DOI

1

Instability in electromagnetically driven flows. II - Imazio, Paola Rodriguez and Gissinger, Christophe

PHYSICS OF FLUIDS 28, (2016)

Abstract : In a previous paper, we have reported numerical simulations of the magnetohydrodynamic flow driven by a travelling magnetic field in an annular channel, at low Reynolds number. It was shown that the stalling of such induction pump is strongly related to magnetic flux expulsion. In the present article, we show that for larger hydrodynamic Reynolds number, and with more realistic boundary conditions, this instability takes the form of a large axisymmetric vortex flow in the (r, z)-plane, in which the fluid is locally pumped in the direction opposite to the one of the magnetic field. Close to the marginal stability of this vortex flow, a low-frequency pulsation is generated. Finally, these results are compared to theoretical predictions and are discussed within the framework of experimental annular linear induction electromagnetic pumps. (C) 2016 AIP Publishing LLC.

PHYSICS OF FLUIDS 28, (2016)

Abstract : In a previous paper, we have reported numerical simulations of the magnetohydrodynamic flow driven by a travelling magnetic field in an annular channel, at low Reynolds number. It was shown that the stalling of such induction pump is strongly related to magnetic flux expulsion. In the present article, we show that for larger hydrodynamic Reynolds number, and with more realistic boundary conditions, this instability takes the form of a large axisymmetric vortex flow in the (r, z)-plane, in which the fluid is locally pumped in the direction opposite to the one of the magnetic field. Close to the marginal stability of this vortex flow, a low-frequency pulsation is generated. Finally, these results are compared to theoretical predictions and are discussed within the framework of experimental annular linear induction electromagnetic pumps. (C) 2016 AIP Publishing LLC.

DOI

2

Instability in electromagnetically driven flows. I - Gissinger, Christophe and Imazio, Paola Rodriguez and Fauve, Stephan

PHYSICS OF FLUIDS 28, (2016)

Abstract : The magnetohydrodynamic flow driven by a travelling magnetic field in an annular channel is investigated numerically. For sufficiently large magnetic Reynolds number Rm, or if a large enough pressure gradient is externally applied, the system undergoes an instability in which the flow rate in the channel dramatically drops from synchronism with the wave to much smaller velocities. This transition takes the form of a saddle-node bifurcation for the time-averaged quantities. In this first paper, we characterize the bifurcation and study the stability of the flow as a function of several parameters. We show that the bifurcation of the flow involves a bistability between Poiseuille-like and Hartman-like regimes and relies on magnetic flux expulsion. Based on this observation, new predictions are made for the occurrence of this stalling instability. (C) 2016 AIP Publishing LLC.

PHYSICS OF FLUIDS 28, (2016)

Abstract : The magnetohydrodynamic flow driven by a travelling magnetic field in an annular channel is investigated numerically. For sufficiently large magnetic Reynolds number Rm, or if a large enough pressure gradient is externally applied, the system undergoes an instability in which the flow rate in the channel dramatically drops from synchronism with the wave to much smaller velocities. This transition takes the form of a saddle-node bifurcation for the time-averaged quantities. In this first paper, we characterize the bifurcation and study the stability of the flow as a function of several parameters. We show that the bifurcation of the flow involves a bistability between Poiseuille-like and Hartman-like regimes and relies on magnetic flux expulsion. Based on this observation, new predictions are made for the occurrence of this stalling instability. (C) 2016 AIP Publishing LLC.

DOI

3

Generation of a mean flow by an internal wave - Semin, B. and Facchini, G. and Petrelis, F. and Fauve, S.

PHYSICS OF FLUIDS 28, (2016)

Abstract : We experimentally study the generation of a mean flow by a two-dimensional progressive internal gravity wave. Due to the viscous damping of the wave, a non-vanishing Reynolds stress gradient forces a mean flow. When the forcing amplitude is low, the wave amplitude is proportional to the forcing and the mean flow is quadratic in the forcing. When the forcing amplitude is large, the mean flow decreases the wave amplitude. This feedback saturates both the wave and the mean flow. The profiles of the mean flow and the wave are compared with a one-dimensional analytical model. Decreasing the forcing frequency leads to a wave and a mean flow localized on a smaller height, in agreement with the model. Published by AIP Publishing.

