The 3D Incompressible Euler Equations with a Passive Scalar: A Road to Blow-Up?

abstract

• The three-dimensional incompressible Euler equations with a passive scalar are considered in a smooth domain with no-normal-flow boundary conditions = 0. It is shown that smooth solutions blow up in a finite time if a null (zero) point develops in the vector B=q, provided B has no null points initially: = {u} is the vorticity and q= is a potential vorticity. The presence of the passive scalar concentration is an essential component of this criterion in detecting the formation of a singularity. The problem is discussed in the light of a kinematic result by Graham and Henyey (Phys. Fluids 12:744-746, 2000) on the non-existence of Clebsch potentials in the neighbourhood of null points. 2013 Springer Science+Business Media New York.

authors

• Titi, Edriss

published proceedings

• JOURNAL OF NONLINEAR SCIENCE

author list (cited authors)

• Gibbon, J. D., & Titi, E. S.

citation count

• 9

complete list of authors

• Gibbon, John D||Titi, Edriss S

publication date

• December 2013

publisher

• Springer Nature  Publisher

published in

• Journal of Nonlinear Science  Journal

keywords

• Incompressible Euler Equations
• No-normal-flow Boundary Conditions
• Null Point
• Passive Scalar
• Singularity

Digital Object Identifier (DOI)

• 10.1007/s00332-013-9175-4

start page

• 993

end page

• 1000

volume

• 23

issue

• 6

URL

• http%3A%2F%2Fdx.doi.org%2F10.1007%2Fs00332-013-9175-4