Meroney, Robert N., authorFluid Dynamics and Diffusion Laboratory, Department of Civil Engineering, Colorado State, publisher2019-09-172019-09-171974-04https://hdl.handle.net/10217/198117CER73-74RNM38.April 1974.Includes bibliographical references.Prepared for the National Science Foundation and Office of Naval Research.It has long been recognized that the buoyancy force due to density stratification has pronounced effects on the turbulence structure. A number of investigations have utilized stability corrections based on the assumption of the existence of an eddy viscosity or eddy diffusivity. Unfortunately such models are incapable of physically behaving as the measurements in the presence of strong stable or unstable stratifications suggest. Recently Donaldson et al. (1972), Lumley (1972), Daly (1972) and Lee (1974) have proposed closures of the equations of motion in the presence of buoyancy forces which require equations for all Reynold's stresses and heat fluxes. Unfortunately even for a one-dimensional model one must at a minimum then solve simultaneously nine partial differential equations and one algebraic equation. Other theories suggest an even higher total. Utilizing a simple time dependent one-dimensional example as a test case this report discusses a solution which represents the important characteristics of a buoyancy dominated shear flow by solving four partial differential equations in addition to the mean equations of motion. This suggested model solves equations for total turbulent kinetic energy, k, total turbulent temperature fluctuations, kt, eddy dissipation, E, and thermal eddy dissipation, Et. Three separate versions of this model are discussed--an algebraic length scale version, a Prandtl-Kolmogorov eddy viscosity version, and an algebraic stress and heat flux model. The final version (requiring six partial differential equations) manages to replicate results for a much more complicated version (requiring ten partial differential equation). The advantages for two and three dimensional problems are even greater.technical reportsengCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.Fluid dynamicsText