Numerical investigation of turbulence generation in non-breaking potential waves

Theoretically, potential waves cannot generate the vortex motion, but scale considerations indicate that if the steepness of waves is not too small, Reynolds number can exceed critical values. This means that in presence of initial non-potential disturbances the orbital velocities can generate the vortex motion and turbulence. In the paper, this problem was investigated numerically on basis of full two-dimensional (x-z) equations of potential motion with the free surface in cylindrical conformal coordinates. It was assumed that all variables are a sum of the 2D potential orbital velocities and 3D non-potential disturbances. The non-potential motion is described directly with 3D Euler equations, with very high resolution. The interaction between potential orbital velocities and non-potential components is accounted through additional terms which include the components of vorticity. Long-term numerical integration of the system of equations was done for different wave steepness. Vorticity and turbulence usually occur in vicinity of wave crests (where the velocity gradients reach their maximum) and then spread over upwind slope and downward. Specific feature of the wave turbulence at low steepness (steepness was kept low in order to avoid wave breaking) is its strong intermittency: the turbulent patches are mostly isolated and intermittency grows with decrease of wave amplitude. Maximum values of energy of turbulence are in agreement with available experimental data. The results suggest that even non-breaking potential waves can generate turbulence, which thus enhances the turbulence created by the shear current.