In fluid dynamics, the radiation stress is the depth-integrated – and thereafter phase-averaged – excess momentum flux caused by the presence of the surface gravity waves, which is exerted on the mean flow. The radiation stresses behave as a second-order tensor. The radiation stress tensor describes the additional forcing due to the presence of the waves, which changes the mean depth-integrated horizontal momentum in the fluid layer. As a result, varying radiation stresses induce changes in the mean surface elevation (wave setup) and the mean flow (wave-induced currents). For the mean energy density in the oscillatory part of the fluid motion, the radiation stress tensor is important for its dynamics, in case of an inhomogeneous mean-flow field. The radiation stress tensor, as well as several of its implications on the physics of surface gravity waves and mean flows, were formulated in a series of papers by Longuet-Higgins and Stewart in 1960–1964. Radiation stress derives its name from the analogous effect of radiation pressure for electromagnetic radiation. Physical significance The radiation stress – mean excess momentum-flux due to the presence of the waves – plays an important role in the explanation and modeling of various coastal processes: Wave setup and setdown – the radiation stress consists in part of a radiation pressure, exerted at the free surface elevation of the mean flow. If the radiation stress varies spatially, as it does in the surf zone where the wave height reduces by wave breaking, this results in changes of the mean surface elevation called wave setup (in case of an increased level) and setdown (for a decreased water level); Wave-driven current, especially a longshore current in the surf zone – for oblique incidence of waves on a beach, the reduction in wave height inside the surf zone (by breaking) introduces a variation of the shear-stress component Sxy of the radiation stress over the width of the surf zone. This provides the forcing of a wave-driven longshore current, which is of importance for sediment transport (longshore drift) and the resulting coastal morphology; Bound long waves or forced long waves, part of the infragravity waves – for wave groups the radiation stress varies along the group. As a result, a non-linear long wave propagates together with the group, at the group velocity of the modulated short waves within the group. While, according to the dispersion relation, a long wave of this length should propagate