Global stability analysis and direct numerical simulation of boundary layers with an isolated roughness element

TL;DR

This study combines global stability analysis and DNS to investigate boundary layer flows over isolated roughness elements, revealing how different instabilities influence vortex formation and transition to turbulence.

Contribution

It provides new insights into the dominant instability modes and their effects on vortex dynamics and turbulence development over roughness elements with varying aspect ratios.

Findings

Varicose instability dominates for η=1, leading to hairpin vortex shedding.

Sinuous instability becomes prominent at higher Re_h for η=0.5, causing vortex wiggling.

Different instability modes significantly affect the transition process and turbulence structure.

Abstract

Global stability analysis and direct numerical simulation (DNS) are performed to study boundary layer flows with an isolated roughness element. Wall-attached cuboids with aspect ratios $\eta=1$ and $\eta=0.5$ are investigated for fixed ratio of roughness height to displacement boundary layer thickness $h/\delta^*=2.86$. Global stability analysis is able to capture the frequency of the primary vortical structures. For $\eta=1$, only varicose instability is seen. For the thinner roughness element ($\eta=0.5$), the varicose instability dominates the sinuous instability, and the sinuous instability becomes more pronounced as $Re_h$ increases, due to increased spanwise shear in the near-wake region. The unstable modes mainly extract energy from the central streak, although the lateral streaks also contribute. The DNS results show that different instability features lead to different behavior and development of vortical structures in the nonlinear transition process. For $\eta=1$, the varicose mode is associated with the shedding of hairpin vortices. As $Re_h$ increases, the breakdown of hairpin vortices occurs closer to the roughness and sinuous breakdown behavior promoting transition to turbulence is seen in the farther wake. A fully-developed turbulent flow is established in both the inner and outer layers farther downstream when $Re_h$ is sufficiently high. For $\eta=0.5$, the sinuous wiggling of hairpin vortices is prominent at higher $Re_h$, leading to stronger interactions in the near wake, as a result of combined varicose and sinuous instabilities. A sinuous mode captured by dynamic mode decomposition (DMD) analysis, and associated with the `wiggling' of streaks persists far downstream.