Capitulo de libro
EULERIAN-LAGRANGIAN FORMULATION FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS
Fecha
2011Registro en:
9789533077123
3110028
Institución
Resumen
The Eulerian-Lagrangian formulation of the (inviscid) Euler dynamics in terms of advected
Weber-Clebsch potentials (Lamb, 1932), was extended by Constantin to cover the viscous
Navier-Stokes dynamics (Constantin, 2001). Numerical studies (Ohkitani & Constantin, 2003),
of this formulation of the Navier-Stokes equations concluded that the diffusive Lagrangian
map becomes non-invertible under time evolution and requires resetting for its calculation.
They proposed the observed sharp increase of the frequency of resettings as a new diagnostic
of vortex reconnection.
In previous work we were able (Cartes et al., 2007; 2009) to complement these results, using
an approach that is based on a generalised set of equations of motion for the Weber-Clebsch
potentials, that turned out to depend on a parameter ?, which has the unit of time for the
Navier-Stokes case. Also to extend our formulation to magnetohydrodynamics, and thereby
obtain a new diagnostic for magnetic reconnection.
In this work we present a generalisation of the Weber-Clebsch variables in order to describe
the compressible Navier-Stokes dynamics. Our main result is a good agreement between the
dynamics for the velocity and density fields that come from the dynamics of Weber-Clebsch
variables and direct numerical simulations of the compressible Navier-Stokes equations.
We first present the inviscid Eulerian-Lagrangian theory, then Constantin’s extension to
viscous fluids and derive our equations of motion for the Weber-Clebsch potentials that
describe the compressible Navier-Stokes dynamics. Then, performing direct numerical
simulations of the Taylor-Green vortex, we check that our formulation reproduces the
compressible dynamics.The Eulerian-Lagrangian formulation of the (inviscid) Euler dynamics in terms of advected
Weber-Clebsch potentials (Lamb, 1932), was extended by Constantin to cover the viscous
Navier-Stokes dynamics (Constantin, 2001). Numerical studies (Ohkitani & Constantin, 2003),
of this formulation of the Navier-Stokes equations concluded that the diffusive Lagrangian
map becomes non-invertible under time evolution and requires resetting for its calculation.
They proposed the observed sharp increase of the frequency of resettings as a new diagnostic
of vortex reconnection.
In previous work we were able (Cartes et al., 2007; 2009) to complement these results, using
an approach that is based on a generalised set of equations of motion for the Weber-Clebsch
potentials, that turned out to depend on a parameter ?, which has the unit of time for the
Navier-Stokes case. Also to extend our formulation to magnetohydrodynamics, and thereby
obtain a new diagnostic for magnetic reconnection.
In this work we present a generalisation of the Weber-Clebsch variables in order to describe
the compressible Navier-Stokes dynamics. Our main result is a good agreement between the
dynamics for the velocity and density fields that come from the dynamics of Weber-Clebsch
variables and direct numerical simulations of the compressible Navier-Stokes equations.
We first present the inviscid Eulerian-Lagrangian theory, then Constantin’s extension to
viscous fluids and derive our equations of motion for the Weber-Clebsch potentials that
describe the compressible Navier-Stokes dynamics. Then, performing direct numerical
simulations of the Taylor-Green vortex, we check that our formulation reproduces the
compressible dynamics.The Eulerian-Lagrangian formulation of the (inviscid) Euler dynamics in terms of advected
Weber-Clebsch potentials (Lamb, 1932), was extended by Constantin to cover the viscous
Navier-Stokes dynamics (Constantin, 2001). Numerical studies (Ohkitani & Constantin, 2003),
of this formulation of the Navier-Stokes equations concluded that the diffusive Lagrangian
map becomes non-invertible under time evolution and requires resetting for its calculation.
They proposed the observed sharp increase of the frequency of resettings as a new diagnostic
of vortex reconnection.
In previous work we were able (Cartes et al., 2007; 2009) to complement these results, using
an approach that is based on a generalised set of equations of motion for the Weber-Clebsch
potentials, that turned out to depend on a parameter ?, which has the unit of time for the
Navier-Stokes case. Also to extend our formulation to magnetohydrodynamics, and thereby
obtain a new diagnostic for magnetic reconnection.
In this work we present a generalisation of the Weber-Clebsch variables in order to describe
the compressible Navier-Stokes dynamics. Our main result is a good agreement between the
dynamics for the velocity and density fields that come from the dynamics of Weber-Clebsch
variables and direct numerical simulations of the compressible Navier-Stokes equations.
