density function can be approximated by a skewed normal distribution as well as by a Tayfun distribution.'
author:
- 'P. Clark di Leoni'
- 'P. J. Cobelli'
- 'P. D. Mininni'
bibliography:
- 'Tesis.bib'
title: Wave turbulence in shallow water models
---

Introduction
============

Turbulence and non-linear wave interactions in the ocean surface are related to important processes in atmospheric sciences and oceanography, such as the exchange of energy between the atmosphere and the ocean [@iafrati_modulational_2013; @dasaro_enhanced_2011]. This exchange, in turn, plays an important role in the dynamics of the planetary and oceanic boundary layers, with consequences on the transport and mixing of momentum, CO$_2$, and heat [@ivey_density_2008]. The incorrect modeling of these phenomena affects climate evolution predictions [@rose_upper-ocean--atmosphere_2010; @cavaleri_wind_2012]. Ocean surface waves are also of interest in the search of renewable energies [@falnes_review_2007].

There are several ocean surface models which provide an excellent framework for studying *weak turbulence theory* [@hasselmann_non-linear_1962; @hasselmann_non-linear_1963; @hasselmann_non-linear_1963-1; @zakharov_kolmogorov_1992]. This theory was developed to describe the out-of-equilibrium behavior of systems of dispersive and weakly non-linear waves (see, e.g., [@newell_wave_2011; @nazarenko_wave_2011]). Unlike theories of strong turbulence, for waves and under the assumption of weak nonlinearities, the equations for two-point correlations can be closed and exact solutions 