Proc. R. Soc. A (2011) 467, 1215–1242 doi:10.1098/rspa.2010.0331 Published online 10 November 2010 Reynolds averaged Navier–Stokes modelling of long waves induced by a transient wave group on a beach BY JAVIER L. LARA*, ANDREA RUJU AND INIGO J. LOSADA Environmental Hydraulics Institute ‘IH Cantabria’, Universidad de Cantabria, Avda. de los Castros s/n, Santander 39005, Spain This paper presents the numerical modelling of the cross shore propagation of infragravity waves induced by a transient focused short wave group over a sloping bottom. A dataset obtained through new laboratory experiments in the wave flume of the University of Cantabria is used to validate the Reynolds averaged Navier–Stokes type model IH- 2VOF. A new boundary condition based on the wave maker movement used in the experiments is implemented in the model. Shoaling and breaking of short waves as well as the enhancement of long waves and the energy transfer to low-frequency motion are well addressed by the model, proving the high accuracy in the reproduction of surf zone hydrodynamics. Under the steep slope regime, a long wave trough is radiated offshore from the breakpoint. Numerical simulations conducted for different bottom slopes and short wave steepness suggest that this low-frequency breakpoint generated wave is controlled by both the bed slope parameter and the Iribarren number. Moreover, the numerical model is used to investigate the influence that a large flat bottom induces on the propagation pattern of long waves. Keywords: surf zone; transient wave groups; infragravity waves; RANS 1. Introduction Sea surface records show the presence of groups of high and low waves as a result of the superposition of wave components with different frequencies. Since in sufficiently deep water, gravity waves are frequency dispersive, the groups are transient. Although the presence of transient groups in the wave field is the result of merely linear processes, nonlinear effects are not negligible in the focused wave groups. Local nonlinear interactions in conjunction with the focusing of wave energy lead to large waves with high and narrow crests that can break even in the deep ocean (Rapp & Melville 1990). Moreover, global nonlinear interactions produce low-frequency changes such as slow varying currents and oscillations of the mean water level known as infragravity waves. In nature, typical periods of wind waves are in the order of 10 s, while infragravity motion evolves slowly with a typical period of several minutes. Two main generation mechanisms have been identified for these low-frequency waves. *Author for correspondence (lopezjav@unican.es). Received 23 June 2010 Accepted 14 October 2010 This journal is © 2010 The Royal Society 1215