Vanishing or Transforming? The journey of classical instabilities from continuum to rarefied Flows

In fluid and gas dynamics, instabilities play a fundamental role in shaping flow behavior. However, instability evolution is profoundly influenced by the Knudsen number (Kn), which quantifies the degree of rarefaction. This talk investigates the transformation of classical instabilities—such as Kelvin-Helmholtz, Rayleigh-Taylor, and lid-driven cavity—as flow transitions from the well-understood continuum regime (Kn ≪ 1) to the more elusive rarefied and ballistic regimes (Kn ≫ 1). The Mach number (Ma) also plays a crucial role in modulating these instabilities, adding another layer of complexity. At high Kn, collective interactions weaken, leading to the suppression of familiar instability patterns, such as vortical structures. Yet, as Kn increases from small values, the onset of rarefaction effects can lead to surprising and counterintuitive behavior. This talk explores the intricate interplay between solenoidal (characterized by Reynolds number, Re), dilatational (Ma), and ballistic (Kn) flow fields, drawing on theoretical insights, numerical simulations, and experimental observations. This journey across scales—from continuum flows to near-collisionless ballistic motion— uncovers some surprising flow mechanisms. The results offer valuable insights into instability behavior in high-altitude aerodynamics, space propulsion, and microfluidics.