Scaling for turbulent viscosity of buoyant plumes in stratified fluids: PIV measurement with implications for submarine hydrothermal plume turbulence

Time-resolved particle image velocimetry (PIV) has been used to measure instantaneous two-dimensional velocity vector fields of laboratory-generated turbulent buoyant plumes in linearly stratified saltwater over extended periods of time. From PIV-measured time-series flow data, characteristics of plume mean flow and turbulence have been quantified. To be specific, maximum plume penetration scaling and entrainment coefficient determined from the mean flow agree well with the theory based on the entrainment hypothesis for buoyant plumes in stratified fluids. Besides the well-known persistent entrainment along the plume stem (i.e., the 'plume-stem' entrainment), the mean plume velocity field shows persistent entrainment along the outer edge of the plume cap (i.e., the 'plume-cap' entrainment), thereby confirming predictions from previous numerical simulation studies. To our knowledge, the present PIV investigation provides the first measured flow field data in the plume cap region. As to measured plume turbulence, both the turbulent kinetic energy field and the turbulence dissipation rate field attain their maximum close to the source, while the turbulent viscosity field reaches its maximum within the plume cap region; the results also show that maximum turbulent viscosity scales as νt,max = 0.030(B/N)1/2, where B is source buoyancy flux and N is ambient buoyancy frequency. These PIV data combined with previously published numerical simulation results have implications for understanding the roles of hydrothermal plume turbulence, i.e. plume turbulence within the cap region causes the 'plume-cap' entrainment that plays an equally important role as the 'plume-stem' entrainment in supplying the final volume flux at the plume spreading level.