Mode-2 internal waves and inter-mode resonance in late winter lakes

In late winter/early spring temperate and northern lakes often experience a so-called weak, inverse stratification.  This occurs since: i) fresh water experiences a maximum density at around four degrees Centigrade, ii) the lake is iced over and thus mechanically isolated from the overlying atmosphere, iii) the increasing solar insolation heats the water column according to the Beer-Lambert-Bouguer law; thereby producing a region of instability that mixes a portion of the water column.  This classical scenario fits some lakes, but the small density differences due to the thermal forcing also imply that very small amounts of dissolved salts could create a more complex, combined solute-thermal stratification.  We explore the behaviour of nonlinear internal waves for one such measured stratification. For mode-1 we find well defined internal solitary waves. For mode-2 the coupling between pycnoclines is weaker leading to a more complex dynamics that we quantify in detail.