Abstract
The previous chapters have been devoted to the linear theory of hydrodynamic instabilities. This means that only the development of disturbances with infinitesimal amplitude can be described reliably. As soon as larger amplitudes are obtained (through an instability, for example), the linearized equations are rendered invalid, and nonlinear effects become important and have to be taken into account. For wavelike disturbances Fourier components no longer evolve independently but are all coupled together through wave-triad interactions. Typically this implies that waves with larger wave numbers than those included in the initial conditions are needed to describe the nonlinearly developing solution. In physical space smaller scales are introduced and the evolution of the disturbance becomes more complicated.
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© 2001 Springer Science+Business Media New York
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Schmid, P.J., Henningson, D.S. (2001). Nonlinear Stability. In: Stability and Transition in Shear Flows. Applied Mathematical Sciences, vol 142. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0185-1_5
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DOI: https://doi.org/10.1007/978-1-4613-0185-1_5
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