Action of pressure fluctuations in turbulent flows – the principle of least effort

In incompressible fluid flow, pressure is a Lagrange multiplier whose sole function is to impose the divergence-free condition on the velocity field. While the role of pressure is well recognized, the manner in which pressure enforces the constraint is not well known. Understanding this action of pressure is important as it plays a critical role in determining characteristics of the turbulence small scales. Following our previous work (Das & Girimaji APS DFD 2018), we examine the hypothesis that pressure accomplishes its task with minimum action or least effort. In recent literature, it has been proven analytically that in elementary flows, pressure gradient is minimized following Gauss' principle of least constraint. For turbulent flows, such analytical treatment is not possible due to flow complexity, non-locality, and nonlinearity. We propose two metrics of pressure effort based on the principle of least constraint. Then, we use direct numerical simulation (DNS) data to demonstrate that pressure action in velocity-gradient dynamics is consistent with the simultaneous minimization of the two proposed metrics. The findings can lead to improved models for anisotropic pressure Hessian tensor.