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Full Equations (FEQ) Model for the Solution of the Full, Dynamic Equations of Motion for One-Dimensional Unsteady Flow in Open Channels and Through Control Structures

U.S. GEOLOGICAL SURVEY WATER-RESOURCES INVESTIGATIONS REPORT 96-4240

13.8 Wind Information Block--Wind Table


Purpose: The information on wind (such as wind-shear coefficient, air density, wind velocity table number, and other information) is supplied with this block. This block is present only when WIND=YES in the Run Control Block (section 13.1). If wind shear is simulated, the azimuth information in the Branch Description Block (section 13.2) should be specified. If the azimuth information is not specified, then all elements will be assigned an azimuth of zero, meaning that downstream direction points north for the computational elements.

Heading: One line of user-selected information. The suggested string is WIND INFORMATION.

LINE 1

Variable: WINTAB

Format: 7X, I5

Example: WINTAB=00007

Explanation: WINTAB is the number of the table specifying wind velocity and direction as a function of time. Function table type 11 is reserved for this purpose. An inconsistency often results in common practice for the designation of wind direction. The direction for wind has traditionally been the point from which the wind is coming and not the direction the wind is going. This traditional designation is retained and applied in FEQ. Thus, the direction of the wind is in degrees clockwise from north for the direction from which the wind is coming. For example, an east wind is given an azimuth of 90 degrees, a south wind an azimuth of 180 degrees, a west wind an azimuth of 270 degrees, and a north wind an azimuth of 0 degrees. The azimuth for the orientation of an element in a branch is based on the downstream direction that water flows, not the direction from which it is coming. Therefore, an element with downstream flow going east also is given an azimuth of 90 degrees. In this case an east wind will be in the opposite direction even though the wind and the downstream flow direction are given the same value for azimuth. One-hundred eighty degrees are added internally in FEQ to convert the wind direction to the same basis as the flow direction.

Estimates of the drag coefficient for wind-shear stress on the water surface are computed with results determined by Wilson (1960). Wilson indicates that the drag coefficient depends on the wind velocity, with the coefficient increasing to a limit as the wind velocity increases. He also stated that there is evidence that the drag coefficient decreases slightly to a minimum at about 13 to 16.5 ft/s for low wind speeds. The variation between low wind and high wind speeds is nonlinear but not well established. This variation is supported in FEQ by requiring the following values: the wind speed at minimum drag coefficient, VAMIN; the minimum drag coefficient, CDMIN; the wind speed at maximum drag coefficient, VAMAX; and the maximum drag coefficient, CDMAX. The minimum drag coefficient is applied to all wind speeds less than VAMIN and the maximum drag coefficient to all wind speeds greater than VAMAX. The drag coefficient for intermediate wind speeds is interpolated by use of a cubic polynomial between the minimum and maximum points, assuming that the slope of the function is zero at both extremes.

The drag-coefficient values given below are computed under the assumption that the point of wind measurement is 33 ft above the water surface. The wind speed can be adjusted to this standard height by assuming an appropriate variation for wind velocity in the vertical (Linsley and others, 1982, p. 37-41).

LINE 2

Variable: AIRSPW

Format: 7X, F10.0

Example: AIRSPW= 0.075

Explanation: AIRSPW is the specific weight of air, in pounds per cubic foot. The specific weight of air varies slightly with temperature, moisture content, and atmospheric pressure. These variations over the course of the
simulation are considered negligible. The specific weight of air can be estimated from

(148)

Equation ,

where

This is the Greek letter Gamma a is the specific weight of air, in pounds per cubic foot;
T is the air temperature, in degrees Fahrenheit;
Pa is the atmospheric pressure, in millibars; and
e is the vapor pressure of water in air, in millibars.

The specific weight of air at standard atmospheric pressure varies from 0.075 lb/ft 3 in dry air at 40° F to 0.0654 lb/ft 3 in fully saturated air at 100° F. The variation is small but might be detectable in a carefully controlled experiment in a laboratory setting. It is unlikely that a field test would require any more than a possible adjustment to average conditions of atmospheric pressure, temperature, and humidity.

LINE 3

Variable: WATSPW

Format: 7X, F10.0

Example: WATSPW= 62.4

Explanation: WATSPW is the specific weight of water, in pounds per cubic foot. The ratio of the specific weight of air to the specific weight of water is used in FEQ computations. The respective specific weights can be supplied in any convenient units so long as the ratio is correct. The specific weight of water varies slightly with temperature but the variation from 62.4 lb/ft 3 over the range of possible temperatures is less than 1 percent.

LINE 4

Variable: VAMIN

Format: 6X,F10.0

Example: VAMIN= 15

Explanation: VAMIN is the velocity of the wind where the drag coefficient reaches an approximate minimum value. The recommended value from Wilson (1960) is about 15 ft/s.

LINE 5

Variable: CDMIN

Format: 6X,F10.0

Example: CDMIN= 0.0015

Explanation: CDMIN is the minimum value of the drag coefficient. The recommended value from Wilson (1960) is 0.0015.

LINE 6

Variable: VAMAX

Format: 6X,F10.0

Example: VAMAX= 75

Explanation: VAMAX is the wind velocity where the drag coefficient reaches an approximate maximum. The recommended value from Wilson (1960) is 75 ft/s (about 50 mi/hr).

LINE 7

Variable: CDMAX

Format: 6X,F10.0

Example: CDMAX= 0.0025

Explanation: CDMAX is the maximum value of the drag coefficient. The recommended value from Wilson (1960) is 0.0025.


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