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Turbulence in the flow of fluid through a pipe can be suppressed by buoyancyforces. As the suppression of turbulence leads to severe heat transferdeterioration, this is an important and undesirable phenomenon in both heatingand cooling applications. Vertical flow is often considered, as the axialbuoyancy force can help drive the flow. With heating measured by the buoyancyparameter $C$, our DNS show that shear-driven turbulence may either becompletely laminarised or transitions to a relatively quiescentconvection-driven state. Buoyancy forces cause a flattening of the base flowprofile, which in isothermal pipe flow has recently been linked to completesuppression of turbulence (K\"{u}hnen et al. Nat. Phys., 2018), and theflattened laminar base profile has enhanced nonlinear stability (Marensi et al.JFM, 2019). In agreement with these findings, the nonlinear lower-branchtravelling-wave solution analysed here, which is believed to mediate transitionto turbulence in isothermal pipe flow, is shown to be suppressed by buoyancy. Alinear instability of the laminar base flow is responsible for the appearanceof the relatively quiescent convection driven state for $C\gtrsim 4$ across therange of Reynolds numbers considered. In the suppression of turbulence,however, i.e. in the transition from turbulence, we find clearer associationwith the analysis of He et al. (JFM, 2016) than with the above dynamicalsystems approach, which describes better the transition to turbulence. Thelaminarisation criterion He et al. propose, based on an apparent Reynoldsnumber of the flow as measured by its driving pressure gradient, is found tocapture the critical $C=C_{cr}(Re)$ above which the flow will be laminarised orswitch to the convection-driven type. Our analysis suggests that it is theweakened rolls, rather than the streaks, which appear to be critical forlaminarisation.

Suppression of turbulence and travelling waves in a vertical heated pipe