Where u _ * is the friction velocity and g is the acceleration due to gravity ( typically the Standard gravity ).
2.
The "'Bagnold formula "', named after Ralph Alger Bagnold, relates the amount of sand moved by the wind to wind speed by friction velocity.
3.
Where \ kappa \ approx 0.40 is the von K�rm�n constant constant, u _ * friction velocity, Q turbulent heat flux, and c _ p heat capacity.
4.
Further " ? " is the von K�rm�n constant being typically 0.41, and u _ \ star is the friction velocity which depends on the shear stress " ? w " at the boundary of the flow:
5.
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.
6.
Where \ overline { ( w'c') _ s } is the corresponding surface flux for a scalar c, and b is a coefficient of proportionality . w _ s is the mixed layer velocity scale defined from surface friction velocity and wind profile function at the surface layer top.
7.
Where " q " represents the mass " transport " of sand across a lane of unit width; " C " is a dimensionless constant of order unity that depends on the sand sorting; " \ rho " is the density of air; " g " is the local gravitational acceleration; " d " is the reference grain size for the sand; " D " is the nearly uniform grain size originally used in Bagnold's experiments ( 250 micrometres ); and, finally, u _ * is friction velocity proportional to the square root of the shear stress between the wind and the sheet of moving sand.
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