On non-Kolmogorov turbulence in blood flow and its possible role in mechanobiological stimulation

Abstract

The study of turbulence in physiologic blood flow is important due to its strong relevance to endothelial mechanobiology and vascular disease. Recently, Saqr et al. (Sci Rep 10, 15,492, 2020) discovered non-Kolmogorov turbulence in physiologic blood flow in vivo, traced its origins to the Navier-Stokes equation and demonstrated some of its properties using chaos and hydrodynamic-stability theories. The present work extends these findings and investigates some inherent characteristics of non-Kolmogorov turbulence in monoharmonic and multiharmonic pulsatile flow under ideal physiologic conditions. The purpose of this work is to propose a conjecture for the origins for picoNewton forces that are known to regulate endothelial cells' functions. The new conjecture relates these forces to physiologic momentum-viscous interactions in the near-wall region of the flow. Here, we used high-resolution large eddy simulation (HRLES) to study pulsatile incompressible flow in a straight pipe of [Formula: see text]. The simulations presented Newtonian and Carreau-Yasuda fluid flows, at [Formula: see text], each represented by one, two and three boundary harmonics. Comparison was established based on maintaining constant time-averaged mass flow rate in all simulations. First, we report the effect of primary harmonics on the global power budget using primitive variables in phase space. Second, we describe the non-Kolmogorov turbulence in frequency domain. Third, we investigate the near-wall coherent structures in time and space domains. Finally, we propose a new conjecture for the role of turbulence in endothelial cells' mechanobiology. The proposed conjecture correlates near-wall turbulence to a force field of picoNewton scale, suggesting possible relevance to endothelial cells mechanobiology.

Figure 1

Boundary conditions waveforms presenting one harmonic (case 1 N/1CY), two harmonics (case 2 N/2CY) and three harmonics (case 3 N/3CY) where the X and Y axis represent dimensionless time and velocity values for one pulse.

Figure 2

The minimum and maximum values of $\stackrel{-}{M(x_i,t)}$ on y-axis for computational grids of 0.1, 0.5 and 1 million mesh cells for mesh1, mesh2 and mesh3, respectively.

Figure 3

Non-dimensional phase diagrams of pulsatile flow showing the effect of harmonics (one, two and three harmonics depicted in the top, middle and bottom rows, respectively). Black and red lines indicate Newtonian (N) and Carreau–Yasuda (CY) fluid models, respectively. Spatial non-similarity is shown by comparing the phase diagrams obtained at a center point (left column) and a near-wall pint 10 $\mu m$ from the wall (right column). Average values are calculated over one cycle for each simulation.

Figure 4

Turbulence Kinetic Energy E(f) cascade in frequency domain (f) at the center point (left column) and 10 $\mu m$ near-wall (right column). The depicted cascades present flows with one harmonic (n1), two harmonics (n1,n2) and three harmonics (n1,n2,n3) in the first, second and third rows, respectively. Black and red lines represent Newtonian and non-Newtonian fluids, respectively.

Figure 5

Iso-volumes of Q-criterion coloured by vorticity magnitude at $(0<Q\le 0.02,0\le \Vert \zeta \Vert \le 500)$ for different harmonics ($n$=1,2,3, columns) at different time instances of the cardiac cycle (rows, right) for Newtonian and non-Newtonian viscosity (N and CY, rows, left).