New linear theory of hydrodynamic instability of the Hagen - Poiseuille flow and the blood swirling flows formation

Abstract

Aims This paper deals with solving of a century-old paradox of linear stability for the Hagen-Poiseuille flow. A new mechanism of dissipative hydrodynamic instability has been established herein, and a basis for the forming of helical structural organization of bloodstream and respective energy effectiveness of the cardiovascular system functioning has been defined by the authors. Materials and methods Theory of hydrodynamic instability, Galerkin's approximation. Results A new condition Re > Re-thmin approximate to 124 of linear (exponential) instability of the Hagen-Poisseuille (HP) flow with respect to extremely small by magnitude axially-symmetric disturbances of the tangential component of the velocity field is obtained. The disturbances necessarily shall have quasi-periodic longitudinal variability along the pipe axis that corresponds to the observed data. Conclusion We show that the obtained estimate of value of Re-thmin corresponds to the condition of independence of the main result (on the linear instability of the HP flow when Re > Re-thmin) from the procedure of averaging used in the Galerkin approximation. Thus, we obtain the possible natural mechanism for the blood swirling flows formations observed in the aorta and the large blood vessels.