| |
| According to the assumption of local equilibrium of non-equilibrium thermodynamics, each small mass element of a fluid is in local equilibrium under usual conditions, so it possesses not only a velocity of bulk translation but also an angular velocity of bulk rotation. Based on this consideration, a new set of hydrodynamic equations which includes a balance equation for angular momentum is presented. Starting from it, we split the motion of a fluid into two parts: a large-scale motion and a small-scale motion. It is shown that for the large-scale motion, Navier-Stokes equations, and thus all the results derived from it, remain valid. However for the small-scale motion in local high-shear regions, the interaction between the velocity and the angular velocity must be taken into consideration because of the high velocity shear. It is shown by numerical analyses with nonlinear wave interaction models that when the local shear flow becomes unstable, the small-scale disturbances may exhibit chaotic behavior if the velocity shear is large enough, which leads to the production of the turbulent spots in local high-shear regions. Based on the new hydrodynamic equations, we can explain the laminar-turbulent transition of shear flows through secondary instability (with the production of turbulent spots in local high-shear regions) and the direct transition from laminar flow to turbulent flow taking place in some cases (the so-called bypass process) consistently. We can also understand the large-scale quasi-ordered structures and the small-scale stochastic motions in a fully developed turbulent flow. |
|
| Keywords:turbulence, shear flow, chaos, hydrodynamic equations |
|
