The application of kinematic wave theory to wave trains and packets with small dissipation

摘要: The validity of kinematic wave theory for linear waves with small dissipation propagating through a homogeneous medium is examined the aid higher‐order Chin. It shown that both nondissipative and weakly‐dissipative holds errors order e2 times e−1 period, where e measure nonuniformity train. For longer times, e−2 secular terms arise, which makes invalid when dispersion becomes vanishingly small. By selecting complex wavenumber chosen such as to make group velocity real, it possible remove first‐order thus produce modified uniformly valid within time period. This modification also applied trains in nonhomogeneous medium. General solutions are presented or packets arbitrary initial conditions.