TY - JOUR
T1 - Statistics of surface renewal of passive scalars in free-surface turbulence
AU - Kermani, Alireza
AU - Khakpour, Hamid R.
AU - Shen, Lian
AU - Igusa, Takeru
PY - 2011/7/10
Y1 - 2011/7/10
N2 - We perform direct numerical simulation to study the transport of gas and heat as passive scalars in free-surface turbulence. Our analysis focuses on the surface age of surface fluid particles, i.e. the time elapsed since the last surface renewal they experienced. Using Lagrangian tracing of fluid particles combined with heat diffusion analysis, we are able to directly quantify surface age to illustrate scalar characteristics at different stages of interfacial transfer. Results show that at the early stage of surface renewal, vertical advection associated with upwellings greatly enhances surface gas flux; random surface renewal model does not apply at this stage when most of the interfacial gas transfer occurs. After a fluid particle leaves the upwelling region, it may enter a nearby downwelling region immediately, where the gas flux is sharply reduced but the variation in surface temperature is small; alternatively, the fluid particle may travel along the surface for some time before it is absorbed by a downwelling, where the surface temperature has changed significantly due to long duration of diffusion and the gas flux is also reduced. To gain further insight into the relationships between surface velocity and scalar quantities, we perform a statistical analysis of upwellings using clustering and nonlinear regression. With this analysis, we are able to provide qualitative and quantitative descriptions of the skewed probability density functions associated with the surface divergence, temperature and gas flux that support our physics-based investigation of surface renewal and surface age.
AB - We perform direct numerical simulation to study the transport of gas and heat as passive scalars in free-surface turbulence. Our analysis focuses on the surface age of surface fluid particles, i.e. the time elapsed since the last surface renewal they experienced. Using Lagrangian tracing of fluid particles combined with heat diffusion analysis, we are able to directly quantify surface age to illustrate scalar characteristics at different stages of interfacial transfer. Results show that at the early stage of surface renewal, vertical advection associated with upwellings greatly enhances surface gas flux; random surface renewal model does not apply at this stage when most of the interfacial gas transfer occurs. After a fluid particle leaves the upwelling region, it may enter a nearby downwelling region immediately, where the gas flux is sharply reduced but the variation in surface temperature is small; alternatively, the fluid particle may travel along the surface for some time before it is absorbed by a downwelling, where the surface temperature has changed significantly due to long duration of diffusion and the gas flux is also reduced. To gain further insight into the relationships between surface velocity and scalar quantities, we perform a statistical analysis of upwellings using clustering and nonlinear regression. With this analysis, we are able to provide qualitative and quantitative descriptions of the skewed probability density functions associated with the surface divergence, temperature and gas flux that support our physics-based investigation of surface renewal and surface age.
KW - Channel flow
KW - turbulent mixing
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U2 - 10.1017/jfm.2011.118
DO - 10.1017/jfm.2011.118
M3 - Article
AN - SCOPUS:79960110137
SN - 0022-1120
VL - 678
SP - 379
EP - 416
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -