Тейлор-Куэтт ағыны: тұрақсыздық пен турбуленттілік құбылыстары

In fluid dynamics, the Taylor–Couette flow consists of a viscous fluid confined in the gap between two rotating cylinders. For low angular velocities, measured by the Reynolds number Re, the flow is steady and purely azimuthal. This basic state is known as circular Couette flow, after Maurice Marie Alfred Couette, who used this experimental device as a means to measure viscosity. Sir Geoffrey Ingram Taylor investigated the stability of Couette flow in a ground breaking paper. Taylor's paper became a cornerstone in the development of hydrodynamic stability theory and demonstrated that the no slip condition, which was in dispute by the scientific community at the time, was the correct boundary condition for viscous flows at a solid boundary. Taylor showed that when the angular velocity of the inner cylinder is increased above a certain threshold, Couette flow becomes unstable and a secondary steady state characterized by axisymmetric toroidal vortices, known as Taylor vortex flow, emerges. Subsequently, upon increasing the angular speed of the cylinder the system undergoes a progression of instabilities which lead to states with greater spatio temporal complexity, with the next state being called wavy vortex flow. If the two cylinders rotate in opposite sense then spiral vortex flow arises. Beyond a certain Reynolds number there is the onset of turbulence. Circular Couette flow has wide applications ranging from desalination to magnetohydrodynamics and also in viscosimetric analysis. Different flow regimes have been categorized over the years including twisted Taylor vortices and wavy outflow boundaries. It has been a well researched and documented flow in fluid dynamics.

Lord Rayleigh studied the stability of the problem with inviscid assumption i. e., perturbing Euler equations. The criterion states that in the absence of viscosity the necessary and sufficient condition for distribution of azimuthal velocity to be stable is

everywhere in the interval; and, further, that the distribution is unstable if should decrease anywhere in the interval. Since represents angular momentum per unit mass, of a fluid element about the axis of rotation, an alternative way of stating the criterion is: a stratification of angular momentum about an axis is stable if and if only it increases monotonically outward. Applying this criterion to the Taylor Couette flow indicates that the flow is stable if , i. e., for stability, the outer cylinder must rotate (in the same sense) with an angular speed greater than times that of the inner cylinder. The Rayleigh's criterion is violated throughout the whole fluid when On the other hand, when the cylinders rotate in opposite directions, i. e., when , Rayleigh's criterion is violated only in the inner region, i. e., for where .

In 1975, J. P. Gollub and H. L. Swinney published a paper on the onset of turbulence in rotating fluid. In a Taylor–Couette flow system, they observed that, as the rotation rate increases, the fluid stratifies into a pile of "fluid donuts". With further increases in the rotation rate, the donuts oscillate and twist and finally become turbulent. Their study helped establish the Ruelle–Takens scenario in turbulence, which is an important contribution by Floris Takens and David Ruelle towards understanding how hydrodynamic systems transition from stable flow patterns into turbulent. While the principal, governing factor for this transition is the Reynolds number, there are other important influencing factors: whether the flow is open (meaning there is a lateral up and downstream) or closed (flow is laterally bound; e. g. rotating), and bounded (influenced by wall effects) or unbounded (not influenced by wall effects). According to this classification the Taylor–Couette flow is an example of a flow pattern forming in a closed, bounded flow system.