Related Experiment Video
Updated: Apr 19, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Variational necessary and sufficient stability conditions for inviscid shear flow
M Hirota1, P J Morrison2, Y Hattori1
1Institute of Fluid Science, Tohoku University , Sendai, Miyagi 980-8677, Japan.
Abstract:
A necessary and sufficient condition for linear stability of inviscid parallel shear flow is formulated by developing a novel variational principle, where the velocity profile is assumed to be monotonic and analytic. It is shown that unstable eigenvalues of Rayleigh's equation (which is a non-self-adjoint eigenvalue problem) can be associated with positive eigenvalues of a certain self-adjoint operator. The stability is therefore determined by maximizing a quadratic form, which is theoretically and numerically more tractable than directly solving Rayleigh's equation. This variational stability criterion is based on the understanding of Kreĭn signature for continuous spectra and is applicable to other stability problems of infinite-dimensional Hamiltonian systems.
More Related Videos
10:28Experimental Measurement of Settling Velocity of Spherical Particles in Unconfined and Confined Surfactant-based Shear Thinning Viscoelastic Fluids
Published on: January 3, 2014
11:00Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
Published on: July 19, 2016
Related Concept Videos
Navier–Stokes Equations
Euler's Equations of Motion
Newtonian Fluid: Problem Solving
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
Irrotational Flow
Viscosity
Viscosity
The SI unit of viscosity is...