Free and Forced Components of Shoaling Long Waves in the Absence of Short-Wave Breaking

Abstract Long waves are generated and transform when short-wave groups propagate into shallow water, but the generation transformation processes not fully understood. In this study we develop an analytical solution to linearized shallow-water equations at wave-group scale, which decomposes long a forced (a bound wave) free solutions (free waves). The relies on hypothesis that continuously as over varying depth. We show superposition of wave results in shift phase between group total wave, depth decreases prior breaking. While it is known breaking leads free-long-wave generation, through breakpoint forcing bound-wave release mechanisms, highlight importance additional mechanism due variations, absence This important because different origins combine, amplitude dependent their relationship. Our verified against linear numerical model, how our consistent with theory does explicitly decouple motions. also validate data from nonlinear phase-resolving model experimental measurements, demonstrating can explain trends observed more complete representations hydrodynamics.