A nonmodal stability analysis of the boundary layer under solitary waves

TL;DR

This paper investigates the stability of the boundary layer under solitary waves using energy bounds and nonmodal theory, revealing how different perturbations dominate at various Reynolds numbers and times, and identifying critical Reynolds numbers for flow stability transitions.

Contribution

It introduces a nonmodal stability analysis of the boundary layer under solitary waves, highlighting the competition between streaks and two-dimensional perturbations and identifying stability transition Reynolds numbers.

Findings

Streamwise streaks dominate at low Reynolds numbers and early times.

Two-dimensional perturbations become dominant at higher Reynolds numbers and later times.

Flow transitions from stable to non-monotonically stable at Re = 18.

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.