Long internal waves of moderate amplitude. Layers of equal depth

The evolution of long, two-dimensional, internal waves of small amplitude is studied for a density stratification that excludes KdV solitary waves. Experimental data are compared with theoretical solutions of inviscid and viscous models of evolution. The inviscid model is the modified KdV equation for which dispersion and (cubic) nonlinear effects occur on a time scale even slower than that of the KdV equation. The viscous model is linear and only accounts for damping of wave amplitudes. It is demonstrated that viscosity dominates early wave evolution in the measured data. Even in these experiments, the major source of viscous effects is the interfacial shear layer; hence, the early dominance of viscosity is probable even for geophysical scale flows with one of these special stratifications. We also show that the finite thickness of the pycnocline in the experiments causes a significantly smaller phase speed than predicted by the theoretical models which utilize a two-layer approximation. A simple calculation based on a model with two homogeneous layers separated by a layer with a linear stratification accurately predicts the observed phase speeds.