A Unified Perspective on Vortical and Interfacial Instabilities in Fluid Layers

Sandeep Saha¹Symphony Chakraborty^2*

• ¹Department of Aerospace Engineering, Indian Institute of Technology Kharagpur, Kharagpur, India
• ²Institute of Applied Mechanics, National Taiwan University, Taipei City, Taiwan

This work presents a comprehensive and unprecedented synthesis that unifies two fundamental, yet separately studied, paradigms of fluid instability: vortical disturbances in high-speed boundary layers and free-surface instabilities in ultra-thin liquid films. We critically examine the boundary layer instability mechanisms using the Orr-Sommerfeld/Squire (O-S/S) formalism, alongside its necessary extensions for hypersonic and multi-phase flows, with focus on the evolution of Tollmien-Schlichting (TS) waves, Görtler vortices, and streak-breakdown phenomena. In parallel, we explore thin-film dynamics via nonlinear long-wave models incorporating the interplay of gravity, surface tension, and complex rheological effects, capturing the physics of pattern formation, wave amplification, and film rupture. The core of this review is a first-of-its-kind comparative analysis that establishes a structural and mathematical equivalence between the two systems across the classic stages of receptivity, linear growth, and nonlinear saturation, despite their contrasting ultimate fates (transition to turbulence vs. catastrophic film rupture). We emphasize the multiphysics couplings and "shared governing principles, defining a new scope for theoretical modeling, particularly for hybrid instability scenarios" found in modern applications. The review concludes by identifying key open challenges in nonlinear predictive capabilities and advanced diagnostics, positioning this unified perspective as crucial for advancing technologies in aerospace drag reduction, microfluidics, and protective coating stability.