Journal
WAVE MOTION
Volume 47, Issue 8, Pages 564-582Publisher
ELSEVIER
DOI: 10.1016/j.wavemoti.2010.04.003
Keywords
Spatio-temporal stability analysis; Normal-mode analysis; Convective instability; Absolute instability; Jump-periodic boundary conditions; Transient growth
Categories
Funding
- NSF [CTS-0138057, MSM-8817372]
- St. Lawrence STEM Partnership
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Integral solutions are found for linear wave equations which depending on the parameters exhibit either absolute or convective instability Series solutions are constructed to examine the instability behavior on a bounded domain Solutions with non-real wave-numbers can be interpreted as a superposition of eigenmodes with jump-periodic boundary conditions We show that an initial disturbance can be represented by not only periodic modes but also spatially growing (or decaying) modes and arbitrary modes using a Galerkin approach For the examples presented here growth in any such series solution matches the growth predictions obtained from the long-time asymptotic behavior of the integral solutions (c) 2010 Elsevier B V All rights reserved
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