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I would like to learn about turbulence of a scalar advected by a random velocity field. I know that this problem can be solved analytically and that the statistics of the scalar field are intermittent.

I have read this which is a nice introduction but not detailed enough and am reading this which I am finding very hard.

The passive scalar is an old problem. Do you know of any textbook where it's solution is explained?

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One of the first complete study was performed by Obukhov in 1949 with his famous paper The structure of the temperature field in a turbulent flow. You can find it here [link] (This is a PDF file, you can check by searching the report title on Google). It is a nice thing to know.

A complete review was written by Warhaft in the Annual Review of Fluid Mechanics in 2000 [link]. The paper title is Passive Scalar in Turbulent Flows. It is a really complete review, and the best starting point I think. You can then follow some references he provides.

If you want a textbook, I think that Tennekes & Lumley wrote something about passive scalar in the classic A First Course in Turbulence.

And finally, you can find papers dealing with different aspects of passive scalar by looking at some common journals, Journal of Fluid Mechanics, Physics of Fluids, Journal of Turbulence or Journal of Fluids Engineering.

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