The nonlinear stage starts when the amplitude of the unstable flow feature becomes significant. This chapter first studies the nonlinear growth of the interface amplitude and its associated terminal velocity with potential flow models, both for RM and RT. Next, one describes several models intended to predict the evolution of the bubble and spike heights, and the corresponding velocities, for the nonlinear stage. The success and limitations of each model are assessed with comparison to experiments and numerical simulations. The sensitivities to viscosity, density ratio and Mach number are discussed.

This concluding chapter offers a few remarks on empirical work and its relation to economic theory. Econometricians have been gaining access to more and better data, and significant progress has been made in the techniques and procedures that are used to extract information from the data. But the data still don’t speak for themselves. Recent contributions on regional fiscal multipliers and state-level inflation in the US are used to illustrate the need for theory to extrapolate from regressions to generalizable implications. Stripped-down New Keynesian Phillips curves, for instance, are used to interpret inflation data, despite the abject empirical failure of these Phillips curves. The imaginative use of new data and careful attempts to identify causal effects clearly can be immensely helpful. But dogmatic adherence to an untenable, scholastically motived theoretical framework can lead to a curious combination of sophisticated econometrics and a willingness to engage in ad hoc handwaving in the interpretation of the data. The ambition in this book is to sketch an alternative framework with behavioral and structural assumptions that are evidence based.