The Experts below are selected from a list of 249 Experts worldwide ranked by ideXlab platform
Bruce Hobbs - One of the best experts on this subject based on the ideXlab platform.
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an experimental and theoretical study of the mixing characteristics of a periodically reoriented Irrotational Flow
Philosophical Transactions of the Royal Society A, 2010Co-Authors: Guy Metcalfe, Daniel R Lester, A Ord, Pandurang Kulkarni, Murray Rudman, Michael G Trefry, Bruce HobbsAbstract:The minimum-energy method to generate chaotic advection should be to use an Irrotational Flow. However, Irrotational Flows have no saddle connections to perturb in order to generate chaotic orbits. To the early work of Jones & Aref (Jones & Aref 1988 Phys. Fluids 31 , 469–485 (doi:10.1063/1.866828)) on potential Flow chaos, we add periodic reorientation to generate chaotic advection with Irrotational experimental Flows. Our experimental Irrotational Flow is a dipole potential Flow in a disc-shaped Hele-Shaw cell called the rotated potential mixing Flow; it leads to chaotic advection and transport in the disc. We derive an analytical map for the Flow. This is a partially open Flow, in which parts of the Flow remain in the cell forever, and parts of it pass through with residence-time and exit-time distributions that have self-similar features in the control parameter space of the stirring. The theory compares well with the experiment.
Adrian Constantin - One of the best experts on this subject based on the ideXlab platform.
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pressure beneath a solitary water wave mathematical theory and experiments
Archive for Rational Mechanics and Analysis, 2011Co-Authors: Adrian Constantin, Joachim Escher, Hungchu HsuAbstract:We study the pressure beneath a solitary water wave propagating in an Irrotational Flow at the free surface of water with a flat bed. The investigation is divided into two parts. The first part concerns a rigorous nonlinear study of the governing equations for water waves. We prove that the pressure in the fluid beneath a solitary wave strictly increases with depth and strictly decreases horizontally away from the vertical line beneath the crest. The second part of the paper describes an experimental study. Excellent agreement is found to exist between the theoretical predictions and the measurements. Our conclusions are also supported by numerical simulations.
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effect of non zero constant vorticity on the nonlinear resonances of capillary water waves
EPL, 2009Co-Authors: Adrian Constantin, Elena KartashovaAbstract:The influence of an underlying current on three-wave interactions of capillary water waves is studied. The fact that in Irrotational Flow resonant three-wave interactions are not possible can be invalidated by the presence of an underlying current of constant non-zero vorticity. We show that: 1) wave trains in Flows with constant non-zero vorticity are possible only for two-dimensional Flows, 2) only positive constant vorticities can trigger the appearance of three-wave resonances, 3) the number of positive constant vorticities which do trigger a resonance is countable and 4) the magnitude of a positive constant vorticity triggering a resonance cannot be too small.
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effect of non zero constant vorticity on the nonlinear resonances of capillary water waves
arXiv: Fluid Dynamics, 2009Co-Authors: Adrian Constantin, Elena KartashovaAbstract:The influence of an underlying current on 3-wave interactions of capillary water waves is studied. The fact that in Irrotational Flow resonant 3-wave interactions are not possible can be invalidated by the presence of an underlying current of constant non-zero vorticity. We show that: 1) wave trains in Flows with constant non-zero vorticity are possible only for two-dimensional Flows; 2) only positive constant vorticities can trigger the appearance of three-wave resonances; 3) the number of positive constant vorticities which do trigger a resonance is countable; 4) the magnitude of a positive constant vorticity triggering a resonance can not be too small.
Daniel D Joseph - One of the best experts on this subject based on the ideXlab platform.
