Wind tides in small closed channels

Abstract

In addition to the generation of waves, a wind produces a mass transport in a body of water resulting in t h e lowering of the level at t h e windward ~ide an~ rise at t he leeward side which is called wind tide or set-up. Two eff ects of the wll1d are Involved: the s urface t raction on the water, and the form resistance of the waves. This paper presents the t heoretical background of t he subject and expcriment al r es ults. It was di scovered t hat formation of waves in an experimental cha nnel could be inhibited by addin g small amounts of soap or detergent to t he water. !his made it P?ssible to study the sl!rface tracti?n effect separately. The eff ect was studied for both lamlIlar and t urbulent motIOn of the dnft and gravi ty currents produced by the wind. The set-up computed from me~s ured wind and water surface veloci ties agreed with theory. Regardless of t he flow regime, the set-up was unaffected by viscosity and independent of t he depth-length ratio of t he channel. The additional set-up due to presence of waves could be correlated only b y int roducin g a characteristic velocity. This additional set-up appears to vary as t h e square root of the d ep th-length rat io. The relation of t he characteristic velocity to t h e criti cal velocity for wind generation is di scussed. The derived empirical formula for set-up is compared with obser vations in Lake Erie.

Wind-induced Stresses on Water Surfaces: A Wind-tunnel Study

“…These displacements must be corrected for the difference in the air pressure along the length of the channel. The equation relating the set-up S to the surface stress TO has been given by Keulegan (1951) as…”

“…Other workers who have studied the surface stresses due to wind on confined water surfaces include Keulegan (1951), Francis (1954), and Vines (1959), using wind tunnels, and Van Dorn (1953), using an open pond. There appears to be much disparity between the experimental conditions prevailing and the conclusions drawn from these various studies, and a closer look at the problem seems to be warranted.…”

The Response of Closed Channels to Wind Stresses

“…There results a slope dh/dx of the water surface at a distance x (cm) down-wind, a flow u (cm/s) at a height z (cm) above the bed of the channel, and a shearing stress TO (dyn/cm 2 ) at the bed. From Keulegan (1951), steady conditions are obtained when (1) where p (g/cm 3 ) is the liquid density, g (cm/s 2 ) is the gravitational acceleration, and H (cm) is the undisturbed depth of the liquid. Relation (1) assumes that any change of air pressure along the channel is negligible or incorporated as a correction to the surface slope.…”

“…The response of the channel to the wind stress has been determined by Keulegan (1951) for the condition that flow everywhere is controlled by molecular viscosity. The velocity profile reads…”

Effets du Vent Sur les Nappes Liquides

“…KEULEGAN [27] a fait quelques essais de laboratoire très intéressants. Il a trouvé que l'addition d'un détergent dans l'eau empêchait la formation des vagues.…”