Shoaling of sixth-order Stokes waves on a current

Jonsson and Arneborg (Jonsson, I.G., Arneborg, L., 1995. Energy properties and shoaling of higher-order Stokes waves on a current. Ocean Engng 22, 819 -857.) combined energy flux and set-down to make shoaling predictions for f ourth-order Stokes waves with and without a net volume flux. With basis in their expressions, sixth-order expressions are derived and combined to make shoaling predictions correct to sixth order with an arbitrary net volume f lux. The new sixth-order results are compared with the fourth-order results and the practically exact results obtained by Sobey and Bando (Sobey R.J., Bando K., 1991. Variations on higher order shoaling. J. Waterway, Port, Co astal Ocean Engng ASCE 117, 348-368) with a Fourier 18 model. The effects o f introducing sixth-order theory rather than the fourth-order theory in sho aling calculations are in general found to be small. As expected the deviat ions increase with increasing wave-steepness, decreasing depth and opposing currents. Also as expected, the results obtained with the sixth-order expr essions improve the results obtained with the fourth-order expressions when compared to the results of Sobey and Bando. As novelties, some considerati ons regarding the consistency of odd- and even-order shoaling calculations, and the magnitude of the bottom slope, are presented. Furthermore a compar ison between the wave-induced current and the total current is given. (C) 2 000 Published by Elsevier Science Ltd.