We first present the inviscid Eulerian-Lagrangian theory, then Constantin’s extension to
viscous fluids and derive our equations of motion for the Weber-Clebsch potentials that
describe the compressible Navier-Stokes dynamics. Then, performing direct numerical
simulations of the Taylor-Green vortex, we check that our formulation reproduces the
compressible dynamics.The Eulerian-Lagrangian formulation of the (inviscid) Euler dynamics in terms of advected
Weber-Clebsch potentials (Lamb, 1932), was extended by Constantin to cover the viscous
Navier-Stokes dynamics (Constantin, 2001). Numerical studies (Ohkitani & Constantin, 2003),
of this formulation of the Navier-Stokes equations concluded that the diffusive Lagrangian
map becomes non-invertible under time evolution and requires resetting for its calculation.
They proposed the observed sharp increase of the frequency of resettings as a new diagnostic
of vortex reconnection.
In previous work we were able (Cartes et al., 2007; 2009) to complement these results, using
an approach that is based on a generalised set of equations of motion for the Weber-Clebsch
potentials, that turned out to depend on a parameter ?, which has the unit of time for the
Navier-Stokes case. Also to extend our formulation to magnetohydrodynamics, and thereby
obtain a new diagnostic for magnetic reconnection.
In this work we present a generalisation of the Weber-Clebsch variables in order to describe
the compressible Navier-Stokes dynamics. Our main result is a good agreement between the
dynamics for the velocity and density fields that come from the dynamics of Weber-Clebsch
variables and direct numerical simulations of the compressible Navier-Stokes equations.
We first present the inviscid Eulerian-Lagrangian theory, then Constantin’s extension to
viscous fluids and derive our equations of motion for the Weber-Clebsch potentials that
describe the compressible Navier-Stokes dynamics. Then, performing direct numerical
simulations of the Taylor-Green vortex, we check that our formulation reproduces the
compressible dynamics.The Eulerian-Lagrangian formulation of the (inviscid) Euler dynamics in terms of advected
Weber-Clebsch potentials (Lamb, 1932), was extended by Constantin to cover the viscous
Navier-Stokes dynamics (Constantin, 2001). Numerical studies (Ohkitani & Constantin, 2003),
of this formulation of the Navier-Stokes equations concluded that the diffusive Lagrangian
map becomes non-invertible under time evolution and requires resetting for its calculation.
They proposed the observed sharp increase of the frequency of resettings as a new diagnostic
of vortex reconnection.
In previous work we were able (Cartes et al., 2007; 2009) to complement these results, using
an approach that is based on a generalised set of equations of motion for the Weber-Clebsch
potentials, that turned out to depend on a parameter ?, which has the unit of time for the
Navier-Stokes case. Also to extend our formulation to magnetohydrodynamics, and thereby
obtain a new diagnostic for magnetic reconnection.
In this work we present a generalisation of the Weber-Clebsch variables in order to describe
the compressible Navier-Stokes dynamics. Our main result is a good agreement between the
dynamics for the velocity and density fields that come from the dynamics of Weber-Clebsch
variables and direct numerical simulations of the compressible Navier-Stokes equations.
We first present the inviscid Eulerian-Lagrangian theory, then Constantin’s extension to
viscous fluids and derive our equations of motion for the Weber-Clebsch potentials that
describe the compressible Navier-Stokes dynamics. Then, performing direct numerical
simulations of the Taylor-Green vortex, we check that our formulation reproduces the
compressible dynamics.The Eulerian-Lagrangian formulation of the (inviscid) Euler dynamics in terms of advected
Weber-Clebsch potentials (Lamb, 1932), was extended by Constantin to cover the viscous
Navier-Stokes dynamics (Constantin, 2001). Numerical studies (Ohkitani & Constantin, 2003),
of this formulation of the Navier-Stokes equations concluded that the diffusive Lagrangian
map becomes non-invertible under time evolution and requires resetting for its calculation.
They proposed the observed sharp increase of the frequency of resettings as a new diagnostic
of vortex reconnection.
In previous work we were able (Cartes et al., 2007; 2009) to complement these results, using
an approach that is based on a generalised set of equations of motion for the Weber-Clebsch
potentials, that turned out to depend on a parameter ?, which has the unit of time for the
Navier-Stokes case. Also to extend our formulation to magnetohydrodynamics, and thereby
obtain a new diagnostic for magnetic reconnection.
