NONLINEAR EFFECTS ON THE INSTABILITY OF THE INTERFACE OF AN INVISCID INCOMPRESSIBLE FLUID AND THE FORMATION OF SPIKES.
Abstract
The present investigation deals with the nonlinear effects of the instability of the accelerated interface separating an inviscid liquid and air, for initial sinusoidal disturbances of wave-number range from well below to well above the cut-off. It is found that the growth of the interface depends explicitly on two dimensionless parameters of the initial disturbance, namely, the dimensionless amplitude (the ratio of the amplitude to wavelength) and the dimensionless wave number (the ratio of the wave number of the initial disturbance to the cut-off wave number). The results of the present third-order theory show some new qualitative features different from the first and second-order theories. The frequency is found to be dependent on the amplitude as well as the wave number, whereas in the linearized and second-order theories, the frequency depends only on the wave number. Another interesting feature of the present theory, which is based on higher approximations, is that the analysis reveals the phenomenon of over stability (waves oscillating with amplitude increasing in time). This behavior of over stability persists only till the amplitude rises to a certain value beyond which instability occurs, resulting in the monotonic growth of the amplitude. Further, the present theory predicts instability even for the wave-number range greater than the cut-off, which is not the case according to the linearized theory. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1966
- Accession Number
- AD0478514
Entities
People
- I-dee Chang
- N. R. Rajappa
Organizations
- Stanford University