Nonlinearity of the equation of state effects dynamics of nonlinear internal waves in late winter lakes

In late winter many lakes are iced over, and hence remain cut off from the mechanical forcing due to wind.  At the same time, strong radiative forcing modifies the inverse stratification associated with wintertime conditions.  The inverse stratification occurs due to the fact that freshwater has a temperature of maximum density (around 4 degrees Centigrade) and the equation state of freshwater is thus nonlinear.  In this talk I will demonstrate that this nonlinearity has a profound influence on the characteristics of nonlinear internal solitary-like waves in the cold water regime.  In particular, predcitions of waves made using a piecewise linear density profile yield waves with the opposite polarity to those calculated using temperature profiles and the full nonlinear equation of state.  I will present results based on the Dubreil-Jacotin Long theory, but similar conclusions can be made based on weakly nonlinear (KdV) theory.  Time permitting I will discuss implications of these results for shoaling.