This paper considers the effect of flow advection on entropy waves. The interest is in whether entropy waves persist in gas turbine combustors, between the flame, where they are generated, and the combustor exit, where their acceleration generates acoustic waves (known as ‘entropy noise’ or ‘indirect combustion noise’). Entropy wave advection within a simplified fully developed turbulent channel-flow simulation is investigated. Entropy wave dissipation is found to be negligible, with loss of entropy wave strength caused predominantly by mean flow shear dispersion. The impulse response of entropy perturbations downstream of where they are generated is shown to be well modelled by a Gaussian profile in time. This yields a (different) Gaussian form for the inlet–outlet transfer function of entropy perturbations. For representative gas turbine flows, the magnitude of this transfer function is such that significant entropy wave strength will remain at the combustor exit, confirming that entropy-generated acoustic waves are likely to be important.