Jerome Anglade Ecole Polytechnique Palaiseau France J. Atmos. This scale reduction is here analysed using simple mathematical models. The first is a simple extension of a random-straining model, with random vertical shear being added to a horizontal random strain field. Analytical progress is possible in the limit where the correlation time for the flow is small or large compared to the inverse strain itself.
Numerical integration allows investigation of the intermediate case.
In all cases the vertical scale decreases exponentially fast, at the same rate as the horizontal scale, with the rate, S say, being controlled by the statistics of the horizontal strain field. As this exponential decrease occurs, the horizontal and vertical scales remain in a characteristic ratio, alpha say, which depends on the statistics of the vertical shear and on S . The second model is based on integration of the differential equation for the wavenumber vector associated with a tracer distribution along a parcel trajectory using velocity fields calculated from large-scale observations of the lower stratosphere. The largeness of alpha implies that vertical constrasts in dynamical and tracer quantities are far more important than horizontal contrasts for dissipative processes such as radiative transfer or diffusion.