TY - JOUR

T1 - A hierarchical random additive model for passive scalars in wall-bounded flows at high Reynolds numbers

AU - Yang, Xiang I.A.

AU - Abkar, Mahdi

N1 - Publisher Copyright:
© 2018 Cambridge University Press.

PY - 2018/5/10

Y1 - 2018/5/10

N2 - The kinematics of a fully developed passive scalar is modelled using the hierarchical random additive process (HRAP) formalism. Here, 'a fully developed passive scalar' refers to a scalar field whose instantaneous fluctuations are statistically stationary, and the 'HRAP formalism' is a recently proposed interpretation of the Townsend attached eddy hypothesis. The HRAP model was previously used to model the kinematics of velocity fluctuations in wall turbulence: , where the instantaneous streamwise velocity fluctuation at a generic wall-normal location is modelled as a sum of additive contributions from wall-attached eddies and the number of addends is . The HRAP model admits generalized logarithmic scalings including , , , where is the streamwise velocity fluctuation, is an outer length scale, is the two-point displacement in the streamwise direction and denotes ensemble averaging. If the statistical behaviours of the streamwise velocity fluctuation and the fluctuation of a passive scalar are similar, we can expect first that the above mentioned scalings also exist for passive scalars (i.e. for being fluctuations of scalar concentration) and second that the instantaneous fluctuations of a passive scalar can be modelled using the HRAP model as well. Such expectations are confirmed using large-eddy simulations. Hence the work here presents a framework for modelling scalar turbulence in high Reynolds number wall-bounded flows.

AB - The kinematics of a fully developed passive scalar is modelled using the hierarchical random additive process (HRAP) formalism. Here, 'a fully developed passive scalar' refers to a scalar field whose instantaneous fluctuations are statistically stationary, and the 'HRAP formalism' is a recently proposed interpretation of the Townsend attached eddy hypothesis. The HRAP model was previously used to model the kinematics of velocity fluctuations in wall turbulence: , where the instantaneous streamwise velocity fluctuation at a generic wall-normal location is modelled as a sum of additive contributions from wall-attached eddies and the number of addends is . The HRAP model admits generalized logarithmic scalings including , , , where is the streamwise velocity fluctuation, is an outer length scale, is the two-point displacement in the streamwise direction and denotes ensemble averaging. If the statistical behaviours of the streamwise velocity fluctuation and the fluctuation of a passive scalar are similar, we can expect first that the above mentioned scalings also exist for passive scalars (i.e. for being fluctuations of scalar concentration) and second that the instantaneous fluctuations of a passive scalar can be modelled using the HRAP model as well. Such expectations are confirmed using large-eddy simulations. Hence the work here presents a framework for modelling scalar turbulence in high Reynolds number wall-bounded flows.

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U2 - 10.1017/jfm.2018.139

DO - 10.1017/jfm.2018.139

M3 - Article

AN - SCOPUS:85043305736

SN - 0022-1120

VL - 842

SP - 354

EP - 380

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

ER -