Turbulent Flow The Reynold’s experiment demonstrates how the mechanism of fluid flow can change as flowrates (or, more precisely, the Reynolds number) increase. The flow structure shifts from being laminar to turbulent. With turbulence, there is a random fluctuating component to the velocities and pressure. vx(x,y,z,t) vx(x,y,z) t t t = + v'x(x,y,z,t) Time averaged velocity with net displacement Fluctuating component with no net displacement vx = vx(x,y,z) + v'x(x,y,z,t) vx is the time averaged component of the turbulent velocity vx.

xy = - dvx -  v'xv'y Turbulent Flow v'x = 1  v'x(x,y,z,t) dt = 0 t1 o vx = 1  vx(x,y,z,t) dt t1 o Length of t1 is much greater than duration of a flucuation y vx = vx(y) vy = v'y and vy = v'y = 0 Overall motion is only in the x-direction for this flow field. x In laminar flow, we said frictional force imparted momentum from one layer to another. Fluid did not cross from one lamina to another. In turbulent flow, fluid elements can cross from one layer to the next due to the fluctuating velocity in the y-direction. These impart momentum in the x-direction. Reynolds Stresses xy = - dvx -  v'xv'y dy