Satish C. Reddy

Energy growth in viscous channel flows

In recent work it has been shown that there can be substantial transient growth in the energy of small perturbations to plane Poiseuille and Couette flows if the Reynolds number is below the critical value predicted by linear stability analysis. This growth, which may be as large as O (1000), occurs in the absence of nonlinear effects and can be explained by the non-normality of the governing linear operator - that is, the non-orthogonality of the associated eigenfunctions. In this paper we study various aspects of this energy growth for two- and three-dimensional Poiseuille and Couette flows using energy methods, linear stability analysis, and a direct numerical procedure for computing the transient growth. We examine conditions for no energy growth, the dependence of the growth on the streamwise and spanwise wavenumbers, the time dependence of the growth, and the effects of degenerate eigenvalues. We show that the maximum transient growth behaves like O ( R 2 ), where R is the Reynolds number. We derive conditions for no energy growth by applying the Hille–Yosida theorem to the governing linear operator and show that these conditions yield the same results as those derived by energy methods, which can be applied to perturbations of arbitrary amplitude. These results emphasize the fact that subcritical transition can occur for Poiseuille and Couette flows because the governing linear operator is non-normal.

Pseudospectra of the Orr-Sommerfeld operator

This paper investigates the pseudospectra and the numerical range of the Orr–Sommerfeld operator for plane Poiseuille flow. A number

How fast are nonsymmetric matrix iterations

z \in {\bf C}

On stability of streamwise streaks and transition thresholds in plane channel flows

is in the

Stability of the method of lines

\epsilon

On the role of linear mechanisms in transition to turbulence

-pseudospectrum of a matrix or operator A if

Lax-stability of fully discrete spectral methods via stability regions and pseudo-eigenvalues

\| ( zI - A )^{ - 1} \| \geq \epsilon ^{ - 1}

Threshold Amplitudes for Transition in Channel Flows

, or, equivalently, if z is in the spectrum of

Transition Thresholds in Boundary Layer and Channel Flows

A + E

Energy Transfer Analysis of Turbulent Plane Couette Flow

for some perturbation E satisfying