TY - JOUR
T1 - A k-ε turbulence model based on the scales of vertical shear and stem wakes valid for emergent and submerged vegetated flows
AU - King, A. T.
AU - Tinoco, R. O.
AU - Cowen, E. A.
N1 - Funding Information:
The authors wish to thank F. Zarama for contributing to the laboratory work discussed in § 5. They also wish to thank F. Rueda for valuable conversations that inspired and informed this work. This material is based upon work supported by the National Science Foundation under grant number CBET-0626164 and the Graduate Research Fellowship Program. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
PY - 2012/6/25
Y1 - 2012/6/25
N2 - Flow and transport through aquatic vegetation is characterized by a wide range of length scales: water depth (H), plant height (H), stem diameter (d), the inverse of the plant frontal area per unit volume ((a-1)) and the scale(s) over which a varies. Turbulence is generated both at the scale(s) of the mean vertical shear, set in part by a, and at the scale(s) of the stem wakes, set by d. While turbulence from each of these sources is dissipated through the energy cascade, some shear-scale turbulence bypasses the lower wavenumbers as shear-scale eddies do work against the form drag of the plant stems, converting shear-scale turbulence into wake-scale turbulence. We have developed a k-ε model that accounts for all of these energy pathways. The model is calibrated against laboratory data from beds of rigid cylinders under emergent and submerged conditions and validated against an independent data set from submerged rigid cylinders and a laboratory data set from a canopy of live vegetation. The new model outperforms existing k-ε models, none of which include the d scale, both in the emergent rigid cylinder case, where existing k-ε models break down entirely, and in the submerged rigid cylinder and live plant cases, where existing k-ε models fail to predict the strong dependence of turbulent kinetic energy on d. The new model is limited to canopies dense enough that dispersive fluxes are negligible.
AB - Flow and transport through aquatic vegetation is characterized by a wide range of length scales: water depth (H), plant height (H), stem diameter (d), the inverse of the plant frontal area per unit volume ((a-1)) and the scale(s) over which a varies. Turbulence is generated both at the scale(s) of the mean vertical shear, set in part by a, and at the scale(s) of the stem wakes, set by d. While turbulence from each of these sources is dissipated through the energy cascade, some shear-scale turbulence bypasses the lower wavenumbers as shear-scale eddies do work against the form drag of the plant stems, converting shear-scale turbulence into wake-scale turbulence. We have developed a k-ε model that accounts for all of these energy pathways. The model is calibrated against laboratory data from beds of rigid cylinders under emergent and submerged conditions and validated against an independent data set from submerged rigid cylinders and a laboratory data set from a canopy of live vegetation. The new model outperforms existing k-ε models, none of which include the d scale, both in the emergent rigid cylinder case, where existing k-ε models break down entirely, and in the submerged rigid cylinder and live plant cases, where existing k-ε models fail to predict the strong dependence of turbulent kinetic energy on d. The new model is limited to canopies dense enough that dispersive fluxes are negligible.
KW - geophysical and geological flows
KW - turbulence modelling
KW - turbulent mixing
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U2 - 10.1017/jfm.2012.113
DO - 10.1017/jfm.2012.113
M3 - Article
AN - SCOPUS:84864203029
SN - 0022-1120
VL - 701
SP - 1
EP - 39
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -