Turbulent boundary-layer flow separation as portrayed by a two-dimensional, second-order closure model

Flow separation at high Reynolds number has long been one of the unsolved frontiers in the study of fluid mechanics. We do not have any theories or hypotheses which can adequately explain this phenomenon that occurs so ubiquitously in nature.; This research models turbulent flow separation over a two-dimensional, aerodynamically rough surface by a numerical simulation based on the equations of a second-order turbulence closure system. Our goals for the model are the achievement of both steady and oscillating separated-flow results. Neither of these goals have been achieved up to now by second-order closure modeling, and the latter goal of oscillating, separated flow has not been achieved by any turbulence model so far. The achievement of oscillating flow separation is important for turbulence modeling because turbulent boundary-layer flows are frequently observed to have oscillating behaviors when they separate.; Both our objectives are satisfied, but it is necessary to discard or improve some of the existing theories and definitions concerning the state of the turbulent flow at the lower boundary of a second-order model. This research uses several concepts and techniques which have never been attempted in turbulence modeling or in any other problems of fluid mechanics. The main concept is the use of group representation theory to describe the turbulent flow state at the lower boundary. Results support the validity of this approach by showing that the flow state at the separation and reattachment points for different types of surface geometry can be classified into a single category by their similar Reynolds stress characteristics. In addition, the results give a more realistic depiction of turbulent flow separation than models using lower-order turbulence closures.