|
|
Articles
Hydrodynamic Stability Without Eigenvalues
1 Department of Computer Science, Cornell University, Ithaca, NY 14853 (Int@cs.cornell.edu)
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 105 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.
THIS ARTICLE HAS BEEN CITED BY OTHER ARTICLES:
|
Science. ISSN 0036-8075 (print), 1095-9203 (online)
Magazine | News | Signaling | Careers | Multimedia | Collections | Help | Site Map | RSS
Subscribe | Feedback | Privacy / Legal | About Us | Advertise With Us | Contact Us
© 1993 American Association for the Advancement of Science. All Rights Reserved.
AAAS is a partner of HINARI, AGORA, PatientInform, CrossRef, and COUNTER.
You have reached the bottom of the page. Back to top