A Study of the Structure of Shear Turbulence in Free Surface Flows

• Main Author: Rao, Maddineni Venkateswara
• Format: Others
• Published: DigitalCommons@USU 1965
• Subjects: shear; turbulence; free surface flow; Engineering
• Online Access: https://digitalcommons.usu.edu/etd/1460; https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=2460&context=etd

Turbulence is a familiar phenomenon which gives rise to complicated problems in many branches of engineering. Hinze has set forth the following definition for turbulence: "Turbulent fluid motion is an irregular condition of flow in which the various quantities show a random variation in time pnd space coordinates, so that statistically distinct average values can be discerned." Osborne Reynolds (1894) was the first to introduce the notion of statistical mean values into the study of turbulence. He visualized turbulent flow as the sum of mean and eddying motion. By introducing this sum of mean velocity and fluctuating velocity into the Navier-Stokes equations and with the aid of the continuity equation, he derived equations giving relationships between the various components of the fluctuating velocity. It was soon realized that before any further results could be obtained from a theoretical analysis of Reynold;s equations of motion, a mechanism had to be postulated for the ihteraction of fluctuating v~locity components at different points in the turbulent field. Consequently, three decades after Reynold's: work, phenomenological theories of turbulence, such as the momentum-transfer theory of Prandtl (1926), the vorticity transport theory of Taylor (1932) and the similarity theory of Karman (1930) were introduced. Not only are they based on unrealistic physical models, but they do not furnish any information beyond temporal-mean velocity distribution. A complete theory of turbulence should describe the mechanism of production of turbulence, its convection, diffusion, distribution, and eventual dissipation for any given boundary conditions.