# Stability of slip channel flow revisited

## TL;DR

This study revisits the stability of slip channel flow, revealing that anisotropic slip can induce three-dimensional instabilities and significantly alter flow stability, with implications for flow control and understanding of slip effects.

## Contribution

It provides a detailed analysis of how streamwise and spanwise slip individually affect flow stability, extending previous work by exploring a broader slip range and anisotropic slip effects.

## Key findings

- Large spanwise slip decreases critical Reynolds number significantly.
- Streamwise slip suppresses transient growth, while spanwise slip enlarges it.
- Equal slip in both directions stabilizes the flow and eliminates 3D instabilities.

## Abstract

In this work, we revisit the temporal stability of slip channel flow. Lauga & Cossu (Phys. Fluids 17, 088106 (2005)) and Min & Kim (Phys. Fluids 17, 108106 (2005)) have investigated both modal stability and non-normality of slip channel flow and concluded that the velocity slip greatly suppresses linear instability and only modestly affects the non-normality. Here we study the stability of channel flow with streamwise and spanwise slip separately as two limiting cases of anisotropic slip and explore a broader range of slip length than previous studies did. We find that, with sufficiently large slip, both streamwise and spanwise slip trigger three-dimensional leading instabilities. Overall, the critical Reynolds number is only slightly increased by streamwise slip, whereas it can be greatly decreased by spanwise slip. Streamwise slip suppresses the non-modal transient growth, whereas spanwise slip enlarges the non-modal growth although it does not affect the base flow. Interestingly, as the spanwise slip length increases, the optimal perturbations exhibit flow structures different from the well-known streamwise rolls. However, in the presence of equal slip in both directions, the three-dimensional leading instabilities disappear and the flow is greatly stabilized. The results suggest that earlier instability and larger transient growth can be triggered by introducing anisotropy in the velocity slip.