398
12. Special Topics
layer that has dimensions of hundreds of meters. The next scale may be called
the basin scale and consists of a city and its surroundings. On the regional- or
meso-scale, one considers a domain that is a significant part of a continent or
ocean. Finally there are the continental (or ocean) and global scales. In each
case, computational resources dictate the number of grid points that can be
used and thus the grid size. Phenomena that occur on smaller scales must be
represented by an approximate model. Even on the smallest scales of interest,
the size of the regions over which averaging must be done is obviously much
larger than in engineering flows. Consequently, the models used to represent
the smaller scales are much more important than in the engineering largeeddy simulations discussed in Chap. 9.
The fact that significant structures cannot be resolved in simulations at
the largest scales requires that calculations be performed a t a number of
different scales; on each scale, the aim is to study phenomena particular t o
that scale. Meteorologists distinguish four to ten scales on which simulations
are performed (depending on who does the counting). As one might expect,
the literature on this subject is vast and we cannot even begin to cover all of
what has been done.
As already noted, on the largest scales, atmospheric and oceanic flows
are essentially two-dimensional (although there are important influences of
vertical motion). In simulations of the global atmosphere or an entire ocean
basin, the capacity of current computers requires the grid size in the horizontal directions be about a hundred kilometers. As a result, in these types
of simulations, significant structures such as fronts (zones that exist between
masses of fluid of different properties) have to be treated by approximate
models to render their thickness sufficiently large that the grid can resolve
them. Models of this kind are very difficult to construct and are a major
source of error in predictions.
Three-dimensional motion is important only on the smallest scales of atmospheric of oceanographic motion. It is also important to note that, despite
the high Reynolds numbers, only the portion of the atmosphere closest to the
surface is turbulent; this is the atmospheric boundary layer and usually occupies a region about 1-3 km thick. Above the boundary layer, the atmosphere
is stratified and remains laminar. Similarly, only the top layer of the ocean
is turbulent; it is 100-300 m thick and is called the mixed layer. Modeling
these layers is important because it is within them that the atmosphere and
ocean interact and their impact on large-scale behavior is very important.
These have been treated by large-eddy simulation methods similar to those
described in Chap. 9.
The numerical methods used in these simulations vary somewhat with the
scale on which the simulation is performed. For simulations at the smallest
atmospheric scale, the boundary layer, one may use methods similar to those
used in large-eddy simulation of engineering flows. For example, Coleman
et al. (1992) used a spectral method originally designed for the engineering
12. Special Topics
layer that has dimensions of hundreds of meters. The next scale may be called
the basin scale and consists of a city and its surroundings. On the regional- or
meso-scale, one considers a domain that is a significant part of a continent or
ocean. Finally there are the continental (or ocean) and global scales. In each
case, computational resources dictate the number of grid points that can be
used and thus the grid size. Phenomena that occur on smaller scales must be
represented by an approximate model. Even on the smallest scales of interest,
the size of the regions over which averaging must be done is obviously much
larger than in engineering flows. Consequently, the models used to represent
the smaller scales are much more important than in the engineering largeeddy simulations discussed in Chap. 9.
The fact that significant structures cannot be resolved in simulations at
the largest scales requires that calculations be performed a t a number of
different scales; on each scale, the aim is to study phenomena particular t o
that scale. Meteorologists distinguish four to ten scales on which simulations
are performed (depending on who does the counting). As one might expect,
the literature on this subject is vast and we cannot even begin to cover all of
what has been done.
As already noted, on the largest scales, atmospheric and oceanic flows
are essentially two-dimensional (although there are important influences of
vertical motion). In simulations of the global atmosphere or an entire ocean
basin, the capacity of current computers requires the grid size in the horizontal directions be about a hundred kilometers. As a result, in these types
of simulations, significant structures such as fronts (zones that exist between
masses of fluid of different properties) have to be treated by approximate
models to render their thickness sufficiently large that the grid can resolve
them. Models of this kind are very difficult to construct and are a major
source of error in predictions.
Three-dimensional motion is important only on the smallest scales of atmospheric of oceanographic motion. It is also important to note that, despite
the high Reynolds numbers, only the portion of the atmosphere closest to the
surface is turbulent; this is the atmospheric boundary layer and usually occupies a region about 1-3 km thick. Above the boundary layer, the atmosphere
is stratified and remains laminar. Similarly, only the top layer of the ocean
is turbulent; it is 100-300 m thick and is called the mixed layer. Modeling
these layers is important because it is within them that the atmosphere and
ocean interact and their impact on large-scale behavior is very important.
These have been treated by large-eddy simulation methods similar to those
described in Chap. 9.
The numerical methods used in these simulations vary somewhat with the
scale on which the simulation is performed. For simulations at the smallest
atmospheric scale, the boundary layer, one may use methods similar to those
used in large-eddy simulation of engineering flows. For example, Coleman
et al. (1992) used a spectral method originally designed for the engineering