It has been experimentally shown that an increase in the water depth from 2 to 4 cm leads to a transition from two-dimensional turbulence to three-dimensional. Waves with a frequency of 6 Hz (wavelength λ = 5.6 cm), propagating on the water surface, generate vortex flows penetrating into the water volume. The experiments show that in shallow water with a depth of h = 2 cm, the vortex flow is homogeneous and quasi-two-dimensional: the vertical velocity component of tracer particles is zero, and the vorticity vector is oriented vertically. In deep water (h = 4 cm), a developed three-dimensional chaotic liquid motion is observed: the water layers are mixed due to solenoidal flows with both vertical and horizontal velocity components. Vortices in the fluid interact with surface flows, leading to an increase in their energy. As a result of this interaction, the energy of surface vortices, E(t), after turning off the pump demonstrates a non-monotonic dependence on the time, which differs from the exponential decay characteristic of shallow water.
Poplevin et al. (Wed,) studied this question.