2,515 research outputs found
Dynamics of scaled norms of vorticity for the three-dimensional Navier-Stokes and Euler equations
A series of numerical experiments is suggested for the three-dimensional
Navier-Stokes and Euler equations on a periodic domain based on a set of
-norms of vorticity for . These are scaled to
form the dimensionless sequence where is a constant
frequency and . A numerically testable Navier-Stokes
regularity criterion comes from comparing the relative magnitudes of
and while another is furnished by imposing a critical lower bound on
. The behaviour of the is also important in
the Euler case in suggesting a method by which possible singular behaviour
might also be tested.Comment: To appear in the Procedia IUTAM volume of papers Topological Fluid
Dynamic
Quasi-conservation laws for compressible 3D Navier-Stokes flow
We formulate the quasi-Lagrangian fluid transport dynamics of mass density
and the projection q=\bom\cdot\nabla\rho of the vorticity \bom onto
the density gradient, as determined by the 3D compressible Navier-Stokes
equations for an ideal gas, although the results apply for an arbitrary
equation of state. It turns out that the quasi-Lagrangian transport of
cannot cross a level set of . That is, in this formulation, level sets of
(isopychnals) are impermeable to the transport of the projection .Comment: 2 page note, to appear in Phys Rev
Stretching and folding processes in the 3D Euler and Navier-Stokes equations
Stretching and folding dynamics in the incompressible, stratified 3D Euler
and Navier-Stokes equations are reviewed in the context of the vector \bdB =
\nabla q\times\nabla\theta where q=\bom\cdot\nabla\theta. The variable
is the temperature and \bdB satisfies \partial_{t}\bdB =
\mbox{curl}\,(\bu\times\bdB). These ideas are then discussed in the context of
the full compressible Navier-Stokes equations where takes the two forms q
= \bom\cdot\nabla\rho and q = \bom\cdot\nabla(\ln\rho).Comment: UTAM Symposium on Understanding Common Aspects of Extreme Events in
Fluid
Lagrangian analysis of alignment dynamics for isentropic compressible magnetohydrodynamics
After a review of the isentropic compressible magnetohydrodynamics (ICMHD)
equations, a quaternionic framework for studying the alignment dynamics of a
general fluid flow is explained and applied to the ICMHD equations.Comment: 12 pages, 2 figures, submitted to a Focus Issue of New Journal of
Physics on "Magnetohydrodynamics and the Dynamo Problem" J-F Pinton, A
Pouquet, E Dormy and S Cowley, editor
Conditional regularity of solutions of the three dimensional Navier-Stokes equations and implications for intermittency
Two unusual time-integral conditional regularity results are presented for
the three-dimensional Navier-Stokes equations. The ideas are based on
-norms of the vorticity, denoted by , and particularly
on , where for . The first result, more appropriate for the unforced case, can be stated
simply : if there exists an for which the integral condition
is satisfied () then no singularity can occur on . The
constant for large . Secondly, for the forced case, by
imposing a critical \textit{lower} bound on , no
singularity can occur in for \textit{large} initial data. Movement
across this critical lower bound shows how solutions can behave intermittently,
in analogy with a relaxation oscillator. Potential singularities that drive
over this critical value can be ruled out whereas
other types cannot.Comment: A frequency was missing in the definition of D_{m} in (I5) v3. 11
pages, 1 figur
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