Geoscience Reference
In-Depth Information
6
Large-eddy dynamics, the energy cascade,
and large-eddy simulation
6.1 Introduction
As we have seen, the huge range of spatial scales in large- R t 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 evo-
lution equations for their fluxes, and discuss the modeling of these fluxes. This
modeling is of two broad types depending on the spatial scale of the averaging
relative to the size of the energy-containing eddies. In what we shall call “coarse
resolution” applications
.
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
; in “fine resolution” ones
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 coarse-
resolution category.
The first successful high-resolution application was Deardorff's ( 1970a ) study of
turbulent channel flow. He used 6720 uniform grid elements (24 in the streamwise
direction, 14 in the lateral, 20 in the vertical), and Lilly's ( 1967 ) specification for
the effects of the unresolvable (now called subfilter-scale) turbulence. His results
generally agreed well with measurements, and also revealed aspects of eddy struc-
ture that had not been measured. The calculation attracted strong interest in the
×
115
Search WWH ::




Custom Search