Laboratory measurements of limiting freak waves on currents

Abstract

[1] The results of laboratory measurements on limiting freak waves in the presence of currents are reported. Both dispersive spatial-temporal focusing and wave-current interaction are used to generate freak waves in a partial random wave field in the presence of currents. Wave group structure, for example, spectral slope and frequency bandwidth, is found to be critical to the formation and the geometric properties of freak waves. A nondimensional spectral bandwidth is shown to well represent wave group structure and proves to be a good indicator in determining limiting freak wave characteristics. The role of a co-existing current in the freak wave formation is recognized. Experimental results confirm that a random wave field does not prevent freak wave formation due to dispersive focusing. Strong opposing currents inducing partial wave blocking significantly elevate the limiting steepness and asymmetry of freak waves. At the location where a freak wave occurs, the Fourier spectrum exhibits local energy transfer to high-frequency waves. The Hilbert-Huang spectrum, a time-frequency-amplitude spectrum, depicts both the temporal and spectral evolution of freak waves. A strong correlation between the magnitude of interwave instantaneous frequency modulation and the freak wave nonlinearity (steepness) is observed. The experimental results provide an explanation to address the occurrence and characteristic of freak waves in consideration of the onset of wave breaking.

Occurrence and Breaking of Rogue Waves in Deep Waters: A Stochastic Approach Revisit

“…These relationships suggest that the local maximum steepness (ak) cr of rogue waves may be a function of the spectral bandwidth , as the latter is a function of § , provided that § and 1 are interrelated. This finding is consistent with the results of Wu and Yao ( [5], cf. their Fig.…”

“…), and on whether the orbital velocity (at the wave crest), c orb u , on the RHS of the first inequality (18) is compared with the phase velocity, c, or with the group velocity, C g . Phillips [13] and Longuet-Higgins [27] have suggested =1, for spilling breakers, whereas Wu and Yao [5] have suggested = 0.5 (as C g = 0.5c). On the other hand, Wu and Nepf [26] have suggested = 1.5 for plunging breakers.…”

“…The investigations of Wu and Yao [5] and Wu and Nepf [26] have added new insights, with respect to the breaking criteria that Phillips [13] and Longuet-Higgins [27] had suggested much earlier for spilling breaking and other types of wave breaking, in the presence or absence of swell. Among the three categories of breaking criteria used, namely the kinematic, dynamic, and the slope (or geometric) criterion, it appears that the kinematic one is the most fundamental.…”

“…In summary, rogue waves may be generated by meteorological, dispersive and/or topographic focusing, wave-current and wave-wave interactions. The generation of rogue waves can also be experienced in laboratory experiments, where waves propagate along co-flowing and/or opposing currents [5].…”

Comparison Study of Experiments and Predictions of Wave Kinematics for Rogue Wave

“…Grue [27], and Clamond and Grue [28] performed a fully nonlinear numerical simulation of a long time evolution using a two-dimensional localized long wave packet. In a 2-D wave tank, Wu and Yao [29] investigated rogue wave kinematics using a combined mechanism of dispersion enhancement and wave-current interaction. Zou and Kim [30] generated a strongly asymmetric wave in the 2-D wave tank by the time series distortion to the highest wave in irregular wave train.…”