THEORETICAL MEAN WAVE RESISTANCE OF PRECURSOR SOLITON GENERATION IN 2-LAYER FLOW

A new concept of pseudo mean wave resistance is introduced to find the oretical mean wave resistances of the precursor soliton generation in two-layer how over a localized topography at near-resonance in this pa per. The pseudo mean wave resistance of the precursor soliton generati on of two-layer how is determined in terms of the AfKdV equation. From the theoretical results it is shown that the theoretical mean wave re sistance is equal to the pseudo mean wave resistance times 1/m(1), whe re m(1) is the coefficient of the fKdV equation. From the regional dis tribution of the energy of the precursor soliton generation at the res onant points, it is shown that ratios of the theoretical mean wave res istance and regional mean energy to the total mean energy are invarian t constants, i.e. <(E)over circle (1)>/(E) over circle : <(E)over circ le (2)>/(E) over circle: <(E)over circle (3)>(E) over circle :< D > /( E) over circle = (1/2) : (-1/2) : 1 : 1, in which <(E)over circle 1>,< (E)over circle (2)> and <(E)over circle (3)> are the mean energy of th e generating regions of the precursor solitons, of the depression and of the trailing wavetrain at the resonant points respectively, (E) ove r circle and < D > are the total energy of the system and the theoreti cal mean wave resistance at the resonant points. A prediction of the t heoretical mean wave resistances of two-layer how over the semicircula r topography is carried out in terms of the theoretical results of the present paper. The comparison shows that the theoretical mean wave re sistance is in good agreement with the numerical calculation.