Theoretical mean wave resistance of precursor solition generation in two-layer flow

Abstract

A new concept of pseudo mean wave resistance is introduced to find theoretical mean wave resistances of the precursor soliton generation in two-layer flow over a localized topography at near-resonance in this paper. The pseudo mean wave resistance of the precursor soliton generation of two-layer flow is determined in terms of the AfKdV equation. From the theoretical results it is shown that the theoretical mean wave resistance is equal to the pseudo mean wave resistance times 1/m ₁, wherem ₁ is the coefficient of the fKdV equation. From the regional distribution of the energy of the precursor soliton generation at the resonant points, it is shown that ratios of the theoretical mean wave resistance and regional mean energy to the total mean energy are invariant constants, i.e.$\mathop E\limits^ \circ _1 /\mathop E\limits^ \circ :\mathop E\limits^ \circ _2 /\mathop E\limits^ \circ :\mathop E\limits^ \circ _3 /\mathop E\limits^ \circ :< D > /\mathop E\limits^ \circ = (1/2)$: (−1/2):1:1, in which$\mathop E\limits^ \circ _1 ,\mathop E\limits^ \circ _2$ and$\mathop E\limits^ \circ _3$ are the mean energy of the generating regions of the precursor solitons, of the depression and of the trailing, wavetrain at the resonant points respectively,$\mathop E\limits^ \circ$ and <D> are the total energy of the system and the theoretical mean wave resistance at the resonant points. A prediction of the theoretical mean wave resistance flow over the semicircular topography is carried out in terms of the theoretical results of the present paper. The comparison shows that the theoretical mean wave resistance is in good agreement with the numerical calculation.