Introduction

The mean structure of the convective boundary layer (CBL) is sketched in Figure 11.1. The surface layer (the lowest 10%, say) is the most accessible to observation and therefore the best understood. Above it lies the mixed layer (not “mixing” layer; that is the turbulent shear layer between parallel streams of different speeds). Here the turbulent diffusivity tends to be largest and mean gradients of wind and conserved scalars smallest. The interfacial layer buffers the mixed layer from the free atmosphere. Its top at mean height h2 can be thought of as the greatest height reached by the surface-driven convective elements, and its bottom at h1 the deepest penetrations of the nonturbulent free atmosphere. The mean CBL depth zi lies between these two; it is often taken as the height at which the vertical turbulent flux of virtual potential temperature has its negative maximum.

The mixed layer: velocity fields

Mixed-layer similarity

A mimimal set of governing parameters for the quasi-steady mixed layer is the M-O group u*, z, g/θ0, Q0 (the surface flux of virtual temperature), (the surface flux of a conserved scalar) plus the boundary-layer depth zi. The dimensional analysis (Chapter 10) here has m − 1 = 6 governing parameters and n = 4 dimensions, so there are m − n = 3 independent dimensionless quantities. One is the dimensionless dependent variable; it is conventional to take the other two as z/zi and zi/L.

I doubt if many students have started out to be a “turbulence person.” I suspect it usually just happens, perhaps like meeting the person you marry. I was an engineering graduate student, nibbling at convective heat transfer, when a friend steered me to a turbulence course taught by John Lumley. It was not rollicking fun – we went through Townsend's The Structure of Turbulent Shear Flow page by page – but it was a completely new field.

I began to explore the turbulence literature, particularly that by the heavy hitters of theoretical physics and applied mathematics. To my engineering eyes it was impregnable; I would need much more coursework before I could even put it in a context. Today I can understand why those theoretical struggles continue. Phil Thompson, a senior scientist in the early NCAR explained it this way:

Introduction

As we have seen, the huge range of spatial scales in large-Rt turbulent flows makes it impossible to solve their equations of motion numerically. In applications we use ensemble- or space-averaged equations that have a drastically reduced range of scales. In Chapter 3 we saw that this averaging produces new terms involving turbulent fluxes, and in Chapter 5 we discussed the evolution equations for the fluxes produced by ensemble averaging.

In this chapter we discuss the space-averaged equations further, present the evolution equations for their fluxes, and discuss the modeling of these fluxes. This modeling is of two broad types depending on the spatial scale Δ of the averaging relative to the size ℓ of the energy-containing eddies. In what we shall call “coarse resolution” applications Δ ≫ ℓ in “fine resolution” ones Δ ≪ ℓ.

The first numerical solutions of the averaged equations in meteorology appear to be those of Charney et al. (1950). The domain was a limited area of the earth's surface with 15 × 18 grid squares each 736 km on a side, with only one level in the vertical. The study of Phillips (1955, 1956) soon followed. Its spatial resolution was similarly coarse, but it had two grid levels in the vertical. By the 1970s general circulation models were being used fairly widely, and “mesoscale” or “limited area” models were being used in regional domains. Computer size and speed had grown substantially since the 1950s, but these newer models were still in the coarseresolution category.