Shear velocity
Shear velocity, also called friction velocity, is a form by which a shear stress may be re-written in units of velocity. It is useful as a method in fluid mechanics to compare true velocities, such as the velocity of a flow in a stream, to a velocity that relates shear between layers of flow.
Shear velocity is used to describe shear-related motion in moving fluids. It is used to describe:
Shear velocity also helps in thinking about the rate of shear and dispersion in a flow. Shear velocity scales well to rates of dispersion and bedload sediment transport. A general rule is that the shear velocity is between 5% to 10% of the mean flow velocity.
For river base case, the shear velocity can be calculated by Manning's equation.
u*=<u>*(n/a)*(g*Rh^(-1/3))^0.5
Instead of finding n and Rh for your specific river of interest, you can examine the range of possible values and note that for most rivers, u* is between 5% and 10% of <u>:
For general case
where τ is the shear stress in an arbitrary layer of fluid and ρ is the density of the fluid.
Typically, for sediment transport applications, the shear velocity is evaluated at the lower boundary of an open channel:
where τb is the shear stress given at the boundary.
Shear velocity can also be defined in terms of the local velocity and shear stress fields (as opposed to whole-channel values, as given above).
The friction velocity is often used as a scaling parameter for the fluctuating component of velocity in turbulent flows. One method of obtaining the shear velocity is through non-dimensionalization of the turbulent equations of motion. For example, in a fully developed turbulent channel flow or turbulent boundary layer, the streamwise momentum equation in the very near wall region reduces to:
By integrating in the y-direction once, then non-dimensionalizing with an unknown velocity scale u∗ and viscous length scale ν/u∗, the equation reduces down to:
or
Since the right hand side is in non-dimensional variables, they must be of order 1. This results in the left hand side also being of order one, which in turn give us a velocity scale for the turbulent fluctuations (as seen above):
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