The structures of high proper motion knots in both stellar and extragalactic jets could be the result of a time dependence in the ejection mechanism. Supersonic source velocity variations result in the formation of "internal working surfaces" (corresponding to pairs of shocks) that produce regions of enhanced emission and excitation which travel downstream along the jet flow, in qualitative agreement with the observations of astrophysical jets. We model such structures in terms of the one-dimensional viscous Burgers equation, which admits an analytic treatment. These solutions allow us to obtain universal relations between the observed characteristics of the jets (e.g., their velocity profiles, knot separations, and the proper motions and intensities of the knots) and the kinetic energy ejected between two successive pulses of the time- dependent source. In this way, we obtain easily application recipes to interpret the "archeological record" of the past history of the source which is provided by the jet structure observed at the present time.
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Kofman et al. (1992) studied this question.