A Preliminary Experimental Study of the Turbulence Decay in the Wake of a Hemisphere in Free-Surface Flow

Flows observed in open channels are usually turbulent. The word turbulent describes a motion in which an irregular velocity fluctuation (mixing or eddying motion) is superimposed on the main stream motion. The essential characteristic of turbulent flow is that the turbulent fluctuations are random in nature. If Reynold\u27s rule of averaging is used, the Navier-Stokes equations for laminar flow may be transformed into the Reynold\u27s equations, which hold true for turbulent mean motion. The solution of Reynold\u27s equations will properly describe turbulent flow. Unfortunately, the number of unknowns exceeds the number of equations; therefore the use of mathematical method to solve turbulent flow problems is extremely difficult and not possible at present. The details of turbulent flow are so complicated that a statistical approach must be used. Extensive research has been done in this regard during the last few decades. G. I. Taylor (1935) presented a statistical theory of turbulence based on the assumption of homogeneous isotropic turbulence. He introduced various concepts such as turbulence intensity, correlation coefficient, scale of turbulence, and energy spectrum. Kolmogoroff (1941) introduced the theory of locally isotropic turbulence. He postulated that turbulent motion at large Reynold\u27s number is locally isotropic whether or not the large scale motions are isotropic. He also introduced the concept that the small scale motions are mainly governed by viscous forces and the amounts of energy which are handed down to them from the large eddies. Other investigations of isotropic turbulence have been made by Karman (1938), Heisenberg (1948), Lin (1948), etc. Even for the simplest type of turbulence (i.e. isotropic turbulence) , it is not possible to obtain the general solution to the equations because the details of turbulence are so complicated. Present knowledge about the statistical distribution of non-homogeneous turbulence is even less extensive. Therefore, before real use can be made of the statistical theory of turbulence much work must be done