PHYSICS OF FLUIDS 28, (2016)

Abstract : We experimentally study the generation of a mean flow by a two-dimensional progressive internal gravity wave. Due to the viscous damping of the wave, a non-vanishing Reynolds stress gradient forces a mean flow. When the forcing amplitude is low, the wave amplitude is proportional to the forcing and the mean flow is quadratic in the forcing. When the forcing amplitude is large, the mean flow decreases the wave amplitude. This feedback saturates both the wave and the mean flow. The profiles of the mean flow and the wave are compared with a one-dimensional analytical model. Decreasing the forcing frequency leads to a wave and a mean flow localized on a smaller height, in agreement with the model. Published by AIP Publishing.

DOI

4

Self-organisation and non-linear dynamics in driven magnetohydrodynamic turbulent flows - Dallas, V. and Alexakis, A.

PHYSICS OF FLUIDS 27, (2015)

Abstract : Magnetohydrodynamic (MHD) turbulent flows driven by random, large-scale, mechanical and electromagnetic external forces of zero helicities are investigated by means of direct numerical simulations. It is shown that despite the absence of helicities in the forcing, the system is attracted to helical states of large scale condensates that exhibit laminar behaviour despite the large value of the Reynolds numbers examined. We demonstrate that the correlation time of the external forces controls the time spent on these states, i.e., for short correlation times, the system remains in the turbulent state while as the correlation time is increased, the system spends more and more time in the helical states. As a result, time averaged statistics are significantly affected by the time spent on these states. These results have important implications for MHD and turbulence theory and they provide insight into various physical phenomena where condensates transpire. (C) 2015 AIP Publishing LLC.

PHYSICS OF FLUIDS 27, (2015)

Abstract : Magnetohydrodynamic (MHD) turbulent flows driven by random, large-scale, mechanical and electromagnetic external forces of zero helicities are investigated by means of direct numerical simulations. It is shown that despite the absence of helicities in the forcing, the system is attracted to helical states of large scale condensates that exhibit laminar behaviour despite the large value of the Reynolds numbers examined. We demonstrate that the correlation time of the external forces controls the time spent on these states, i.e., for short correlation times, the system remains in the turbulent state while as the correlation time is increased, the system spends more and more time in the helical states. As a result, time averaged statistics are significantly affected by the time spent on these states. These results have important implications for MHD and turbulence theory and they provide insight into various physical phenomena where condensates transpire. (C) 2015 AIP Publishing LLC.

DOI

5

Faraday instability in floating drops - Pucci, G. and Ben Amar, M. and Couder, Y.

PHYSICS OF FLUIDS 27, (2015)

PHYSICS OF FLUIDS 27, (2015)

DOI

6

The Taylor-vortex dynamo - Gissinger, Christophe

PHYSICS OF FLUIDS 26, (2014)

Abstract : The generation of a magnetic field by dynamo action in a Taylor-vortex flow is investigated numerically. We first discuss how the Taylor vortices generate a spatially subharmonic dynamo, for which the axial wavelength of the magnetic field is twice the one of the flow pattern. Then, we investigate the influence of the Reynolds number and the turbulent fluctuations on the structure and the onset of the Taylor-Couette dynamo. Finally, based on the subharmonic nature of this dynamo, we propose new configurations which could be relevant for laboratory experiments. (C) 2014 AIP Publishing LLC.

PHYSICS OF FLUIDS 26, (2014)

Abstract : The generation of a magnetic field by dynamo action in a Taylor-vortex flow is investigated numerically. We first discuss how the Taylor vortices generate a spatially subharmonic dynamo, for which the axial wavelength of the magnetic field is twice the one of the flow pattern. Then, we investigate the influence of the Reynolds number and the turbulent fluctuations on the structure and the onset of the Taylor-Couette dynamo. Finally, based on the subharmonic nature of this dynamo, we propose new configurations which could be relevant for laboratory experiments. (C) 2014 AIP Publishing LLC.

DOI

7

Structures and dynamics of small scales in decaying magnetohydrodynamic turbulence - Dallas, V. and Alexakis, A.

