Caos na camada limite atmosférica noturna - Costa, Felipe Denardin (2009)
A three-equation model, based on prognostic expressions for the Richardson number, turbulent kinetic energy and wind shear is proposed to represent turbulent behavior in the nocturnal boundary layer (NBL). Integration reveals that the model variables have a complex, non-periodic behavior if different vertical levels, with energy transference among them, are considered. The solution is shown to strongly depend on parameters prescribed to the model, such as the NBL thickness (h) and the magnitude of the winds at its top (U). Small perturbations on U, of 0:001 m=s are shown to lead to very distinctive solutions after few hours of integration, and the same occurs for small perturbations in h, indicating that the model is chaotic. Bifurcation diagrams for the friction velocity dependence on both U and h are shown. For the non-periodic states of the system, the model variables relate to each other in a manner suggestive of a strange attractor. When solutions with different values of the external parameters are considered, the average dependence of the friction velocity on the Richardson number is in agreement with field observations. Friction velocity decreases as the Richardson number increases, remaining, however, finite, even for very large stability conditions. Such relationship, commonly prescribed in previous studies, arises naturally in the proposed model.