Compressibility effects in a turbulent transport of temperature field are investigated by applying the quasilinear approach for small Péclet numbers and the spectral $\tau$ approach for large Péclet numbers. The compressibility of a fluid flow reduces the turbulent diffusivity of the mean temperature field similarly to that for the 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. The 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. 84, 735840502 (2018)] for noninertial particles or gaseous admixtures. The gradient of the mean fluid pressure results in an additional turbulent pumping of the mean temperature field. The latter effect is similar to the turbulent barodiffusion of particles and gaseous admixtures. The 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.

中文翻译：

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温度场湍流传输中的压缩性效应

通过应用拟线性方法对小Péclet数和谱进行研究，研究了温度场湍流中的压缩效应。 $\tau$大Péclet数的方法。流体流动的可压缩性与颗粒数密度和磁场的相似，降低了平均温度场的湍流扩散率。但是，可压缩湍流中平均温度场的湍流扩散系数表达式与平均粒子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泵送导致速度波动更大的区域的平均温度升高。从形式上讲，这种作用类似于先前发现的可压缩涡轮电泳现象[ J. Plasma Phys。 84，735840502（2018）]用于非惯性颗粒或气态混合物。平均流体压力的梯度导致平均温度场的附加湍流泵送。后一种效果类似于颗粒和气态混合物的湍流压力扩散。由于平均温度场方程中的附加下陷项，流体流的可压缩性还会引起周围流体的湍流冷却。对于粒子，没有类似的效果。