A note on unsteady laminar plumes/jets

摘要

We consider the laminar downstream evolution of a time-varying source of momentum and buoyancy in a boundary-layer formulation. The recent work of Hewitt and Duck (2011) showed that pulsatile laminar jets (in a boundary-layer model) are susceptible to a propagating wave disturbance that grows downstream. However, the work of Marzouk et al. (2003) presented results for a periodic pulsatile laminar (vertical) jet with heat transfer, for which the pulsation decayed downstream. This motivates the present investigation, to examine if the thermal effects included by Marzouk et al. inhibit the growing wave phenomenon that has been found in the momentum driven case. However, in contrast to Marzouk et al., the present results demonstrate that downstream growth still exists in (vertical) laminar boundary layers when buoyancy effects are included. Our results are carefully validated against known similarity solutions in the steady case, and with both a linearised spectral decomposition for the pulsatile case and an asymptotic description of the resulting wave's spatial growth.