A Viscous Velocity Potential/Stream Function

The motion of fluids presents interesting phenomena including flow separation, wakes, turbulence etc. The physics of these are enshrined in the continuity equation and the NSE. Therefore, their studies are important in mathematics and physics. They also have engineering applications. These studies can either be carried out experimentally, numerically, or theoretically. Theoretical studies using classical potential theory (CPT) have some gaps when compared to experiments. The present publication is part of a series introducing refined potential (RPT) that bridges these gaps. It leverages experimental observations, physical deductions and the match between CPT and experimentally observed flows in the theoretical development. It analytically imitates the numerical source/vortex panel method to describe how wall bounded eddies in a three-dimensional cylinder crossflow are linked to the detached wake eddies. Unlike discrete and arbitrary vortices/sources on the cylinder surface whose strengths are numerically determined in the panel method, the vortices/sources/sinks in RPT are mutually concentric and continuously distributed on the cylinder surface. Their strengths are analytically determined from CPT using physical deductions starting from Reynolds number dependence. This study results in the incompressible Kwasu function which is a Eulerian velocity potential/stream function that captures vorticity, boundary layer, shed wake vortices, three-dimensional effects, and turbulence. This Eulerian Kwasu function also theorizes streaklines. The Lagrangian form of the function is further exploited to obtain flow pathlines.

Reynolds stress scaling in the near-wall region of wall-bounded flows

A new scaling is derived that yields a Reynolds-number-independent profile for all components of the Reynolds stress in the near-wall region of wall-bounded flows, including channel, pipe and boundary layer flows. The scaling demonstrates the important role played by the wall shear stress fluctuations and how the large eddies determine the Reynolds number dependence of the near-wall turbulence behaviour.

Fluctuation-induced force in homogeneous isotropic turbulence

Understanding force generation in nonequilibrium systems is a notable challenge in statistical physics. We uncover a fluctuation-induced force between two plates immersed in homogeneous isotropic turbulence using direct numerical simulations. The force is a nonmonotonic function of plate separation. The mechanism of force generation reveals an intriguing analogy with fluctuation-induced forces: In a fluid, energy and vorticity are localized in regions of defined length scales. When varying the distance between the plates, we exclude energy structures modifying the overall pressure on the plates. At intermediate plate distances, the intense vorticity structures (worms) are forced to interact in close vicinity between the plates. This interaction affects the pressure in the slit and the force between the plates. The combination of these two effects causes a nonmonotonic attractive force with a complex Reynolds number dependence. Our study sheds light on how length scale–dependent distributions of energy and high-intensity vortex structures determine Casimir forces.