Lagrangian model for passive scalar gradients in turbulence

被引:0
|
作者
Zhang, Xiaolong [1 ]
Carbone, Maurizio [2 ,3 ]
Bragg, Andrew D. [1 ]
机构
[1] Duke Univ, Dept Civil & Environm Engn, Durham, NC 27708 USA
[2] Max Planck Inst Dynam & Selforg, Fassberg 17, D-37077 Gottingen, Germany
[3] Univ Bayreuth, Theoret Phys 1, Univ Str 30, D-95447 Bayreuth, Germany
关键词
turbulent flows; mixing; VELOCITY-GRADIENT; DYNAMICS; TEMPERATURE; STATISTICS; VORTICITY; FLUID; SHEAR;
D O I
10.1017/jfm.2023.375
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
The equation for the fluid velocity gradient along a Lagrangian trajectory immediately follows from the Navier-Stokes equation. However, such an equation involves two terms that cannot be determined from the velocity gradient along the chosen Lagrangian path: the pressure Hessian and the viscous Laplacian. A recent model handles these unclosed terms using a multi-level version of the recent deformation of Gaussian fields (RDGF) closure (Johnson & Meneveau, Phys. Rev. Fluids, vol. 2 (7), 2017, 072601). This model is in remarkable agreement with direct numerical simulations (DNS) data and works for arbitrary Taylor Reynolds numbers Re-lambda. Inspired by this, we develop a Lagrangian model for passive scalar gradients in isotropic turbulence. The equation for passive scalar gradients also involves an unclosed term in the Lagrangian frame, namely the scalar gradient diffusion term, which we model using the RDGF approach. However, comparisons of the statistics obtained from this model with DNS data reveal substantial errors due to erroneously large fluctuations generated by the model. We address this defect by incorporating into the closure approximation information regarding the scalar gradient production along the local trajectory history of the particle. This modified model makes predictions for the scalar gradients, their production rates, and alignments with the strain-rate eigenvectors that are in very good agreement with DNS data. However, while the model yields valid predictions up to Re-lambda approximate to 500, beyond this, the model breaks down.
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页数:28
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