Abstract:
The well known Taylor-Couette flow, the flow between two rotating concentric cylinders
is used for studies on hydrodynamic stability, flow transitions and pattern formation
(Andereck et al., 1986; Benjamin, 1978a,b; Coles, 1965; Fardin et al., 2014; Grossmann
et al., 2016; Taylor, 1923, 1936a,b).
The concentric cylinder geometry was initially used by Henry Mallock and Maurice
Couette to measure viscosity of water (Couette, 1890; Mallock, 1889) and both came
up with this idea independently. Mallock (1889) rotated inner cylinder keeping the
outer cylinder fixed; he also did experiments with fixed inner cylinder and rotating
outer cylinder. He found that at high velocities simple laminar flow was replaced by a
complicated eddying flow. Couette (1890) kept the inner cylinder fixed and only rotated
the outer cylinder. He measured the viscosity of water and found that it was constant
up to a critical rotation rate.
Rayleigh (1917) derived the inviscid instability criterion for cylindrical Couette flow
between infinitely long concentric cylinders. He found that the flow is linearly stable if
only the outer cylinder rotates, i.e. inner cylinder is at rest. Another form of the criteria
is that the potential flow is unstable if the square of the circulation decreases outwards.
This implies that the flow is centrifugally unstable for any inner cylinder rotation rate
with a stationary outer cylinder.
