140 Shallow Water Wave Transformation through External Factors 



damping liquid reduces consequently the surface tension of the upper layer 

 and capillary wave action of the oily surface is started more easily than with 

 sea water alone and, therefore, a damping action cannot set. The calming 

 effect of the waves by oil cannot be attributed to the difference in surface 

 tension of water and oil alone. 



Because the surface tension of sea water is greater than the tensions at the 

 surfaces of separation of oil-water and oil-air, a drop of oil on the water will 

 spread rapidly into a very thin film. If this layer becomes sufficiently thin, that 

 is of the order of magnitude of one-hundred thousandth or one-millionth of 

 a millimetre, it is found that the surface tension is no longer constant but 

 increases when thickness of the layer is reduced and vice versa. Each expansion 

 of the surface results in a reduction of the thickness of the oil film and, conse- 

 quently, an increase in surface tension and vice versa. Therefore a surface 

 opposes any motion connected with an expansion of the surface. The conta- 

 minated water surface therefore behaves as an elastic skin. The expanding and 

 contracting movements of the surface accompanying the wave motion generate 

 alternating tangential drag on the water, with a consequent increase in the rate 

 of dissipation of energy and reducing the possibility of wave formation. The 

 expansions are greater where the waves are shorter and steeper. Moreover, the 

 expansions are greater in the place where the waves are cusped than in the flat 

 troughs and consequently the calming effect of the oils will be more apparent 

 with shorter waves, and will be more visible at the wave crests than in the 

 wave troughs. This is exactly what has been observed. 



The calming effect of a thin layer of oil can also be considered as a result of the greater viscosity 

 of the oils, even though this explanation, physically speaking, is not as correct as the one mentioned 

 before. The damping time for waves, according to equation (IV. 23) is 



A. 2 

 Stzv ' 



in which v — fiJQ is the kinematic viscosity of the liquid. For water v is of the order of magni- 

 tude 01, for petroleum and liquid oils only little more (0011-006), for olive oil v is already 

 80 times (v — 0808), for rape seed oil 70 to 100 times (v = 1-2) greater than for pure water. The 

 damping time for such liquids is, therefore, many times smaller than for water. A capillary wave 

 of X = 5 cm vanishes on water in 32 sec, on rape seed oil in 0-26 sec; a wave of A = 20 cm needs 

 for this 507 sec, on rape seed oil only 0-4 sec; a wave 1 m long on water takes 3i h, on rape seed 

 oil only 1-75 min. One also observes that petroleum, due to its small viscosity, similar to that of 

 water, cannot have a great wave calming effect. The great viscosity of the new surface should there- 

 fore, be decisive. In this explanation little consideration is given to the effect of the abnormal behav- 

 iour of the water surface contaminated by oils in regard to the surface tension, also the fact that 

 the oil spreads on the water in an extremely thin layer, which makes the effect of the alternating 

 variations in the surface tension possible. 



An exact theory by Reynolds (1880) and Aitken(1883, p. 56) starts with these variations 

 considering the oil layer as a quasi-elastic skin, the effect of which is the greater, the shorter the 

 wave length is. If this wave length becomes sufficiently small, the surface is practically inexpandible 

 and the horizontal velocity at the surface will vanish. In deriving the relations on the influence of 



