Suppose that there is an air pollutant called galactica that is found within long, narrow spaceships. This pollutant decomposes faster in warmer air than in cooler air. Hence, the conservation equation for gallacticum is Dc Dt = acT, (1) where c is the concentration of gallacticum, a is a constant, T is the absolute air temperature, and t is time. Derive the prognostic equation for the mean concentration of gallacticum that applies to turbulent flow within the space ship. You can scale your equations to the forced ventilation current, U , down the length of the space ship (in the x-direction). There is, however, horizontal homogeneity of mean quantities in the x-direction only. 2