Fractal Scaling of Moffatt Vortices in Triangular Cavity Flow

Abstract

This study examines the formation, quantification, and fractal characterization of corner vortices in slow viscous incompressible flow within a triangular cavity. The governing Navier-Stokes equations are solved numerically using a pressure-based coupled solver, and the resulting vortex cascade is analyzed through the size and intensity ratios of successive eddies in the spirit of Moffatt's theory of corner vortices. The fractal properties of the vortex sequence are then investigated using the area-perimeter method. An empirical relation is proposed to estimate the fractal dimension of any successive vortex in the cascade for arbitrary grid resolution. The results demonstrate that the corner vortices possess non-integer fractal dimensions between 1 and 2, and that this dimension is systematically linked to vortex size and intensity. The influence of Reynolds number on the fractal scaling is also examined. Finally, a comparative analysis of self-similarity in triangular and square cavities confirms that the observed corner-vortex cascade exhibits robust fractal behavior across geometries and flow regimes.