Freak Waves
                              Exploration, Occurrence, and Prediction
         Freak waves, alternatively called rogue waves or giant waves, are exceptionally large, steep, and asymmetric waves whose heights usually exceed by 2 times the significant wave height. They have also been described as ‘‘holes in the sea’’ or ‘‘walls of waters’’. These waves have been long known to be notorious hazards to navigation vessels and marine structures. Our research aims to explore the occurrence of freak waves and investigate the mechanisms to generate freak waves. Specifically, we are interested in further understanding the formation mechanisms, limiting characteristics, and temporal-spatial-spectral evolution of freak waves on currents. 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 inter-wave instantaneous frequency modulation and the freak wave non-linearity (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.
following   opposing
             freak wave on a 10 cm/s following current                                                             freak wave on a 10 cm/s opposing current                             

       To capture freak waves, we have been developing a novel Automated Trinocular Stereo Imaging System (ATSIS), a non-intrusive remote sensing technique, to measure temporal evolution of three-dimensional wave characteristics. The system consists of three progressive digital cameras to accurately estimate depth of a scene. In addition the advantage of using extra camera resolves the correspondence problems due to specular reflection on the water surface and provides additional constraints on image matching, dramatically reducing the chance of a mismatch. An oblique configuration for the trinocular system effectively increases spatial coverage, allowing observations of wave phenomena over a broad range of spatial scales. A new exterior calibration procedure is also developed to determine the orientation of cameras in the field. The height resolution is increased with the optical axes of the cameras pointed at an oblique angle with respect to vertical surface wave displacements. 

Stereo-imaging of a 3D breaking wave                              3D view of the processed image                                               Virtual wave gauge array

       Furthermore. we also developing the-state-of-the art
models for depict freak wave motions. For several decades, a great deal of efforts has been paid to develop unified models that can effectively predict water wave propagation with varying degree of dispersive and nonlinear effects. Our research group is focusing on develop an efficient and accurate non-hydrostatic modeling frame to predict large scale surface wave dynamics. Overall the goal is to develop full non-hydrostatic model using a small number of vertical layers (two ~ five layers) to simulate nearshore wave transformation including shoaling, dispersion, refraction, and diffraction phenomena. Furthermore we are also working on developing a non-hydrostatic model that can examine deep-water wave-wave interactions including slowly modulated and rapidly evolving wave processes leading to the formation of freak waves.  

f_w       near         freak                   Shoaling and diffraction                                                        Refraction and diffraction                                                          Frequency dispersion focusing


  • Characteristics and Occurrence of Freak Waves in the Apostle Islands, Lake Superior, Submitted 2019.
  • Anderson, J.D. and Wu, C.H., Development and Application of a real-time water environment cyber-infrastructure for kayaker safety in the Apostle Islands, Lake Superior, Lake Superior. J. of Great Lakes Research, 44(5), 990-1001,, 2018
  • Anderson, J.D., Wu, C.H., and Schwab, D.J., Wave climatology in the Apostle Islands, Lake Superior, J. Geophysical Research-Oceans, 120(7), 4869-4890, 2015.
  • Liu, P.C., Wu, C.H., Bechle, A.J., MacHutchon, K.R., and Chen, H.S., What do we know about freaque waves in the ocean and lakes and how do we know it, Natural Hazards and Earth System Sciences, 10, 2191-2196, 2010.
  • Young C.C. and Wu, C.H., A σ - coordinate non-hydrostatic model with embedded Boussinesq-type like equations for modeling deep-water waves, International J. for Numerical Methods in Fluids, 63(12),1448-1470, 2010.
  • Young, C.C. and Wu, C.H., Non-hydrostatic modeling of nonlinear deep-water wave groups, J. of Engineering Mechanics-ASCE, 136(2), 155-167, 2010.
  • Young, C.C. and Wu, C.H., An efficient and accurate non-hydrostatic model with embedded Boussinesq-type like equations for surface wave modeling, International J. for Numerical Methods in Fluids, 60(1), 27-53, 2009.
  • Yao, A. and Wu, C.H., Spatial and temporal characteristics of transient extreme waves on depth-varying currents, J. of Engineering Mechanics-ASCE, 132 (9), 1015-1025, 2006.
  • Yao, A. and Wu, C.H., Incipient breaking of unsteady waves on sheared currents, Physics of Fluids, 17, 082104, 2005.
  •  Wu, C.H. and Yao, A., Laboratory measurements of limiting freak waves on currents, J. Geophysical Research-Oceans, 109, C12, C12002, 1-18, 10.1029/2004JC002612, 2004.
  • Yao, A. and Wu, C.H., Energy dissipation of unsteady wave breaking on currents, J. Physical Oceanography, 34, N10, 2288-2304, 2004.
  • Wu, C.H. and Nepf, H. M, Breaking wave criteria and energy losses for three-dimensional breaking waves, C10, 3177, 10.1029 2001JC001077, 41-1-18, J. Geophysical Research-Oceans, 2002

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