Shear velocity scales well to rates of dispersion and bedload sediment transport.
2.
Most eddy viscosity SGS models model the eddy viscosity as the product of a characteristic length scale and a characteristic velocity scale.
3.
It is a special case of the Magnetic Reynolds number when the Alfv�n velocity is the typical velocity scale of the system, and is given by
4.
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 ):
5.
The sizes define a characteristic length scale for the eddies, which are also characterized by flow velocity scales and time scales ( turnover time ) dependent on the length scale.
6.
By choosing a length scale, L, and velocity scale, U, the equation can be expressed in nondimensional form containing the Reynolds number, Re = UL / ?.
7.
As it eliminates the effects of inertia and the need for a velocity scale, it is oftentimes more convenient to express scaling relationships in terms of the Ohnesorge number rather than the Reynolds and Weber number individually.
8.
By integrating in the " y "-direction once, then non-dimensionalizing with an unknown velocity scale " u " " and viscous length scale, the equation reduces down to:
9.
The new " inner length scale " \ eta is a viscous length scale, and is of order \ frac { \ nu } { u _ * }, with u _ * being the velocity scale of the turbulent fluctuations, in this case a friction velocity.
10.
The channel depth " H " is chosen as a length scale, the mean velocity " V " is taken as a velocity scale, and the pressure scale is taken to be P _ 0 = k \ left ( V / H \ right ) ^ n.
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