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frictionVelocity.m
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frictionVelocity.m
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function ustar = frictionVelocity(meanupwp, meanvpwp)
%
% Matt Werner ([email protected]) - June 25, 2021
%
% Calculate the friction velocity, u*. The friction velocity is generally
% defined by (Aerial Dispersion of Pollen and Spores, Aylor, Eq. 7.18b)
% / _____ 2 _____ 2 \ 1/4
% u* = | u' w' + v' w' | ,
% \ /
% where appears the mean product of the fluctuations in the horizontal
% directions with the vertical direction.
%
% Note: This form of u* is used as it provides a more general description
% for the orientation of the coordinate system. In the case that the
% coordinate system has its x axis aligned with the mean flow
% direction, the mean product of (v' w') vanishes.
%
% Inputs:
%
% mean(u|v)pwp - Mean product of the fluctuations in u and v
% corresponding to the x and y directions,
% respectively.
% Size: 1-by-1 (scalar)
% Units: m2/s2 (square meter per square second)
%
% Outputs:
%
% ustar - The friction velocity.
% Size: 1-by-1 (scalar)
% Units: m/s (meters per second)
%
%% Checks
% No checks
%% Computation
% Calculate the friction velocity
if (nargin == 1)
% Calculate the friction velocity in the sense that the x axis is
% aligned exactly with the wind such that there is absolutely no
% correlation with the crossrange and vertical wind fluctuations
ustar = sqrt(abs(meanupwp));
else
% Calculate the friction velocity in the sense that the x axis is not
% aligned with the wind direction (Stull, 1988)
ustar = (meanupwp^2 + meanvpwp^2)^0.25;
end