Survival of entropy waves during their advection throughout a combustor is central to the generation of entropic sound and the subsequent effects upon thermoacoustic stability of the system. However, the decay and spatial non-uniformity of entropy waves are largely ignored by the existing models used for the calculation of entropy noise generation. Recent investigations have demonstrated the complex spatio-temporal dynamics of entropy waves and cast doubts on the sufficiency of the one-dimensional approach, conventionally used for the analysis of these waves. Hence, this paper proposes a novel approach to the low-order modelling of entropy wave evolution wherein the wave is described by the two states of position and amplitude in the streamwise direction. A high-order model is first developed through direct numerical simulation of the advection of entropy waves in a fully developed, heat transferring, compressible, turbulent channel flow. The data are then utilised to build and validate a series of nonlinear, low-order models that provide an unsteady two-dimensional representation of the decaying and partially annihilating entropy waves. It is shown that these models need, at most, approximately
of the total trace of entropy wave advection to predict the wave dynamics accurately. The results further reveal that the existing linear low-order models are truly predictive only for the entropy waves with less than
increase in the gas temperature compared to that of the surrounding flow. Yet, in agreement with the assumption of existing models, it is shown that entropy waves travel with the mean flow speed.