PHYSICS OF FLUIDS 25, (2013)

Abstract : The topological and dynamical features of small scales are studied in the context of decaying magnetohydrodynamic turbulent flows using direct numerical simulations. Joint probability density functions (PDFs) of the invariants of gradient quantities related to the velocity and the magnetic fields demonstrate that structures and dynamics at the time of maximum dissipation depend on the large scale initial conditions at the examined Reynolds numbers. This is evident in particular from the fact that each flow has a different shape for the joint PDF of the invariants of the velocity gradient in contrast to the universal teardrop shape of hydrodynamic turbulence. The general picture that emerges from the analysis of the invariants is that regions of high vorticity are correlatedwith regions of high strain rate S also in contrast to hydrodynamic turbulent flows. Magnetic strain dominated regions are also well correlated with region of high current density j. Viscous dissipation (proportional to S-2) as well as Ohmic dissipation (proportional to j(2)) resides in regions where strain and rotation are locally almost in balance. The structures related to the velocity gradient possess different characteristics than those associated with the magnetic field gradient with the latter being locally more quasi-two dimensional. (C) 2013 AIP Publishing LLC.

PHYSICS OF FLUIDS 25, (2013)

Abstract : The topological and dynamical features of small scales are studied in the context of decaying magnetohydrodynamic turbulent flows using direct numerical simulations. Joint probability density functions (PDFs) of the invariants of gradient quantities related to the velocity and the magnetic fields demonstrate that structures and dynamics at the time of maximum dissipation depend on the large scale initial conditions at the examined Reynolds numbers. This is evident in particular from the fact that each flow has a different shape for the joint PDF of the invariants of the velocity gradient in contrast to the universal teardrop shape of hydrodynamic turbulence. The general picture that emerges from the analysis of the invariants is that regions of high vorticity are correlatedwith regions of high strain rate S also in contrast to hydrodynamic turbulent flows. Magnetic strain dominated regions are also well correlated with region of high current density j. Viscous dissipation (proportional to S-2) as well as Ohmic dissipation (proportional to j(2)) resides in regions where strain and rotation are locally almost in balance. The structures related to the velocity gradient possess different characteristics than those associated with the magnetic field gradient with the latter being locally more quasi-two dimensional. (C) 2013 AIP Publishing LLC.

DOI

8

Thin viscous sheets with inhomogeneous viscosity - Pfingstag, G. and Audoly, B. and Boudaoud, A.

PHYSICS OF FLUIDS 23, (2011)

Abstract : We derive the equations governing the dynamics of thin viscous sheets having non-homogeneous viscosity, via asymptotic expansion methods. We consider distributions of viscosity that are inhomogeneous in the longitudinal and transverse directions and arbitrary (bulk and surface) external forces. Two specific problems are solved as an illustration. In a first example, we study the effects of purely in-plane variations of viscosity, which lead to thickness modulations when the sheet is stretched or compressed. In a second example, we study a stretched viscous sheet whose viscosity varies both across thickness and in-plane; in that case, we find that in-plane strain leads to out-of-plane displacement as the in-plane forces become coupled to transverse ones. (C) 2011 American Institute of Physics. [doi:10.1063/1.3602507]

PHYSICS OF FLUIDS 23, (2011)

Abstract : We derive the equations governing the dynamics of thin viscous sheets having non-homogeneous viscosity, via asymptotic expansion methods. We consider distributions of viscosity that are inhomogeneous in the longitudinal and transverse directions and arbitrary (bulk and surface) external forces. Two specific problems are solved as an illustration. In a first example, we study the effects of purely in-plane variations of viscosity, which lead to thickness modulations when the sheet is stretched or compressed. In a second example, we study a stretched viscous sheet whose viscosity varies both across thickness and in-plane; in that case, we find that in-plane strain leads to out-of-plane displacement as the in-plane forces become coupled to transverse ones. (C) 2011 American Institute of Physics. [doi:10.1063/1.3602507]

DOI

9

Destabilizing Taylor-Couette flow with suction - Gallet, Basile and Doering, Charles R. and Spiegel, Edward A.

PHYSICS OF FLUIDS 22, (2010)

Abstract : We consider the effect of radial fluid injection and suction on Taylor-Couette flow. Injection at the outer cylinder and suction at the inner cylinder generally result in a linearly unstable, steady, spiraling flow, even for cylindrical shears that are linearly stable in the absence of a radial flux. We study nonlinear aspects of the unstable motions with the energy stability method. Our results, though specialized, may have implications for drag reduction by suction, accretion in astrophysical disks, and perhaps even in the flow in Earth's polar vortex. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3319824]

PHYSICS OF FLUIDS 22, (2010)

Abstract : We consider the effect of radial fluid injection and suction on Taylor-Couette flow. Injection at the outer cylinder and suction at the inner cylinder generally result in a linearly unstable, steady, spiraling flow, even for cylindrical shears that are linearly stable in the absence of a radial flux. We study nonlinear aspects of the unstable motions with the energy stability method. Our results, though specialized, may have implications for drag reduction by suction, accretion in astrophysical disks, and perhaps even in the flow in Earth's polar vortex. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3319824]

