TY - JOUR
T1 - Turbulent Prandtl number and characteristic length scales in stably stratified flows
T2 - steady-state analytical solutions
AU - Basu, Sukanta
AU - Holtslag, Albert A.M.
PY - 2021
Y1 - 2021
N2 - In this study, the stability dependence of turbulent Prandtl number (Prt) is quantified via a novel and simple analytical approach. Based on the variance and flux budget equations, a hybrid length scale formulation is first proposed and its functional relationships to well-known length scales are established. Next, the ratios of these length scales are utilized to derive an explicit relationship between Prt and gradient Richardson number. In addition, theoretical predictions are made for several key turbulence variables (e.g., dissipation rates, normalized fluxes). The results from our proposed approach are compared against other competing formulations as well as published datasets. Overall, the agreement between the different approaches is rather good despite their different theoretical foundations and assumptions.
AB - In this study, the stability dependence of turbulent Prandtl number (Prt) is quantified via a novel and simple analytical approach. Based on the variance and flux budget equations, a hybrid length scale formulation is first proposed and its functional relationships to well-known length scales are established. Next, the ratios of these length scales are utilized to derive an explicit relationship between Prt and gradient Richardson number. In addition, theoretical predictions are made for several key turbulence variables (e.g., dissipation rates, normalized fluxes). The results from our proposed approach are compared against other competing formulations as well as published datasets. Overall, the agreement between the different approaches is rather good despite their different theoretical foundations and assumptions.
KW - Anisotropy
KW - Buoyancy length scale
KW - Gradient Richardson number
KW - Shear length scale
KW - Stable boundary layer
UR - http://www.scopus.com/inward/record.url?scp=85118396398&partnerID=8YFLogxK
U2 - 10.1007/s10652-021-09820-7
DO - 10.1007/s10652-021-09820-7
M3 - Article
AN - SCOPUS:85118396398
SN - 1567-7419
VL - 21
SP - 1273
EP - 1302
JO - Environmental Fluid Mechanics
JF - Environmental Fluid Mechanics
IS - 6
ER -