An analytical study of the effect of surface roughness on the stability of a heated water boundary layer

The onset of transition from laminar to turbulent flow in a high Reynolds number, water boundary layer was investigated with emphasis on predicting the global effects of distributed surface roughness on transition. The authors used the results of linear stability theory as an indicator of transition, but, this paper presents only comparisons of the stability results (not actual transition predictions). The effects of surface roughness on transition were induced by means of an existing phenomenological model for the effects of distributed roughness on the mean flow profiles. This model, originally developed for high Mach number, compressible boundary layers, was applied without change to the present incompressible, water boundary-layer environment, and identical values of the required empirical constants were used in both cases. One conclusion obtained from the numerical results is that the presence of favorable pressure gradients and/or surface heating make the boundary layer more susceptible to roughness, not only when compared in terms of the actual roughness height, but also when compared in terms of the roughness height to momentum thickness ratio. When the roughness is sufficiently large, its presence can change the effect of surface heat addition from a strongly stabilizing factor to a strongly destabilizing phenomena.