Theoretical and numerical study on random square waves as a statistical tool for transport in turbulent flows

• Grant number: 13/00096-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2013
• End date: May 31, 2014
• Field of knowledge: Engineering - Mechanical Engineering - Transport Phenomena
• Principal Investigator: Harry Edmar Schulz
• Grantee: Marcus Vinicius Gomes de Sousa
• Host Institution: Escola de Engenharia de São Carlos (EESC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Turbulence, while a phenomenon with erratic characteristics, has been quantified in a statistical way. A common approach in Statistical Fluid Mechanics is to operate on the variable in question and on the equations. This procedure leads, for nonlinear phenomena, to systems with more unknowns than equations. Despite this inconsistency, the statistical approach is then supplied with information (equations) that allow achieving very appropriate solutions. Existing solutions utilize approaches that can be called "a posteriori", because they incorporate corrective proposals (originated from experience, dimensional analysis, constituting ad hoc"models"), also setting new parameters, after the emergence of the mentioned new statistical variables. The current study uses an "a priori" approximation which operates on the variables and inserts parameters before operating on the equations. This implies that all subsequent statistical variables depend on these initial parameters. Although simple, this conception still presents mathematical problems of convergence, discontinuity, appropriate boundary conditions, which still need to be studied in this new approach. The present project is concerned with this formulation, and considers a one-dimensional turbulent transport problem, checking discontinuities in the solutions and their consequences.(AU)