynne Set 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

Journal article

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

Journal article

Cendra H, Holm DD, Hoyle MJW, Marsden JEet al., 1998, The Maxwell-Vlasov equations in Euler-Poincare form, JOURNAL OF MATHEMATICAL PHYSICS, Vol: 39, Pages: 3138-3157, ISSN: 0022-2488

Journal article

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

Journal article

Holm DD, Zeitlin V, 1998, Hamilton's principle for quasigeostrophic motion, PHYSICS OF FLUIDS, Vol: 10, Pages: 800-806, ISSN: 1070-6631

Journal article

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

Conference paper

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

Journal article

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

Journal article

Aceves A, Holm DD, Kovacic G, Timofeyev Iet al., 1997, Homoclinic orbits and chaos in a second-harmonic generating optical cavity, PHYSICS LETTERS A, Vol: 233, Pages: 203-208, ISSN: 0375-9601

Journal article

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

Journal article

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

Journal article

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

Conference paper

Holm DD, 1996, Hamiltonian balance equations, Publisher: ELSEVIER SCIENCE BV, Pages: 379-414, ISSN: 0167-2789

Conference paper

This data is extracted from the Web of Science and reproduced under a licence from Thomson Reuters. You may not copy or re-distribute this data in whole or in part without the written consent of the Science business of Thomson Reuters.

Request URL: http://wlsprd.imperial.ac.uk:80/respub/WEB-INF/jsp/search-html.jsp Request URI: /respub/WEB-INF/jsp/search-html.jsp Query String: limit=30&id=00385675&person=true&page=8&respub-action=search.html