Caminhos para a complexidade na camada limite atmosférica noturna

Abstract

The focus of the present thesis is the nocturnal atmospheric boundary layer, under very stable conditions. In such situation, the turbulence production by the vertical wind shear may have similar magnitude to the total turbulence destruction by the thermal stratification and molecular dissipation terms. Besides being in near balance, the turbulence production and destruction are, each of them, functions of the turbulence intensity itself. This condition causes situations on which the system behaves on a manner different than that expected from each of its parts individually. Such processes are characterized, in the present study, as paths to complexity, and are analyzed separately in the different chapters that compose the thesis. In chapter 2, the coupling state between the surface and the top of the stable boundary layer (SBL) is investigated using four different schemes to represent the turbulent exchange. An idealized SBL is assumed, with fixed wind speed and temperature at its top. The formulations compared are those that solve a prognostic equation for turbulent kinetic energy (TKE) and those that directly prescribe turbulence intensity as a function of atmospheric stability. The formulation influence on the coupling state is analyzed and it is concluded that, in general, the simple TKE formulation has a better response, although it also tends to overestimate turbulent mixing. The consequences are discussed. In chapter 3, a simplified new model for the exchange between the surface and the atmosphere under stable conditions is proposed. Its main difference from previous works consists in the fact that the turbulent intensity is determined by a prognostic equation for turbulent kinetic energy (TKE), rather than by using stability functions that arbitrarily relate it to atmospheric stability. Its main novelty is the fact that, when multiple atmospheric levels are considered, it leads to complex solutions, characterizing the occurrence of the phenomenon known as global intermittency. The vertical structure of the intermittent events is analyzed, and it shown that they are generated at the surface by a local shear increase above a threshold, propagating upward through the turbulence transfer term in the TKE equation. It is proposed that such events constitute a natural characteristic of the disconnected SBL, which occurs along with low large-scale winds and clear skies. Chapter 4 is devoted to the purpose of showing that the use of stability functions that represent the turbulence intensity as its average dependence on atmospheric stability reduces the number of degrees of freedom of the system, precluding it from reaching complex solutions. Finally, in chapter 5, a detailed system dynamics analysis is applied to the model proposed in chapter 3, with the aim of identifying whether it is or not chaotic. It is shown that the system bifurcates as the wind speed at the SBL top increases, reaching period 3 for a range of situations, a sufficient condition for chaos existence. Furthermore, positive Lyapunov exponents are found, again confirming the chaotic character of the system. It is shown that the complexity arises from the nonlinear interactions between the different vertical levels considered, through the vertical turbulence transport terms.