Rogue waves in opposing currents

When a perfectly stable wave or wave packet enters into a region of strong adverse current gradient (an accelerating opposing current or a decelerating following current), its dynamical behaviour is expected to change. As such, waves become higher and shorter. This increases wave steepness, which in turn enhances nonlinear properties. As a result, the interaction with the current amplifies wave modulation and accelerates nonlinear wave focusing. If enough space is allowed for wave evolution, rogue waves will appear eventually, even if the initial wave conditions are less prone

to extremes. An example of wave evolution on an adverse current in a laboratory facility is shown in Fig. 1.

FIGURE 1: Spatial evolution of an initially stable wave packet over an opposing current: no current U/cg = 0, with U the background current and cg the group velocity, (left panel); with current U/cg = 0.1 (right panel).

To verify the effect of an opposing current on wave dynamics, a theoretical study (Onorato et al. 2011) and laboratory experiments in three independent facilities (Toffoli et al. 2015) were carried out. Results demonstrate in a consistent and robust manner that opposing currents induce a modification of nonlinear dynamics (see Fig. 2). For random sea state, this means that a sharp and rapid transition from weakly to strongly non-Gaussian properties occurs. This is associated with a substantial increase in the probability of occurrence of rogue waves for both unidirectional and directional sea states (Toffoli et al. 2015), for which the occurrence of extreme and rogue waves is normally the least expected (see Figs. 2 and 3).

Figure 2: Effect on an opposing current on regular and irregular wave fields (unidirectional case)

FIGURE 3: Exceedance probability of wave crests for a directional sea state with spreading coefficient N = 50 (a narrow swell).