## Info

Re* > 70 ! hydraulically rough flow

It is the convention of this literature to represent velocity with U, depth with D, and the constant for kinesmatic viscosity of water as v

It is the convention of this literature to represent velocity with U, depth with D, and the constant for kinesmatic viscosity of water as v

Re quantifies the ratio of inertial forces of the moving fluid to the viscous properties of a fluid that resist mixing (Newbury and Bates 2006). It is a dimensionless number that can be used to distinguish types of flow and the forces experienced by an organism. Depth of flow is used to estimate Re for the channel, and the length of a fish or insect can be used to estimate the forces that act directly on an organism.

At low Re, flow is laminar and viscous forces predominate, whereas at high Re turbulence occurs and inertial forces predominate. Laminar flow usually requires current velocities well below 10 cm s_1, especially if depth exceeds

0.1 m; in short, quite shallow and slow moving water. Hence turbulent flow is the norm in the channels of rivers and streams. Fr is a dimen-sionless velocity to depth ratio, and differentiates tranquil flow from broken and turbulent flow (Davis and Barmuta 1989). Low values of Fr are characteristic of pool habitats and higher values of riffle habitats. In some New Zealand streams, Fr generally was <0.18 and rarely as high as 0.4 in pools, >0.41, and as high as 1 in riffles, and intermediate in runs (Jowett 1993).

Using an estimate of shear velocity (U*), which can be derived from the velocity profile near the streambed, and substituting the height of roughness elements for water depth, one can estimate roughness (boundary) Reynolds number (Re*) (Table 5.1). This variable and the dimen-sionless shear stress, which is related to the square of shear velocity and inversely related to particle size, describe the conditions under which particle movement is likely (Section 3.3 2). Both near-bed velocity and bed shear stress increase with increasing relative roughness and mean velocity

Physical conditions between the extremes of low and high Re differ greatly (Vogel 1994). At high Re's, pressure drag is the important force and streamlining is an adaptive countermeasure. An airfoil, a trout, and a Baetis, each with blunt front and tapered rear, are ideal shapes to minimize turbulent drag that results from the rejoining of flow streams downstream of the object. By minimizing wake turbulence, streamlined shapes reduce the pressure differential between front and rear, which creates the drag we experience on our legs as we wade through a swift stream. At low Re, water is more viscous, flow is much more laminar, and the force exerted as layers of water slide over one another is greater. This last force, due to the no-slip condition, results in skin friction. It is minimized by reduction in surface area, and so stubby or rotund shapes might be advantageous. Streamlining will be of little benefit due to the reduced role of pressure drag and the increased surface area that streamlining entails. These are only generalizations, however; at Re between 102 and 104, the best shapes to minimize total drag are not known.

Lastly, it should be noted that these equations characterize the flow environment based on average or mean conditions. In the complex, three-dimensional flow environment of turbulent streams, velocity measured at a point fluctuates markedly, and it is this temporal variance that defines turbulence. How organisms and substrate particles respond to the forces of moving water may be influenced more by spikes than by the mean condition.

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