Mixing in fluvial systems, as characterised by longitudinal dispersion, may be thought intuitively to scale with the river discharge or flow rate. Here, this tenet is demonstrated theoretically to be well-founded during normal flows but to be perfidious during flood conditions. The results suggest that during goods longitudinal mixing rates in rivers can be several orders of magnitude larger than during normal flows and can actually decrease with further increases in flow magnitude. The very large longitudinal dispersion coefficients found during extreme flows cannot be predicted using existing empirical equations; neither can the rapid decrease with increasing flow rate. This is not surprising because these equations do not cater for the extremely strong transverse velocity shear that exists in these flows that contain zones of quite different velocity and depth. The conclusions are important because it appears that the great majority of observations of fluvial mixing have been made during normal flows when a scaling with flow rate occurs. During floods, however, this behaviour switches and longitudinal dispersion scales inversely and non-linearly with flow rate. Copyright 2004 by the American Geophysical Union.