DOI

10

The impulsive motion of a small cylinder at an interface - Vella, Dominic and Li, Jie

PHYSICS OF FLUIDS 22, (2010)

Abstract : We study the unsteady motion caused by an impulse acting at time t=0 on a small cylinder floating horizontally at a liquid-gas interface. This is a model for the impact of a cylinder onto a liquid surface after the initial splash. Following the impulse, the motion of the cylinder is determined by its weight per unit length (pulling it into the bulk liquid) and resistance from the liquid, which acts to keep the cylinder at the interface. The range of cylinder radii r and impact speeds U considered is such that the resistance from the liquid comes from both the interfacial tension and hydrodynamic pressures. We use two theoretical approaches to investigate this problem. In the first, we apply the arbitrary Lagrangian Eulerian (ALE) method developed by Li [''An arbitrary Lagrangian Eulerian method for moving-boundary problems and its application to jumping over water,'' J. Comput. Phys. 208, 289 (2005)] to compute the fluid flow caused by the impulse and the (coupled) motion of the cylinder. We show that at early times the interfacial deformation is given by a family of shapes parametrized by r/t(2/3). We also find that for a given density and radius there is a critical impulse speed below which the cylinder is captured by the interface and floats but above which it pierces the interface and sinks. Our second theoretical approach is a simplified one in which we assume that the interface is in equilibrium and derive an ordinary differential equation for the motion of the cylinder. Solving this we again find the existence of a critical impulse speed for sinking giving us some quantitative understanding of the results from the ALE simulations. Finally, we compare our theoretical predictions with the results of experiments for cylinder impacts by Vella and Metcalfe [''Surface tension dominated impact,'' Phys. Fluids 19, 072108 (2007)]. This comparison suggests that the influence of contact line effects, neglected here, may be important in the transition from floating to sinking. (C) 2010 American Institute of Physics. [doi:10.1063/1.3427241]

PHYSICS OF FLUIDS 22, (2010)

Abstract : We study the unsteady motion caused by an impulse acting at time t=0 on a small cylinder floating horizontally at a liquid-gas interface. This is a model for the impact of a cylinder onto a liquid surface after the initial splash. Following the impulse, the motion of the cylinder is determined by its weight per unit length (pulling it into the bulk liquid) and resistance from the liquid, which acts to keep the cylinder at the interface. The range of cylinder radii r and impact speeds U considered is such that the resistance from the liquid comes from both the interfacial tension and hydrodynamic pressures. We use two theoretical approaches to investigate this problem. In the first, we apply the arbitrary Lagrangian Eulerian (ALE) method developed by Li [''An arbitrary Lagrangian Eulerian method for moving-boundary problems and its application to jumping over water,'' J. Comput. Phys. 208, 289 (2005)] to compute the fluid flow caused by the impulse and the (coupled) motion of the cylinder. We show that at early times the interfacial deformation is given by a family of shapes parametrized by r/t(2/3). We also find that for a given density and radius there is a critical impulse speed below which the cylinder is captured by the interface and floats but above which it pierces the interface and sinks. Our second theoretical approach is a simplified one in which we assume that the interface is in equilibrium and derive an ordinary differential equation for the motion of the cylinder. Solving this we again find the existence of a critical impulse speed for sinking giving us some quantitative understanding of the results from the ALE simulations. Finally, we compare our theoretical predictions with the results of experiments for cylinder impacts by Vella and Metcalfe [''Surface tension dominated impact,'' Phys. Fluids 19, 072108 (2007)]. This comparison suggests that the influence of contact line effects, neglected here, may be important in the transition from floating to sinking. (C) 2010 American Institute of Physics. [doi:10.1063/1.3427241]

DOI

11

The von Karman Sodium experiment: Turbulent dynamical dynamos - Monchaux, Romain and Berhanu, Michael and Aumaitre, Sebastien and Chiffaudel, Arnaud and Daviaud, Francois and Dubrulle, Berengere and Ravelet, Florent and Fauve, Stephan and Mordant, Nicolas and Petrelis, Francois and Bourgoin, Mickael and Odier, Philippe and Pinton, Jean-Francois and Plihon, Nicolas and Volk, Romain

PHYSICS OF FLUIDS 21, (2009)

Abstract : The von Karman Sodium (VKS) experiment studies dynamo action in the flow generated inside a cylinder filled with liquid sodium by the rotation of coaxial impellers (the von Karman geometry). We first report observations related to the self-generation of a stationary dynamo when the flow forcing is R-pi-symmetric, i.e., when the impellers rotate in opposite directions at equal angular velocities. The bifurcation is found to be supercritical with a neutral mode whose geometry is predominantly axisymmetric. We then report the different dynamical dynamo regimes observed when the flow forcing is not symmetric, including magnetic field reversals. We finally show that these dynamics display characteristic features of low dimensional dynamical systems despite the high degree of turbulence in the flow.

