The hydraulics of rotating-channel flow

Abstract

Flow of a homogeneous inviscid fluid down a rotating channel of slowly varying crosssection is considered, with particular reference to conditions under which the flow is ‘hydraulically controlled’. This problem is a member of a general class of problems of which gas flow through a nozzle and flow over a broad-crested weir are examples (Binnie 1949). A general discussion of such problems gives the means for determining the position of the control section (which is generally flow dependent) and shows that at this position there always exist long-wave disturbances with zero phase speed (i.e. disturbances are always ‘critical’ at the control section). The general theory is applied to the rotating-channel problem for the case of uniform potential vorticity. For this problem, three parameters are needed to specify the upstream flow, and the control theory gives a relationship between these parameters which depends on the geometry of the channel.