Evolution of extreme wave statistics in surface elevation and velocity field over a non-uniform depth
Authors: Lawrence Christopher , Trulsen Karsten , Gramstad Odin 
Published: March 2020

&lt;pre&gt;It was shown experimentally in Trulsen et al. (2012) that irregular water waves propagating over a slope&lt;br /&gt;may have a local maximum of kurtosis and skewness in surface elevation near the shallower side of the&lt;br /&gt;slope. Later on, Raust&amp;#248;l (2014) did laboratory experiments for irregular water waves propagating over a&lt;br /&gt;shoal and found the surface elevation could have a local maximum of kurtosis and skewness on top of the&lt;br /&gt;shoal, and a local minimum of skewness after the shoal for sufficiently shallow water. Numerical results&lt;br /&gt;by Sergeeva et al. (2011), Zeng &amp; Trulsen (2012), Gramstad et al. (2013) and Viotti &amp; Dias (2014)&lt;br /&gt;support the experimental results mentioned above. Just recently, Jorde (2018) did new experiment with&lt;br /&gt;the same shoal as in Raust&amp;#248;l (2014) but with additional measurement of the interior horizontal velocity.&lt;br /&gt;The experimental results from Raust&amp;#248;l (2014) and Jorde (2018) were reported in Trulsen et al. (2020)&lt;br /&gt;and it was found the evolution of skewness for surface elevation and horizontal velocity have the same&lt;br /&gt;behaviour but the kurtosis of horizontal velocity has local maximum in downslope area which is different&lt;br /&gt;with the kurtosis of surface elevation.&lt;br /&gt;In present work, we utilize numerical simulation to study the effects of incoming significant wave height,&lt;br /&gt;peak wave frequency on evolution of wave statistics for both surface elevation and velocity field with&lt;br /&gt;more general bathymetry. Numerical simulations are based on High Order Spectral Method (HOSM)&lt;br /&gt;for variable depth Gouin et al. (2016) for wave evolution and Variational Boussinesq model (VBM)&lt;br /&gt;Lawrence et al. (2018) for velocity field calculation.&lt;br /&gt;References&lt;br /&gt;GOUIN, M., DUCROZET, G. &amp; FERRANT, P. 2016 Development and validation of a non-linear spectral&lt;br /&gt;model for water waves over variable depth. Eur. J. Mech. B Fluids 57, 115&amp;#8211;128.&lt;br /&gt;GRAMSTAD, O., ZENG, H., TRULSEN, K. &amp; PEDERSEN, G. K. 2013 Freak waves in weakly nonlinear&lt;br /&gt;unidirectional wave trains over a sloping bottom in shallow water. Phys. Fluids 25, 122103.&lt;br /&gt;JORDE, S. 2018 Kinematikken i b&amp;#248;lger over en grunne. Master&amp;#8217;s thesis, University of Oslo.&lt;br /&gt;LAWRENCE, C., ADYTIA, D. &amp; VAN GROESEN, E. 2018 Variational Boussinesq model for strongly&lt;br /&gt;nonlinear dispersive waves. Wave Motion 76, 78&amp;#8211;102.&lt;br /&gt;RAUST&amp;#216;L, A. 2014 Freake b&amp;#248;lger over variabelt dyp. Master&amp;#8217;s thesis, University of Oslo.&lt;br /&gt;SERGEEVA, A., PELINOVSKY, E. &amp; TALIPOVA, T. 2011 Nonlinear random wave field in shallow water:&lt;br /&gt;variable Korteweg&amp;#8211;de Vries framework. Nat. Hazards Earth Syst. Sci. 11, 323&amp;#8211;330.&lt;br /&gt;TRULSEN, K., RAUST&amp;#216;L, A., JORDE, S. &amp; RYE, L. 2020 Extreme wave statistics of long-crested&lt;br /&gt;irregular waves over a shoal. J. Fluid Mech. 882, R2.&lt;br /&gt;TRULSEN, K., ZENG, H. &amp; GRAMSTAD, O. 2012 Laboratory evidence of freak waves provoked by&lt;br /&gt;non-uniform bathymetry. Phys. Fluids 24, 097101.&lt;br /&gt;VIOTTI, C. &amp; DIAS, F. 2014 Extreme waves induced by strong depth transitions: Fully nonlinear results.&lt;br /&gt;Phys. Fluids 26, 051705.&lt;br /&gt;ZENG, H. &amp; TRULSEN, K. 2012 Evolution of skewness and kurtosis of weakly nonlinear unidirectional&lt;br /&gt;waves over a sloping bottom. Nat. Hazards Earth Syst. Sci. 12, 631&amp;#8211;638.&lt;/pre&gt;