PHYSICS OF FLUIDS 21, (2009)

Abstract : The von Karman Sodium (VKS) experiment studies dynamo action in the flow generated inside a cylinder filled with liquid sodium by the rotation of coaxial impellers (the von Karman geometry). We first report observations related to the self-generation of a stationary dynamo when the flow forcing is R-pi-symmetric, i.e., when the impellers rotate in opposite directions at equal angular velocities. The bifurcation is found to be supercritical with a neutral mode whose geometry is predominantly axisymmetric. We then report the different dynamical dynamo regimes observed when the flow forcing is not symmetric, including magnetic field reversals. We finally show that these dynamics display characteristic features of low dimensional dynamical systems despite the high degree of turbulence in the flow.

DOI

12

Stratified shear flow instabilities at large Richardson numbers - Alexakis, Alexandros

PHYSICS OF FLUIDS 21, (2009)

Abstract : Numerical simulations of stratified shear flow instabilities are performed in two dimensions in the Boussinesq limit. The density variation length scale is chosen to be four times smaller than the velocity variation length scale so that Holmboe or Kelvin-Helmholtz unstable modes are present depending on the choice of the global Richardson number Ri. Three different values of Ri were examined Ri=0.2, 2, and 20. The flows for the three examined values are all unstable due to different modes, namely: the Kelvin-Helmholtz mode for Ri=0.2, the first Holmboe mode for Ri=2, and the second Holmboe mode for Ri=20 that has been discovered recently and this is the first time that it is examined in the nonlinear stage. It is found that the amplitude of the velocity perturbation of the second Holmboe mode at the nonlinear stage is smaller but comparable to first Holmboe mode. The increase in the potential energy, however, due to the second Holmboe modes is greater than that of the first mode. The Kelvin-Helmholtz mode is larger by two orders of magnitude in kinetic energy than the Holmboe modes and about ten times larger in potential energy than the Holmboe modes. The effect of increasing Prandtl number is also investigated, and a weak dependence on the Prandtl number is observed. The results in this paper suggest that although mixing is suppressed at large Richardson numbers it is not negligible, and turbulent mixing processes in strongly stratified environments cannot be excluded.

PHYSICS OF FLUIDS 21, (2009)

Abstract : Numerical simulations of stratified shear flow instabilities are performed in two dimensions in the Boussinesq limit. The density variation length scale is chosen to be four times smaller than the velocity variation length scale so that Holmboe or Kelvin-Helmholtz unstable modes are present depending on the choice of the global Richardson number Ri. Three different values of Ri were examined Ri=0.2, 2, and 20. The flows for the three examined values are all unstable due to different modes, namely: the Kelvin-Helmholtz mode for Ri=0.2, the first Holmboe mode for Ri=2, and the second Holmboe mode for Ri=20 that has been discovered recently and this is the first time that it is examined in the nonlinear stage. It is found that the amplitude of the velocity perturbation of the second Holmboe mode at the nonlinear stage is smaller but comparable to first Holmboe mode. The increase in the potential energy, however, due to the second Holmboe modes is greater than that of the first mode. The Kelvin-Helmholtz mode is larger by two orders of magnitude in kinetic energy than the Holmboe modes and about ten times larger in potential energy than the Holmboe modes. The effect of increasing Prandtl number is also investigated, and a weak dependence on the Prandtl number is observed. The results in this paper suggest that although mixing is suppressed at large Richardson numbers it is not negligible, and turbulent mixing processes in strongly stratified environments cannot be excluded.

