Chaos and the dynamics of biological populations

Abstract

The behaviour of short capillary-gravity waves under the action of a wind has been investigated in a laboratory wind-water tunnel. Waves of known constant frequency were generated by a paddle and their amplitude was measured as they progressed along the tunnel. The growth rate was calculated from these measurements and compared with theoretical predictions using the linearized theory of Miles and Benjamin to calculate the stresses exerted by the wind on the wavy surface. The liquids used were water, dilute glycerol solutions and solutions of a surface active agent, sodium lauryl sulphate. Agreement with the theory was very good for wind speeds up to 3 m/s. In most cases where theory and experiment disagreed the reason appeared to be failure of the linear theory for the liquid. The minimum velocity necessary to produce neutral waves on water occurred at U$_{\ast}$ $\sim $ 5 cm/s in agreement with the theory. This value was independent of wavelength for lengths between 4 and 8 cm. In the presence of the surfactant this minimum velocity could be increased by a factor of four. The surface velocity of the liquid was found to be increased substantially by the presence of a surface active agent.