In this work we present a generalisation of the Weber-Clebsch variables in order to describe
the compressible Navier-Stokes dynamics. Our main result is a good agreement between the
dynamics for the velocity and density fields that come from the dynamics of Weber-Clebsch
variables and direct numerical simulations of the compressible Navier-Stokes equations.
We first present the inviscid Eulerian-Lagrangian theory, then Constantin’s extension to
viscous fluids and derive our equations of motion for the Weber-Clebsch potentials that
describe the compressible Navier-Stokes dynamics. Then, performing direct numerical
simulations of the Taylor-Green vortex, we check that our formulation reproduces the
compressible dynamics.The Eulerian-Lagrangian formulation of the (inviscid) Euler dynamics in terms of advected
Weber-Clebsch potentials (Lamb, 1932), was extended by Constantin to cover the viscous
Navier-Stokes dynamics (Constantin, 2001). Numerical studies (Ohkitani & Constantin, 2003),
of this formulation of the Navier-Stokes equations concluded that the diffusive Lagrangian
map becomes non-invertible under time evolution and requires resetting for its calculation.
They proposed the observed sharp increase of the frequency of resettings as a new diagnostic
of vortex reconnection.
In previous work we were able (Cartes et al., 2007; 2009) to complement these results, using
an approach that is based on a generalised set of equations of motion for the Weber-Clebsch
potentials, that turned out to depend on a parameter ?, which has the unit of time for the
Navier-Stokes case. Also to extend our formulation to magnetohydrodynamics, and thereby
obtain a new diagnostic for magnetic reconnection.
In this work we present a generalisation of the Weber-Clebsch variables in order to describe
the compressible Navier-Stokes dynamics. Our main result is a good agreement between the
dynamics for the velocity and density fields that come from the dynamics of Weber-Clebsch
variables and direct numerical simulations of the compressible Navier-Stokes equations.
We first present the inviscid Eulerian-Lagrangian theory, then Constantin’s extension to
viscous fluids and derive our equations of motion for the Weber-Clebsch potentials that
describe the compressible Navier-Stokes dynamics. Then, performing direct numerical
simulations of the Taylor-Green vortex, we check that our formulation reproduces the
compressible dynamics.The Eulerian-Lagrangian formulation of the (inviscid) Euler dynamics in terms of advected
Weber-Clebsch potentials (Lamb, 1932), was extended by Constantin to cover the viscous
Navier-Stokes dynamics (Constantin, 2001). Numerical studies (Ohkitani & Constantin, 2003),
of this formulation of the Navier-Stokes equations concluded that the diffusive Lagrangian
map becomes non-invertible under time evolution and requires resetting for its calculation.
They proposed the observed sharp increase of the frequency of resettings as a new diagnostic
of vortex reconnection.
In previous work we were able (Cartes et al., 2007; 2009) to complement these results, using
an approach that is based on a generalised set of equations of motion for the Weber-Clebsch
potentials, that turned out to depend on a parameter ?, which has the unit of time for the
Navier-Stokes case. Also to extend our formulation to magnetohydrodynamics, and thereby
obtain a new diagnostic for magnetic reconnection.
In this work we present a generalisation of the Weber-Clebsch variables in order to describe
the compressible Navier-Stokes dynamics. Our main result is a good agreement between the
dynamics for the velocity and density fields that come from the dynamics of Weber-Clebsch
variables and direct numerical simulations of the compressible Navier-Stokes equations.
We first present the inviscid Eulerian-Lagrangian theory, then Constantin’s extension to
viscous fluids and derive our equations of motion for the Weber-Clebsch potentials that
describe the compressible Navier-Stokes dynamics. Then, performing direct numerical
simulations of the Taylor-Green vortex, we check that our formulation reproduces the
compressible dynamics.The Eulerian-Lagrangian formulation of the (inviscid) Euler dynamics in terms of advected
Weber-Clebsch potentials (Lamb, 1932), was extended by Constantin to cover the viscous
Navier-Stokes dynamics (Constantin, 2001). Numerical studies (Ohkitani & Constantin, 2003),
of this formulation of the Navier-Stokes equations concluded that the diffusive Lagrangian
map becomes non-invertible under time evolution and requires resetting for its calculation.
They proposed the observed sharp increase of the frequency of resettings as a new diagnostic
of vortex reconnection.
