CMS-Flow:Wind Pressure

Wind

In CMS-Flow the wind shear stress is calculated as \begin{equation} \tag{1} \tau_{Wi} = \rho_a C_d |W| W_i \end{equation}

where $W$ is the 10-min average wind speed at a height of 10 m, $C_{d}$ is the drag coefficient, and $\rho _{a}$ is the atmospheric density (~1.2 kg/m^3).

The wind drag coefficient $C_{d}$ is calculated using the Hsu (1988)

\begin{equation} \tag{2} C_d = \biggl ( \frac{\kappa}{14.56 - 2 \ln W} \biggr ) ^2 \end{equation}

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)

\begin{equation} \tag{3} W = W_z \biggl ( \frac{10}{z} \biggr )^{1/7} \end{equation}

Pressure

The atmospheric pressure is included in the momentum equations as an additional pressure gradient term \begin{equation} \tag{4} \frac{h}{\rho_0} \frac{\partial p_a }{\partial x_j} \end{equation}

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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