Temporal stability of asymptotic suction boundary layer with spectral collocation method

TL;DR

This study investigates the temporal stability of the asymptotic suction boundary layer using spectral collocation, identifying critical Reynolds numbers and effects of spanwise disturbances on transition delay.

Contribution

It applies spectral collocation to analyze the stability of the boundary layer and explores how spanwise disturbances influence transition delay.

Findings

Critical Reynolds number identified at 47145 for specific wavenumber.

Spectral collocation effectively solves the stability eigenvalue problem.

Spanwise disturbances can delay laminar-to-turbulent transition.

Abstract

In this paper, the linear stability theory of an incompressible asymptotic suction boundary layer was studied. A small disturbance was introduced spatially in a streamwise direction to the laminar base flow with various wavenumber $\alpha = 0.01 - 0.3$ to investigate its temporal stability. A spectral collocation method was used to solve the fourth-order ordinary differential equation (ODE) of the generalized eigenvalues problem. From the neutral stability curve, the result showed that the critical Reynolds number occurred at $Re_{c}= 47145$ for $\alpha=0.161$. By taking into account that the disturbance traveled in spanwise direction, the transition can be delayed.