Stokes Waves at Finite Depth

Chalikov D. V., Bulgakov K. Yu.

The main properties of the Stokes waves are considered. Several methods of numerical investigation of wave dynamics are discussed. A conformal surface-following coordinate system is defined. Sta-tionary potential waves equation in this coordinate system are represented. Algorithm of very fast numerical solving of stationary one-dimensional potential equations for the case of optional depth is described. The characteristics of numerical runs for the deep depth case are investigated: time of ex-periments, iteration number, potential, kinetic and total energy, asymmetry, excess. Area in coordi-nates of depth and steepness where solution exists is specificated. The geometrical characteristics of the Stokes waves as function of steepness and depth are investigated: asymmetry, maximum of the local steepness, maximum of the local second derivate and also phase velocity. The forms of waves for steepness 0.01 are shown. Possible application of obtained results is considered.

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