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Stochastic forcing of the linearized Navier–Stokes equations

Author(s): Brian F. Farrell , Petros J. Ioannou

Publication date Created: November 1993

Publication date (Print): November 1993

Journal: Physics of Fluids A: Fluid Dynamics

Publisher: AIP Publishing

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Hydrodynamic stability without eigenvalues.

L N Trefethen, A E Trefethen, S Reddy … (1993)

Fluid flows that are smooth at low speeds become unstable and then turbulent at higher speeds. This phenomenon has traditionally been investigated by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem, but the results of such investigations agree poorly in many cases with experiments. Nevertheless, linear effects play a central role in hydrodynamic instability. A reconciliation of these findings with the traditional analysis is presented based on the "pseudospectra" of the linearized problem, which imply that small perturbations to the smooth flow may be amplified by factors on the order of 10(5) by a linear mechanism even though all the eigenmodes decay monotonically. The methods suggested here apply also to other problems in the mathematical sciences that involve nonorthogonal eigenfunctions.

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An Experimental Investigation of the Circumstances Which Determine Whether the Motion of Water Shall Be Direct or Sinuous, and of the Law of Resistance in Parallel Channels

O. Reynolds (1883)

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Three‐dimensional optimal perturbations in viscous shear flow

Kathryn Butler, Brian F. Farrell (1992)

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Author and article information

Journal

Title: Physics of Fluids A: Fluid Dynamics

Abbreviated Title: Physics of Fluids A: Fluid Dynamics

Publisher: AIP Publishing

ISSN (Print): 0899-8213

Publication date Created: November 1993

Publication date (Print): November 1993

Volume: 5

Issue: 11

Pages: 2600-2609

Article

DOI: 10.1063/1.858894

SO-VID: da9f9344-4cea-4842-b9b4-febfbdee27f5

Copyright © © 1993

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