In previous work we were able (Cartes et al., 2007; 2009) to complement these results, using
an approach that is based on a generalised set of equations of motion for the Weber-Clebsch
potentials, that turned out to depend on a parameter ?, which has the unit of time for the
Navier-Stokes case. Also to extend our formulation to magnetohydrodynamics, and thereby
obtain a new diagnostic for magnetic reconnection.
In this work we present a generalisation of the Weber-Clebsch variables in order to describe
the compressible Navier-Stokes dynamics. Our main result is a good agreement between the
dynamics for the velocity and density fields that come from the dynamics of Weber-Clebsch
variables and direct numerical simulations of the compressible Navier-Stokes equations.
We first present the inviscid Eulerian-Lagrangian theory, then Constantin’s extension to
viscous fluids and derive our equations of motion for the Weber-Clebsch potentials that
describe the compressible Navier-Stokes dynamics. Then, performing direct numerical
simulations of the Taylor-Green vortex, we check that our formulation reproduces the
compressible dynamics.The Eulerian-Lagrangian formulation of the (inviscid) Euler dynamics in terms of advected
Weber-Clebsch potentials (Lamb, 1932), was extended by Constantin to cover the viscous
Navier-Stokes dynamics (Constantin, 2001). Numerical studies (Ohkitani & Constantin, 2003),
of this formulation of the Navier-Stokes equations concluded that the diffusive Lagrangian
map becomes non-invertible under time evolution and requires resetting for its calculation.
They proposed the observed sharp increase of the frequency of resettings as a new diagnostic
of vortex reconnection.
In previous work we were able (Cartes et al., 2007; 2009) to complement these results, using
an approach that is based on a generalised set of equations of motion for the Weber-Clebsch
potentials, that turned out to depend on a parameter ?, which has the unit of time for the
Navier-Stokes case. Also to extend our formulation to magnetohydrodynamics, and thereby
obtain a new diagnostic for magnetic reconnection.
In this work we present a generalisation of the Weber-Clebsch variables in order to describe
the compressible Navier-Stokes dynamics. Our main result is a good agreement between the
dynamics for the velocity and density fields that come from the dynamics of Weber-Clebsch
variables and direct numerical simulations of the compressible Navier-Stokes equations.
We first present the inviscid Eulerian-Lagrangian theory, then Constantin’s extension to
viscous fluids and derive our equations of motion for the Weber-Clebsch potentials that
describe the compressible Navier-Stokes dynamics. Then, performing direct numerical
simulations of the Taylor-Green vortex, we check that our formulation reproduces the
compressible dynamics.The Eulerian-Lagrangian formulation of the (inviscid) Euler dynamics in terms of advected
Weber-Clebsch potentials (Lamb, 1932), was extended by Constantin to cover the viscous
Navier-Stokes dynamics (Constantin, 2001). Numerical studies (Ohkitani & Constantin, 2003),
of this formulation of the Navier-Stokes equations concluded that the diffusive Lagrangian
map becomes non-invertible under time evolution and requires resetting for its calculation.
They proposed the observed sharp increase of the frequency of resettings as a new diagnostic
of vortex reconnection.
In previous work we were able (Cartes et al., 2007; 2009) to complement these results, using
an approach that is based on a generalised set of equations of motion for the Weber-Clebsch
potentials, that turned out to depend on a parameter ?, which has the unit of time for the
Navier-Stokes case. Also to extend our formulation to magnetohydrodynamics, and thereby
obtain a new diagnostic for magnetic reconnection.
In this work we present a generalisation of the Weber-Clebsch variables in order to describe
the compressible Navier-Stokes dynamics. Our main result is a good agreement between the
dynamics for the velocity and density fields that come from the dynamics of Weber-Clebsch
variables and direct numerical simulations of the compressible Navier-Stokes equations.
We first present the inviscid Eulerian-Lagrangian theory, then Constantin’s extension to
viscous fluids and derive our equations of motion for the Weber-Clebsch potentials that
describe the compressible Navier-Stokes dynamics. Then, performing direct numerical
simulations of the Taylor-Green vortex, we check that our formulation reproduces the
compressible dynamics.The Eulerian-Lagrangian formulation of the (inviscid) Euler dynamics in terms of advected
Weber-Clebsch potentials (Lamb, 1932), was extended by Constantin to cover the viscous
Navier-Stokes dynamics (Constantin, 2001). Numerical studies (Ohkitani & Constantin, 2003),
of this formulation of the Navier-Stokes equations concluded that the diffusive Lagrangian
map becomes non-invertible under time evolution and requires resetting for its calculation.
