Agradecimentos: The authors acknowledge Dr. Jean-Phillipe Laval for providing the MFLOPS3D simulation tool. This work is partially supported by Fundação de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP) under Research Grant Nos. 2013/07375-0 and 2013/03413-4. Partial support is also provided by Conselho Nacional de Desenvolvimento Cient'ifico e Tecnologico (CNPq) under the Research Grant Nos. 309985/2013-7 and 305277/2015-4. The support provided by Fundac¸ao Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) and FAPESP through a Ph.D. scholarship for the first author under the Research Grant Nos. 2014/07623-6 and 2016/03985-6 is likewise gratefully appreciated. Further support from CNPq through Research Grant Nos. 400844/2014-1 and 443839/2014-0 is also appreciated. The computational resources provided by CENAPAD-SP through Project No. 551 are also gratefully acknowledged Ver menos

Numerical simulations are employed to investigate the turbulent kinetic energy (TKE) budgets in turbulent channel flows with pressure gradients and separation. Incompressible, highly resolved large eddy simulations are performed for Reτ = 170 and 615 to investigate the flow developing along a convergent-divergent channel. The aim of this work is to analyze the TKE budgets both in physical and Fourier spaces to characterize the important scales in the individual processes in such turbulent flows. The study is performed for different positions along the channel where favorable and adverse pressure gradients are present. Proper orthogonal decomposition is employed to understand the role of the most energetic structures in the TKE budgets. Results indicate that such structures account for most of the turbulent effects present in the flow, except for the transport term. A spectral TKE equation in Fourier space is developed for flows with one homogeneous direction to characterize the turbulent processes as a function of the wavelength in the channel spanwise direction. The results show that viscous effects occur at the same range of wavelengths for which production is found and that TKE is transported to the near-wall region, being dissipated by large spanwise scale motion. They also show that favorable pressure gradients change the distribution of processes along the spanwise wavelengths. In the adverse pressure gradient region, TKE is transported both toward the wall and toward the center of the channel, where it is balanced by the advection term Ver menos