Figure 1
From: Understanding turbulent free-surface vortex flows using a Taylor-Couette flow analogy
The analogue between secondary flow in the (a) Taylor-Couette flow (TCF) system (b) a laminar free-surface vortex (FSV) and (c) a turbulent vortex flow in a vortex chamber. (d) and (e) are images of the TCF and the FSV. In (a) the classic Taylor-Couette flow system is outlined where the internal cylinder of diameter 2 r i is rotating at Ω i and the external chamber is stationary. Rotation of the inner cylinder introduces centrifugal instabilities in the secondary flow field, which manifest as Taylor-vortices. On the other hand, Figure (b) and (c) outlines the strong full air core laminar and turbulent free-surface vortex structure, which receives energy by inflow to impart rotation or circulation Γ∞ on the flow field resulting in a depression of the free-surface around the outlet producing an air core of diameter a c = 2r a . Taylor-like vortices superimposed on the flow processes outlined by Anwar10 and Daggett and Keulegan9 are presented in the secondary flow field of the vortex chamber together with an upwards flow in the far field as observed in this study. Figure 1 (f) provides a schematic example of ‘particle swaps’ of particles P1 and P2 demonstrating how the flow can become unstable as a result of the centrifugal driving force. The analogy between the Taylor-Couette and the free-surface vortex is realised if one replaces the air core a c region of the free-surface vortex with a virtual inner cylinder 2 r i rotating at the speed of the air core. In this way, equations representing the free-surface vortex flow field can be replaced with the angular velocity conditions of the virtual cylinder to yield equations for the TCF system. TCF flow image courtesy of Michael J. Burin63 (M.J. Burin, CSU San Marcos (2010)).
