Average vertical profiles of simulated eddy diffusion coefficients and velocities. Left: vertical profile of the equivalent vertical mixing coefficient derived from the simulation using both the eddy flux (Eq. (18)) and integral (Eq. (20)) methods. The dotted line shows the $1/\sqrt{\rho }$ trend for comparison. The horizontal lines depict the same levels as in Fig. 1. Right: profile of the vertical velocity showing the root-mean-square (solid), maximum upward (dotted), and downward velocity (dashed). Averages and maximum values are computed over temporal and horizontal dimensions.