Abstract
Primary and secondary instabilities arising in fluid flows need not have the same absolute/convective character. The Newell-Whitehead-Segel evolution model is chosen to illustrate this phenomenon. It is shown that the Eckhaus instability can be either absolute or convective in a parameter domain of absolute primary instability. In the case of the cubic Nonlinear Schrodinger Equation, the Benjamin-Feir instability is determined to be absolute as soon as the amplitude of the Stokes wavetrain exceeds a certain threshold. These two problems also provide simple examples of application of the absolute/convective instability criterion.
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Huerre, P. (1988). On the Absolute/Convective Nature of Primary and Secondary Instabilities. In: Wesfreid, J.E., Brand, H.R., Manneville, P., Albinet, G., Boccara, N. (eds) Propagation in Systems Far from Equilibrium. Springer Series in Synergetics, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73861-6_33
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DOI: https://doi.org/10.1007/978-3-642-73861-6_33
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