Generalized Burgers equation for plane waves

Burgers’ equation, an equation for plane waves of finite amplitude in thermoviscous fluids, is generalized by replacing the thermoviscous term Aut’t’ (A is the thermoviscous coefficient, u particle velocity, and t’ retarded time) with an operator L(u). This operator represents the effect of attenuation and dispersion, even if known only empirically. Specific forms of L(u) are given for thermoviscous fluids, relaxing fluids, and fluids for which viscous and thermal boundary layers are important. A method for specifying L(u) when the attenuation and dispersion properties are known only empirically is described. A perturbation solution of the generalized Burgers equation is carried out to third order. An example is discussed for the case α2=2α1, where α1 and α2 are the small‐signal attenuation coefficients at the fundamental and second‐harmonic frequencies, respectively. The growth/decay curve of the second harmonic component is given both with and without the inclusion of dispersion. Dispersion causes a sma...