One of the key parameters for the wall-bounded flows is the mean friction velocity
([u.sub.[tau]]), which can be calculated from the simulation results using the local wall-shear stress (near-wall velocity gradient), and the friction Reynolds number ([Re.sub.[tau]]):
where [u.sub.*] = [([<u'w'>.sup.2] + [<v'w'>.sup.2]).sup.1/4] is the friction velocity
, u', v', and w' are fluctuations in longitudinal, transversal, and vertical velocity components, respectively, T is air temperature, k is von-Karman's constant, g is the gravitational acceleration, and (w'T') is the covariance between vertical velocity and temperature fluctuations which represents the mean kinematic sensible heat flux.
or bed shear velocity is a significant term in the context of computing the velocity profile as well as for determining the bed roughness.
and herein k is the von Karman constant, [u.sup.*], is the mean friction velocity
, and y is the vertical direction.
Here, d is the diameter of the longitudinal coherent vortices [m], and [u.sub.[tau]] is the friction velocity
[m/s] defined as below,
These two parameters of the wind wave spectrum were related, in dimensionless forms, to the fetch X and the friction velocity
of the wind [U.sub.*] which was determined from the wind profile over the water surface.
The Reynolds number of flow is [Re.sub.b] = 2100 based on averse velocity ([u.sub.b] = 1.65 m x [s.sup.-1]) and half-width channel (h = 0.02 m), the Karman number of channel flow is equal to 150, where friction velocity
is [u.sub.[tau]] = 0.11775 m x [s.sup.-1].
There are several factors influencing dry deposition of aerosol, mainly the friction velocity
, the particle size, boundary layer conditions (turbulence intensity), atmospheric stability, and collecting properties of the surface.
. Friction velocity
([u.sub.*]) is a scaling variable for characterizing the near-surface friction stress (i.e., momentum flux).
While friction velocity
[u.sub.[tau]] and external velocity [U.sub.e] have mostly been employed as velocity scales for boundary layers undergoing favorable pressure gradient, there have been several alternate propositions for the velocity scales of turbulent boundary layers undergoing adverse pressure gradients due to the failure of [u.sub.[tau]] to collapse the velocity profiles for flows with pressure gradients.
where [u.sup.*] is the friction velocity
, K is the von Karman constant ([approximately equal to]0,41), g is the acceleration due to gravity, [z.sub.om] is the roughness length for momentum transport.
where, [u.sub.*e], g, h and [S.sub.f] are the friction velocity
, acceleration of gravity, flow depth, and energy gradient, respectively.