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arXiv 2008.00964physics.flu-dyn
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温度场湍流输运中的可压缩性效应

Compressibility effects in a turbulent transport of temperature field

I. Rogachevskii, N. Kleeorin

摘要:

本文用准线性方法研究了小Péclet数时湍流温度场输运的可压缩性效应,用谱$τ$方法研究了大Péclet数时湍流温度场输运的可压缩性效应。流体流动的可压缩性降低了平均温度场的湍流扩散率,类似于颗粒数密度和磁场的湍流扩散率。然而,在可压缩湍流中,平均温度场的湍流扩散系数的表达式与平均颗粒数密度和平均磁场的表达式不同。湍流的可压缩性和不均匀性的综合作用导致湍流抽运引起的速度脉动更强烈的区域的平均温度升高。形式上,这种效应类似于先前发现的非惯性颗粒或气体混合物的可压缩湍流电泳现象[J. Plasma Phys. { \bf 84},735840502(2018)]。平均流体压力的梯度导致平均温度场的附加湍流泵送。后一种效应类似于颗粒和气体混合物的湍流气压扩散。流体流的可压缩性也会导致周围流体的湍流冷却,这是由于平均温度场方程中的附加下沉项。对于粒子,没有类似的效果。

英文摘要:

Compressibility effects in a turbulent transport of temperature field are investigated applying the quasi-linear approach for small Péclet numbers and the spectral $τ$ approach for large Péclet numbers. Compressibility of a fluid flow reduces the turbulent diffusivity of the mean temperature field similarly to that for particle number density and magnetic field. However, expressions for the turbulent diffusion coefficient for the mean temperature field in a compressible turbulence are different from those for the mean particle number density and the mean magnetic field. Combined effect of compressibility and inhomogeneity of turbulence causes an increase of the mean temperature in the regions with more intense velocity fluctuations due to a turbulent pumping. Formally, this effect is similar to a phenomenon of compressible turbophoresis found previously [J. Plasma Phys. {\bf 84}, 735840502 (2018)] for non-inertial particles or gaseous admixtures. Gradient of the mean fluid pressure results in an additional turbulent pumping of the mean temperature field. The latter effect is similar to turbulent barodiffusion of particles and gaseous admixtures. Compressibility of a fluid flow also causes a turbulent cooling of the surrounding fluid due to an additional sink term in the equation for the mean temperature field. There is no analog of this effect for particles.

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