They proposed the observed sharp increase of the frequency of resettings as a new diagnostic
of vortex reconnection.
In previous work we were able (Cartes et al., 2007; 2009) to complement these results, using
an approach that is based on a generalised set of equations of motion for the Weber-Clebsch
potentials, that turned out to depend on a parameter ?, which has the unit of time for the
Navier-Stokes case. Also to extend our formulation to magnetohydrodynamics, and thereby
obtain a new diagnostic for magnetic reconnection.
In this work we present a generalisation of the Weber-Clebsch variables in order to describe
the compressible Navier-Stokes dynamics. Our main result is a good agreement between the
dynamics for the velocity and density fields that come from the dynamics of Weber-Clebsch
variables and direct numerical simulations of the compressible Navier-Stokes equations.
We first present the inviscid Eulerian-Lagrangian theory, then Constantin’s extension to
viscous fluids and derive our equations of motion for the Weber-Clebsch potentials that
describe the compressible Navier-Stokes dynamics. Then, performing direct numerical
simulations of the Taylor-Green vortex, we check that our formulation reproduces the
compressible dynamics.The Eulerian-Lagrangian formulation of the (inviscid) Euler dynamics in terms of advected
Weber-Clebsch potentials (Lamb, 1932), was extended by Constantin to cover the viscous
Navier-Stokes dynamics (Constantin, 2001). Numerical studies (Ohkitani & Constantin, 2003),
of this formulation of the Navier-Stokes equations concluded that the diffusive Lagrangian
map becomes non-invertible under time evolution and requires resetting for its calculation.
They proposed the observed sharp increase of the frequency of resettings as a new diagnostic
of vortex reconnection.
In previous work we were able (Cartes et al., 2007; 2009) to complement these results, using
an approach that is based on a generalised set of equations of motion for the Weber-Clebsch
potentials, that turned out to depend on a parameter ?, which has the unit of time for the
Navier-Stokes case. Also to extend our formulation to magnetohydrodynamics, and thereby
obtain a new diagnostic for magnetic reconnection.
In this work we present a generalisation of the Weber-Clebsch variables in order to describe
the compressible Navier-Stokes dynamics. Our main result is a good agreement between the
dynamics for the velocity and density fields that come from the dynamics of Weber-Clebsch
variables and direct numerical simulations of the compressible Navier-Stokes equations.
We first present the inviscid Eulerian-Lagrangian theory, then Constantin’s extension to
viscous fluids and derive our equations of motion for the Weber-Clebsch potentials that
describe the compressible Navier-Stokes dynamics. Then, performing direct numerical
simulations of the Taylor-Green vortex, we check that our formulation reproduces the
compressible dynamics.The Eulerian-Lagrangian formulation of the (inviscid) Euler dynamics in terms of advected
Weber-Clebsch potentials (Lamb, 1932), was extended by Constantin to cover the viscous
Navier-Stokes dynamics (Constantin, 2001). Numerical studies (Ohkitani & Constantin, 2003),
of this formulation of the Navier-Stokes equations concluded that the diffusive Lagrangian
map becomes non-invertible under time evolution and requires resetting for its calculation.
They proposed the observed sharp increase of the frequency of resettings as a new diagnostic
of vortex reconnection.
In previous work we were able (Cartes et al., 2007; 2009) to complement these results, using
an approach that is based on a generalised set of equations of motion for the Weber-Clebsch
potentials, that turned out to depend on a parameter ?, which has the unit of time for the
Navier-Stokes case. Also to extend our formulation to magnetohydrodynamics, and thereby
obtain a new diagnostic for magnetic reconnection.
In this work we present a generalisation of the Weber-Clebsch variables in order to describe
the compressible Navier-Stokes dynamics. Our main result is a good agreement between the
dynamics for the velocity and density fields that come from the dynamics of Weber-Clebsch
variables and direct numerical simulations of the compressible Navier-Stokes equations.
We first present the inviscid Eulerian-Lagrangian theory, then Constantin’s extension to
viscous fluids and derive our equations of motion for the Weber-Clebsch potentials that
describe the compressible Navier-Stokes dynamics. Then, performing direct numerical
simulations of the Taylor-Green vortex, we check that our formulation reproduces the
compressible dynamics.