  Intuitively, crest speeds of water waves are assumed to match their phase
velocities. However, this is generally not the case for natural waves within
unsteady wave groups. This motivates our study, which presents new insights
into the generic behavior of crest speeds of linear to highly nonlinear
unsteady waves. While our major focus is on gravity waves where a generic crest
slowdown occurs cyclically, results for capillary-dominated waves are also
discussed, for which crests cyclically speed up. This curious phenomenon arises
when the theoretical constraint of steadiness is relaxed, allowing waves to
change their form, or shape. In particular, a kinematic analysis of both
simulated and observed open ocean gravity waves reveals a forward-to-backward
leaning cycle for each individual crest within a wave group. This is clearly
manifest during the focusing of dominant wave groups essentially due to the
dispersive nature of waves. It occurs routinely for focusing linear
(vanishingly small steepness) wave groups, and it is enhanced as the wave
spectrum broadens. It is found to be relatively insensitive to the degree of
phase coherence and focusing of wave groups. The nonlinear nature of waves
limits the crest slowdown. This reduces when gravity waves become less
dispersive, either as they steepen or as they propagate over finite water
depths. This is demonstrated by numerical simulations of the unsteady evolution
of 2D and 3D dispersive gravity wave packets in both deep and intermediate
water depths, and by open ocean space-time measurements.
