On the intracyclic instability in Stokes layers

TL;DR

This paper investigates the intracyclic instability in Stokes layers using FTLE analysis, revealing a linear energy amplification mechanism that explains observed turbulence, and compares favorably with experimental data.

Contribution

It introduces FTLE-based analysis to explain intracyclic instability in Stokes layers, providing new insights beyond traditional Floquet and instantaneous analyses.

Findings

Linear energy amplification explains intracyclic instability.

Energy amplification decreases with more confined Stokes layers.

Oscillating frequency non-monotonically affects transient growth.

Abstract

Time-dependent fluid dynamics plays a crucial role in both natural phenomena and industrial applications. Understanding the flow instabilities and transitions within these dynamical systems is essential for predicting and controlling their unsteady behaviour. A classic example of time-dependent flow is the Stokes layer. To study the transition mechanism in this flow, we employ the Finite-Time Lyapunov Exponent (FTLE) to demonstrate that a linear energy amplification mechanism may explain the intracyclic instability in the transitional Stokes layer, supported by favourable comparisons with experimental measurements of axial turbulence intensity. This complements existing theories applied to the Stokes layer in the literature, including the Floquet analysis and the instantaneous/momentary analyses, which have struggled to capture this experimental observation accurately. The FTLE analysis is closely related to the transient growth analysis, formulated as an optimisation problem of the disturbance energy growth over time. We found that the energy amplification weakens as the finite Stokes layer becomes more confined and the oscillating frequency has a non-monotonic effect on the maximum transient growth. Based on these results, we recommend future experimental studies to validate this linear mechanism.