A theory is developed for the speed and structure of steady-state non-dissipative gravity
currents in rotating channels. The theory is an extension of that of Benjamin (1968)
for non-rotating gravity currents, and in a similar way makes use of the steady-state
and perfect-fluid (incompressible, inviscid and immiscible) approximations, and supposes
the existence of a hydrostatic ‘control point’ in the current some distance away
from the nose. The model allows for fully non-hydrostatic and ageostrophic motion
in a control volume V ahead of the control point, with the solution being determined
by the requirements, consistent with the perfect-fluid approximation, of energy and
momentum conservation in V, as expressed by Bernoulli's theorem and a generalized
flow-force balance. The governing parameter in the problem, which expresses the
strength of the background rotation, is the ratio W = B/R, where B is the channel
width and R = (g′H)1/2/f
is the internal Rossby radius of deformation based on the
total depth of the ambient fluid H. Analytic solutions are determined for the particular
case of zero front-relative flow within the gravity current. For each value of W there is a unique
non-dissipative two-layer solution, and a non-dissipative one-layer solution which is specified by the value of the
wall-depth h0. In the two-layer case, the non-dimensional propagation speed
c = cf(g′H)−1/2 increases smoothly
from the non-rotating value of 0.5 as W increases, asymptoting to unity for W → ∞. The
gravity current separates from the left-hand wall of the channel at W = 0.67 and thereafter
has decreasing width. The depth of the current at the right-hand wall, h0, increases,
reaching the full depth at W = 1.90, after which point the interface outcrops on both
the upper and lower boundaries, with the distance over which the interface slopes being 0.881R. In the
one-layer case, the wall-depth based propagation speed Froude number c0
= cf(g′h0)−1/2 = 21/2,
as in the non-rotating one-layer case. The current separates from the left-hand wall of the channel at
W0 ≡ B/R0 = 2−1/2, and thereafter
has width 2−1/2R0, where
R0 = (g′h0)1/2/f is the
wall-depth based deformation radius.