CMS-Flow:Wind Pressure

Wind Surface Stress

The wind surface stress is calculated as

$\tau _{si}=\rho _{a}C_{D}WW_{i}$

(1)

where

$\rho _{a}$ = air density at sea level [~1.2 kg/m³]

$C_{D}$ = wind drag coefficient [-]

$W_{i}$ = 10-m wind speed [m/s]

$W={\sqrt {W_{i}W_{i}}}$= 10-m wind velocity magnitude [m/s].

The wind speed is calculated using either an Eulerian or Lagrangian reference frame as

$W_{i}=W_{i}^{E}-\gamma _{W}U_{i}$

(2)

where:

$W_{i}^{E}$ = 10-m atmospheric wind speed relative to the solid earth (Eulerian wind speed) [m/s]

$\gamma _{W}$= equal to zero for the Eulerian reference frame or one for the Lagrangian reference frame

$U_{i}$= current velocity [m/s].

Using the Lagrangian reference frame or relative wind speed is more accurate and realistic for field applications (Bye 1985; Pacanowski 1987; Dawe and Thompson 2006), but the option to use the Eulerian wind speed is provided for idealized cases and backward compatibility. The drag coefficient is calculated using the formula of Hsu (1988) and modified for high wind speeds based on field data by Powell et al. (2003) (Figure 2-2):

$C_{d}={\biggl (}{\frac {\kappa }{14.56-2\ln W}}{\biggr )}^{2}$

(2)

For measurements of wind speed made at heights other than 10 m, an approximation of the 10-m wind speed is (Shore Protection Manual 1984)

$W=W_{z}{\biggl (}{\frac {10}{z}}{\biggr )}^{1/7}$

(3)

Pressure

The atmospheric pressure is included in the momentum equations as an additional pressure gradient term

${\frac {h}{\rho _{0}}}{\frac {\partial p_{a}}{\partial x_{j}}}$

(4)

Symbol Index

Symbol	Description	Units
$\tau _{W}$	Wind shear stress	Pa
$\rho _{a}$	Atmospheric density (~1.2 kg/m^3)	kg/m^3
$C_{d}$	Wind drag coefficient	none
$W$	10-min averaged wind speed at 10 m above the sea surface	m/sec
$\theta$	Wind direction	m/sec

References

• Hsu, S.A. (1988) Coastal meteorology. Academic Press, San Diego, CA.

• Shore Protection Manual (1984) 4th ed., 2nd Vol, U.S. Army Engineer Waterways Experiment Station, U.S. Government Printing Office, Washington, DC.

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