BIFURCATION FROM INFINITY.

S. Rosenblat*, Stephen H. Davis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

Poiseuille flow in a pipe and plane Couette flow of a viscous incompressible fluid are stable in the linear approximation at all Reynolds numbers, yet these flows certainly do not remain laminar as the Reynolds number is increased indefinitely. In this paper a study is made of some nonlinear differential equations, containing a parameter, which model this aspect of the fluid-mechanical problems. In the model equations there is no finite value of the parameter at which bifurcation occurs, but there are solutions whose norm tends to zero as the parameter tends to infinity. It is shown that these small-norm bifurcating solutions are characterized by strongly-nonlinear balances. In the fluid-mechanical context the viscous and inertial terms would be comparable.

Original languageEnglish (US)
Pages (from-to)1-19
Number of pages19
JournalSIAM Journal on Applied Mathematics
Volume37
Issue number1
DOIs
StatePublished - Jan 1 1979

ASJC Scopus subject areas

  • Applied Mathematics

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