DOI

13

The von Karman Sodium experiment: Turbulent dynamical dynamos (vol 21, 035108, 2009) - Monchaux, Romain and Berhanu, Michael and Aumaitre, Sebastien and Chiffaudel, Arnaud and Daviaud, Francois and Dubrulle, Berengere and Ravelet, Florent and Fauve, Stephan and Mordant, Nicolas and Petrelis, Francois and Bourgoin, Mickael and Odier, Philippe and Pinton, Jean-Francois and Plihon, Nicolas and Volk, Romain

PHYSICS OF FLUIDS 21, (2009)

PHYSICS OF FLUIDS 21, (2009)

DOI

14

Influence of an external magnetic field on forced turbulence in a swirling flow of liquid metal - Gallet, Basile and Berhanu, Michael and Mordant, Nicolas

PHYSICS OF FLUIDS 21, (2009)

Abstract : We report an experimental investigation on the influence of an external magnetic field on forced three-dimensional turbulence of liquid gallium in a closed vessel. We observe an exponential damping of the turbulent velocity fluctuations as a function of the interaction parameter N (ratio of Lorentz force over inertial terms of the Navier-Stokes equation). The flow structures develop some anisotropy but do not become bidimensional. From a dynamical viewpoint, the damping first occurs homogeneously over the whole spectrum of frequencies. For larger values of N, a very strong additional damping occurs at the highest frequencies. However, the injected mechanical power remains independent of the applied magnetic field. The simultaneous measurement of induced magnetic field and electrical potential differences shows a very weak correlation between magnetic field and velocity fluctuations. The observed reduction in the fluctuations is in agreement with a previously proposed mechanism for the saturation of turbulent dynamos and with the order of magnitude of the Von Karman sodium dynamo magnetic field. (C) 2009 American Institute of Physics. [DOI: 10.1063/1.3194304]

PHYSICS OF FLUIDS 21, (2009)

Abstract : We report an experimental investigation on the influence of an external magnetic field on forced three-dimensional turbulence of liquid gallium in a closed vessel. We observe an exponential damping of the turbulent velocity fluctuations as a function of the interaction parameter N (ratio of Lorentz force over inertial terms of the Navier-Stokes equation). The flow structures develop some anisotropy but do not become bidimensional. From a dynamical viewpoint, the damping first occurs homogeneously over the whole spectrum of frequencies. For larger values of N, a very strong additional damping occurs at the highest frequencies. However, the injected mechanical power remains independent of the applied magnetic field. The simultaneous measurement of induced magnetic field and electrical potential differences shows a very weak correlation between magnetic field and velocity fluctuations. The observed reduction in the fluctuations is in agreement with a previously proposed mechanism for the saturation of turbulent dynamos and with the order of magnitude of the Von Karman sodium dynamo magnetic field. (C) 2009 American Institute of Physics. [DOI: 10.1063/1.3194304]

DOI

15

Generalized Eulerian-Lagrangian description of Navier-Stokes dynamics - Cartes, Carlos and Bustamante, Miguel D. and Brachet, Marc E.

PHYSICS OF FLUIDS 19, (2007)

Abstract : Generalized equations of motion for the Weber-Clebsch potentials that reproduce Navier-Stokes dynamics are derived. These depend on a new parameter, with the dimension of time, and reduce to the Ohkitani and Constantin equations in the singular special case where the new parameter vanishes. Let us recall that Ohkitani and Constantin found that the diffusive Lagrangian map became noninvertible under time evolution and required resetting for its calculation. They proposed that high frequency of resetting was a diagnostic for vortex reconnection. Direct numerical simulations are performed. The Navier-Stokes dynamics is well reproduced at small enough Reynolds number without resetting. Computation at higher Reynolds numbers is achieved by performing resettings. The interval between successive resettings is found to abruptly increase when the new parameter is varied from 0 to a value much smaller than the resetting interval. (c) 2007 American Institute of Physics.

PHYSICS OF FLUIDS 19, (2007)

Abstract : Generalized equations of motion for the Weber-Clebsch potentials that reproduce Navier-Stokes dynamics are derived. These depend on a new parameter, with the dimension of time, and reduce to the Ohkitani and Constantin equations in the singular special case where the new parameter vanishes. Let us recall that Ohkitani and Constantin found that the diffusive Lagrangian map became noninvertible under time evolution and required resetting for its calculation. They proposed that high frequency of resetting was a diagnostic for vortex reconnection. Direct numerical simulations are performed. The Navier-Stokes dynamics is well reproduced at small enough Reynolds number without resetting. Computation at higher Reynolds numbers is achieved by performing resettings. The interval between successive resettings is found to abruptly increase when the new parameter is varied from 0 to a value much smaller than the resetting interval. (c) 2007 American Institute of Physics.