Abstract

Abstract The combined effects of advection and diffusion on the equilibrium spatial structure of a tracer whose spatial variation is maintained by a large-scale forcing are considered. Motivated by the lower stratosphere, the flow is taken to be large-scale, time-dependent, and purely horizontal but varying in the vertical, with the vertical shear much larger than horizontal velocity gradients. As a result, the ratio α between horizontal and vertical tracer scales is large. (For the lower stratospheric surf zone α has been shown to be about 250.) The diffusion parameterizes the mixing effects of small-scale processes. The three space dimensions and the large range between the forcing scale and the diffusive scale mean that direct numerical simulation would be prohibitively expensive for this problem. Instead, an ensemble approach is used that takes advantage of the separation between the large scale of the flow and the small scale of the tracer distribution. This approach, which has previously been used i...

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