MATLAB Code for Rayleigh–Couette Flow with Airy-Mode Shear Structures, Resonance Conditions, and Countercurrent Visualization

This MATLAB code provides a comprehensive analysis of Rayleigh-Couette flow with Rayleigh friction, a fundamental configuration in fluid dynamics. The implementation focuses on resonant shear modes, velocity profiles, and the emergence of countercurrents in a viscous layer between moving boundaries.

The computational package generates eight distinct figures:

Resonance conditions in the parameter space (velocity versus angle)

Comparative velocity profiles (Rayleigh versus classical Couette flow)

Shear modal structures obtained from Airy function solutions

Two-dimensional velocity vector fields

Influence of the friction coefficient on the flow structure

Development of countercurrents at different transverse coordinates

Spatial mapping of reverse flow regions in the (y,z) plane

Visualization of vortex structures and streamlines

Key features include parametric resonance analysis, modal decomposition of shear layers, identification of reverse flow conditions, and comprehensive flow field visualization. The code uses built-in MATLAB functions without requiring specialized toolboxes.

This resource is intended for researchers in fluid mechanics, applied mathematics, and engineering, serving both as an educational demonstration and a research tool for boundary layer flows with friction effects. The modular code structure allows easy modification of parameters for various physical scenarios.