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# Difference between revisions of "Wind Stress"

When wind blows over the water, it exerts a shear stress at the water surface that transfers horizontal momentum vertically downward across the air–sea interface, driving circulation. In ADCIRC, wind stress is an input forcing term, with several different formats provided. See the NWS parameter for available formats. In most cases, the exact wind stress to be applied to the model is not provided, therefore ADCIRC must determine how to convert a given wind speed to the actual stress applied at the ocean surface. This page covers the various aspects of this process, as well as the options available to the user.

## Definition of Winds

The characteristics of wind forcing are often broken down in three ways:

1. Whether the winds are considered to be over-water (termed "marine exposure") or over-land
2. The elevation above the sea (or ground) surface of the winds
3. The time-averaging (if any) that has been applied

ADCIRC generally expects 10-meter, 10-minute winds at their actual exposure, although the exact expectations vary depending on the input type. For instance, when Holland-type wind inputs are provided (e.g. NWS=8 or NWS=20), the wind speed is expected to be the 1-minute maximum sustained wind at 10 meters elevation. If marine-exposure winds are provided, then surface roughness reductions may be needed [1] [2] . If winds are provided with a different averaging time, then an appropriate correction may be needed, though winds with averaging times of 10 to 60 minutes are generally considered to be quite similar; this is the so-called mesoscale gap. For recommendations on wind time-scale conversions not handled internally by ADCIRC, for tropical cyclones, see the WMO guidelines of Harper et al. [3] .

## Roughness Reductions

Reductions in wind speed to convert to the appropriate exposure come from a logarithmic boundary layer formulation (see, e.g. [1] [2]) to determine a fraction ${\displaystyle f}$ to reduce the winds,

${\displaystyle f=\left({\frac {z_{0l}}{z_{0m}}}\right)^{0.0706}\left({\frac {\ln {\frac {10}{z_{0l}}}}{\ln {\frac {10}{z_{0m}}}}}\right)}$

for marine roughness length ${\displaystyle z_{0m}}$ and reduced ("land") roughness length ${\displaystyle z_{0l}}$. Wind speed is then reduced as,

${\displaystyle \mathbf {w} '=f\mathbf {w} =f\cdot [u,v]}$

for x- and y- wind vector components ${\displaystyle u}$ and ${\displaystyle v}$. The marine roughness length is,

${\displaystyle z{0m}={\frac {0.018}{g}}\left\Vert \mathbf {w} \right\|}$

for acceleration due to gravity ${\displaystyle g}$. As previously noted, the reduced ("land") roughness length ${\displaystyle z_{0l}}$ is specified by the user via the surface roughness nodal attribute. The fraction ${\displaystyle f}$ is bounded on ${\displaystyle [0,1]}$, meaning the winds cannot be increased, nor change direction.

### Older Behavior

Note that before version 54, there was a bug in this calculation. The mistake and its effects are addressed in this PDF document: ADD A LINK TO A PDF HERE YOOOOO.

## Conversion to Wind Stress

In ADCIRC, two formulations are available to convert wind speeds to the wind stresses applied in the momentum equations. The default is the Garratt formulation, [4] and an alternative is the Powell formulation [5] .

## References

1. Simiu, E., Scanlan, R.H., 1996. Wind effects on structures: fundamentals and applications to design, 3rd ed. ed. John Wiley, New York.
2. Simiu, E., Yeo, D., 2018. Wind effects on structures: modern structural design for wind, Fourth edition. ed. John Wiley & Sons, Hoboken, NJ.
3. Harper, B., Kepert, J., Ginger, J., 2010. Guidelines for converting between various wind averaging periods in tropical cyclone conditions (No. WMO/TD-No. 1555). WMO, Geneva, Switzerland.
4. Garratt, J.R., 1977. Review of Drag Coefficients over Oceans and Continents. Mon. Wea. Rev. 105, 915–929. https://doi.org/10.1175/1520-0493(1977)105<0915:RODCOO>2.0.CO;2
5. Powell, M.D., Vickery, P.J., Reinhold, T.A., 2003. Reduced drag coefficient for high wind speeds in tropical cyclones. Nature 422, 279–283. https://doi.org/10.1038/nature01481