On the Spatial Instability of a Conical Sheet

A temporal instability analysis of a conical sheet is carried out.A dispersion relation of a conical sheet for both axisymmetrical and antisymmetrical disturbances is presented.The dispersion relation has been solved numerically and typical results are given.For both axisymmetrical and antisymmetrical disturbances,the increase in sheet cone half-angle reduces the wave growth rate and the range of instability,and shifts the dominant wave of the disturbances to a longer wavelength.For antisymmetrical disturbances,the sheet cone half-angle inhibits the reduction of the growth rate, and two local maxima of the growth rate exist in this case.The two maximum growth rates correspond to waves with different wavelengths,and the growth rate and the range of instability of the short wavelength wave are much less than that of the long one.It is shown that both long and short wavelength waves affect the breakup of the conical sheet,and sheet is easy to breakup under the effect of short wavelength wave.