Robust Computations of Runup in Inclined U- and V-Shaped Bays

We present an exact analytical solution for computations of runup in constantly inclined U- and V-shaped bays. The provided solution avoids integration of indefinite double integrals in (Rybkin et al., Water Waves 3(1):267–296, 2021) and is based on a simple analytic expression for the Green’s function. We analyze wave runup in parabolic and certain V-shaped bays, for which a particularly wide class of solutions are determinable analytically and for which a robust computational algorithm could be developed. Our results are effective in the context of narrow bays, where a generalized form of the Carrier-Greenspan transformation has been developed.