LAUSR

This develops a recent analysis of gentle undular tidal bores (New. J. Phys. 20 (2018) 053066) and corrects an error. The simplest linear-wave superposition, of monochromatic waves propagating according to the shallow-water dispersion relation, leads to a family of profiles, satisfying natural tidal bore boundary conditions. These profiles can be uniformly approximated to high accuracy in terms of the integral of an Airy function with deformed argument. For the long times corresponding to realistic bores, the profiles condense asymptotically onto the previously obtained integral-Airy function with linear argument, but this now expands slowly as the cube root of time rather than advancing rigidly. This 'minimal model' leads to simple formulas for the main properties of the profile: amplitude, maximum slope, 'wavelength', and steepness; and an assumption about energy loss suggests how the bore weakens as it propagates.