The persistence of logarithmic solutions in turbulent boundary layer systems

Abstract

from the first principles of mechanics and the formalism of a continuous field characterized by density and viscosity.Thus, the complete absence of a comprehensive theory that can convincingly deal with disordered flows may come to many as a surprise. The crux of the matter, obviously, is the strong non-linear character of the advection terms in the equations of motion. Under certain conditions-in particular, high Reynolds numbers-fluid flows become unstable, growing rapidly to a complicated and confused state that is termed turbulent and has a large number of degrees of freedom.In fact, it can be argued that an exact and detailed description of the manner in which a turbulent flow evolves is physically meaningless due to the inherent difficulty in specifying its boundary and initial conditions for situations that are of interest in practical problems. A microscopic account of the flow behavior is certainly relevant for the understanding of local and instantaneous irregularities, but what is normally of real interest is the behavior of the macroscopic regularities of the flow. Therefore, it seems that the appropriate description of a turbulent flow needs to resort to statistical methods.Provided the irregular variation of the flow properties can be averaged over, say, some interval of time, the field properties can be decomposed into smoothed out (mean part) and rapidly varying quantities (fluctuating part). Once this procedure is accepted, substitution of the decomposed field variables into the Navier-Stokes equations results in a new equation for the mean variables, but with additional terms involving double correlations of the fluctuations, quantities that are formally unknown and that, hence, require modeling. The resulting second-order tensor-the Reynolds stress tensor-represents the transport of momentum due to the turbulent fluctuations and has the Abstract The present work studies the prevalence of logarithmic solutions in the near wall region of turbulent boundary layers. Local solutions for flows subject to such diverse effects as compressibility, wall transpiration, heat transfer, roughness, separation, shock waves, unsteadiness, non-Newtonian fluids or a combination of these factors are discussed. The work also analyzes eleven different propositions by several authors for the near wall description of the mean velocity profile for the incompressible zero-pressuregradient turbulent boundary layer. The asymptotic structure of the flow is discussed from the point of view of double limit processes. Cases of interest include attached and separated flows for the velocity and temperature fields.