A nonmodal stability analysis of the boundary layer under solitary waves
Abstract
In the present treatise, a stability analysis of the bottom boundary layer under solitary waves based on energy bounds and nonmodal theory is performed. The instability mechanism of this flow consists of a competition between streamwise streaks and two- dimensional perturbations. For lower Reynolds numbers and early times, streamwise streaks display larger amplification due to their quadratic dependence on the Reynolds number, whereas two-dimensional perturbations become dominant for larger Reynolds numbers and later times in the deceleration region of this flow, as the maximum amplification of two-dimensional perturbations grows exponentially with the Reynolds number. By means of the present findings, we can give some indications on the physical mecha- nism and on the interpretation of the results by direct numerical simulation in (Vittori & Blondeaux 2008; Ozdemir et al. 2013) and by experiments in (Sumer et al. 2010). In addition, three critical Reynolds numbers can be defined for which the stability prop- erties of the flow change. In particular, it is shown that this boundary layer changes from a monotonically stable to a non-monotonically stable flow at a Reynolds number of 18.
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Cite
@article{arxiv.1701.00025,
title = {A nonmodal stability analysis of the boundary layer under solitary waves},
author = {Joris C. G. Verschaeve and Geir K. Pedersen and Cameron Tropea},
journal= {arXiv preprint arXiv:1701.00025},
year = {2017}
}