A comprehensive investigation of the energy and enstrophy cascade in physical space in a turbulent channel flow is presented for four Reynolds numbers. Bandpass filtering techniques are employed to isolate scales and quantify inter-scale interactions through kinetic energy flux, enstrophy generation, and enstrophy flux. Two bandpass filter formulations used in the literature are quantitatively assessed by comparing the output.

The mean energy and enstrophy cascades are shown to be predominantly local for all the Reynolds numbers. Away from the wall, the degree of locality decreases while a broader range of scales participate in the cascade. Interestingly the distance at which the inter-scale flux peaks shows a distance-from-wall scaling, implying relevance of the attached-eddy formalism to energy cascade in scale space (in addition to its relation ​ to momentum transport in physical space). Vorticity stretching as the underlying mechanism of cascade is studied through vorticity alignment statistics. The vortices show preferential alignment with intermediate eigenvector for smaller scale ratios and closer to the wall, while alignment with the most extensional eigenvector is observed at larger scale ratios and away from the wall. The preferential alignment shows a complex dependence on the wall-normal distance, suggesting that the wall has important influence on both energy transfer rates and the geometry of structures. Notwithstanding this, the contribution from most extensional eigenvector dominates enstrophy generation for all conditions. The scaling of energy flux with scale size, scale ratio, wall-normal distance, and Reynolds number is obtained using dimensional arguments and is validated against numerical results.  As the cascade progresses, the energy at small scales gets concentrated in a small region of space, reflected as intermittency in enstrophy and energy fluxes. The skewness and kurtosis increase at smaller length scales but they show weak increase with the Reynolds number. The morphology of energy flux and enstrophy iso-surfaces are characterized through Minkowski functionals. Enstrophy structures at small scales are like flattened long tubes, while large-scale structures are blob-like or short-tube-like. The large-scale structures generally exhibit lower values of filamentarity. Energy flux structures show a similar behaviour, with near-wall structures being more flattened compared to those farther from the wall. These findings remain unaffected by an increase in threshold for getting the iso-surfaces.

Overall, the present study provides new insights into the locality, scaling, and morphology of the energy and enstrophy cascade in the channel flow, offering a unified framework for interpreting multi-scale turbulence dynamics in wall-bounded flows.

Speaker :  Aditya Anand

Research Supervisor :  Sourabh Suhas Diwan