The warming in the lee of high mountains may not be due to latent-heat released in forming rain or snow on the windward side, as described in Fig 7.2. There is another mechanism too. This operates when stable air is dammed on the windward side, being unable to surmount the range. Then air with a higher potential temperature from above the dammed layer subsides adiabatically on the lee side, through the depth of the cold layer on the upwind side.
The lowest incident layer becomes dammed by a range if the Froude number is (much) less than one, i.e. when the upstream wind is slower than [g.H.DJ/J)0.5 m/s, where DJ is the difference between the potential temperatures at top and bottom, respectively, of the layer, whose mean temperature (Kelvin) is J. The term gDJ/J can be thought of as the reduced gravity (of one fluid relative to the other) and H is the barrier’s height (1).
(1) King, J.C. and J. Turner 1997. Antarctic Meteorlogy and Climatology (Cambridge Univ. Press) 409pp.