What is the right mixing length for water vapor transport in the storm tracks?

Poleward moisture transport across the midlatitude storm tracks is a central control on the global hydrological cycle and equator-pole temperature gradient, a role that becomes even more important as the climate warms. The storm tracks transport tracers downgradient in a way that is well captured by a diffusive approximation, so a robust understanding of the mechanisms controlling storm track moisture diffusivity is crucial to studies of past and future greenhouse climates.

In classical theories, the diffusivity is expressed as the product of a typical velocity and a mixing length, and it is common to assume that the latter coincides with the mean scale of the energy-containing eddies. We discuss the conditions under which this assumption is true in general, and then focus on the case of water vapor by analyzing a suite of aquaplanet simulations using NCAR's CAM3 GCM spanning a broad range of climates. We show that the assumption fails both qualitatively and quantitatively in these simulations: the mixing length is always much smaller than the size of the dominant eddies, and as the climate warms the mixing length decreases while the eddy size increases. We propose a simple scaling that robustly captures the behavior of the mixing length. We also show that the resulting decrease in diffusivity is strong enough that, at sufficiently high temperatures, poleward moisture flux reaches an upper limit and then decreases with further warming.