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helmholtz decomposition coupling rotational to Irrotational Flow of a viscous fluid
Proceedings of the National Academy of Sciences of the United States of America, 2006Co-Authors: Daniel D JosephAbstract:In this work, I present the form of the Navier–Stokes equations implied by the Helmholtz decomposition in which the relation of the Irrotational and rotational velocity fields is made explicit. The idea of self-equilibration of Irrotational viscous stresses is introduced. The decomposition is constructed by first selecting the Irrotational Flow compatible with the Flow boundaries and other prescribed conditions. The rotational component of velocity is then the difference between the solution of the Navier–Stokes equations and the selected Irrotational Flow. To satisfy the boundary conditions, the Irrotational field is required, and it depends on the viscosity. Five unknown fields are determined by the decomposed form of the Navier–Stokes equations for an incompressible fluid: the rotational component of velocity, the pressure, and the harmonic potential. These five fields may be readily identified in analytic solutions available in the literature. It is clear from these exact solutions that potential Flow of a viscous fluid is required to satisfy prescribed conditions, like the no-slip condition at the boundary of a solid or continuity conditions across a two-fluid boundary. It can be said that equations governing the Helmholtz decomposition describe the modification of Irrotational Flow due to vorticity, but the analysis shows the two fields are coupled and cannot be completely determined independently.
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pressure corrections for the effects of viscosity on the Irrotational Flow outside prandtl s boundary layer
Journal of Fluid Mechanics, 2006Co-Authors: Jing Wang, Daniel D JosephAbstract:This work aims at understanding the viscous effects of the outer potential Flow on Prandtl's boundary layer. For a body moving with a constant velocity in an otherwise quiescent liquid, the non-zero viscous dissipation of the outer potential Flow gives rise to an additional drag, increasing the drag calculated from the boundary layer alone. The drag is considered in three cases here, on a two-dimensional circular gas bubble in a streaming Flow, at the edge of the boundary layer around a rapidly rotating cylinder in a uniform Flow, and on an airfoil in a streaming Flow. The drag may be computed using the dissipation method or the viscous pressure correction of the Irrotational pressure. Such a pressure correction can be induced by the discrepancy between the irrotatinal shear stress and the zero shear stress at a fluid-gas interface, or by the discrepancy between the shear stress evaluated from the boundary-layer solution and that evaluated from the outer potential Flow solution at the edge of the boundary layer.
Weicheng Zhan - One of the best experts on this subject based on the ideXlab platform.
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steady vortex patches near a nontrivial Irrotational Flow
Science China-mathematics, 2019Co-Authors: Daomin Cao, Guodong Wang, Weicheng ZhanAbstract:In this paper, we study the vortex patch problem in an ideal fluid in a planar bounded domain. By solving a certain minimization problem and studying the limiting behavior of the minimizer, we prove that for any harmonic function q corresponding to a nontrivial Irrotational Flow, there exists a family of steady vortex patches approaching the set of extremum points of q on the boundary of the domain. Furthermore, we show that each finite collection of strict extreme points of q corresponds to a family of steady multiple vortex patches approaching it.
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steady vortex patches near a nontrivial Irrotational Flow
Science China-mathematics, 2019Co-Authors: Daomin Cao, Guodong Wang, Weicheng ZhanAbstract:In this paper, we study the vortex patch problem in an ideal fluid in a planar bounded domain. By solving a certain minimization problem and studying the limiting behavior of the minimizer, we prove that for any harmonic function q corresponding to a nontrivial Irrotational Flow, there exists a family of steady vortex patches approaching the set of extreme points of q on the boundary of the domain. Furthermore, we show that each finite collection of strict extreme points of q corresponds to a family of steady multiple vortex patches approaching it.
C J Foot - One of the best experts on this subject based on the ideXlab platform.
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direct observation of Irrotational Flow and evidence of superfluidity in a rotating bose einstein condensate
Physical Review Letters, 2002Co-Authors: G Hechenblaikner, E Hodby, S A Hopkins, Onofrio M Marago, C J FootAbstract:We have observed the expansion of vortex-free, rotating Bose condensates after their sudden release from a slowly rotating anisotropic trap. Conservation of angular momentum, combined with the constraint of Irrotational Flow, cause the rotating condensate to expand in a distinctively different way to one released from a static (nonrotating) trap. This difference provides clear experimental evidence of the purely Irrotational velocity field associated with a superfluid. We observed this behavior in absorption images taken along the rotation axis.
