Analysis of coherent structures in plane and ribbed channel flows: insights from proper orthogonal decomposition

This study employs proper orthogonal decomposition (POD) to analyse coherent structures in turbulent flows within plane and surface-mounted longitudinally ribbed channels. Three cases are examined: plane channel flows at Reynolds numbers 180 and 550, and ribbed channel flow at Reynolds number 550. The Reynolds number is defined by friction velocity and channel height ( H ). The ribs have dimensions of 0.2 H in width and 0.1 H in height, spaced 0.8 H apart. This study highlights the differences in flow dynamics between smooth and ribbed channels by comparing energy distributions and dominant POD modes. The first two POD modes capture cut sections of large hairpin vortices, highlighting significant structures, while small-scale structures remain unaffected by the ribs, confirmed by out-of-plane velocity analysis. Careful selection of energy cut-offs for velocity reconstruction enhances the identification of dominant structures. The scatter plot of first two POD coefficients for the plane and ribbed channel cases indicates a strong relationship between the first two modes. Quadrant analysis at varying energy levels reveals Reynolds-stress events, including sweeps, ejections and inward–outward interactions. Most energetic POD mode shows dominance of inward and outward turbulent transport at the rib-top surface over sweep and ejection modes indicating modification of secondary flows.