12.6 Meteorological and Oceanographic Applications
397
Similar hybrid methods, in which both an additional equation for the
volume fraction of one phase and the tracking of the interface are used, have
been reported by Scardovelli and Zaleski et al (1999).
In many applications the interface between two fluids is not sharp; an
example is a breaking wave or a hydraulic jump, where a region exists in
which the water and air form a foamy mixture. In such a case it would be
necessary to add a model for the mixing of the two fluids, similar to the models
of turbulent transport in single-phase flows. Also, cavitation is an important
phenomenon which falls into the class of two-phase flows which require hybrid
methods for their simulation. The equation for the volume fraction of the gas
phase has to have both a diffusion term (to account for turbulent diffusion)
and a source term to account for the phase change; an example of such
a method is the one presented by Sauer (2000). Special treatment is also
required when computing bubble growth due to heat addition during boiling,
as well as in some other flows with free surfaces; it is beyond the scope of
this book to go into details of each particular application, but most of the
methods in use are related to one of the methods described above.
12.6 Meteorological and Oceanographic Applications
The atmosphere and the oceans are the sites of the largest scale flows on
Earth. The velocities may be tens of meters per second and the length scales
are enormous so the Reynolds numbers are huge. Due to the very large aspect ratios of these flows (thousands of kilometers horizontally and a few
kilometers of depth), the large-scale flow is almost two-dimensional (although
vertical motions are important) while the flow a t the small scales is threedimensional. The Earth's rotation is a major force on the large scales but is
less significant at the small scales. Stratification or a stable variation of density is important, mainly a t the smaller scales. The forces and phenomena
that play dominant roles are different on different scales.
Also, one needs predictions on different time scales. In the case of greatest
interest to the public, one wants to predict the state of the atmosphere or
ocean for a relatively short time in the future. In weather forecasting, the
time scale is a few days while in the ocean, which changes more slowly, the
scale is a few weeks to a few months. In either case, a method that is accurate
in time is required. At the other extreme are climate studies, which require
prediction of the average state of the atmosphere over a relatively long time
period. In this case, the short term time behavior can be averaged out and
the time accuracy requirement relaxed; however, it is essential to model the
ocean as well as the atmosphere in this case. Because the actual state of
the atmosphere or ocean is required, computations in these fields are nearly
always large-eddy simulations.
Computations are done on a wide range of different length scales. The
smallest region of interest is the atmospheric boundary layer or ocean mixed
397
Similar hybrid methods, in which both an additional equation for the
volume fraction of one phase and the tracking of the interface are used, have
been reported by Scardovelli and Zaleski et al (1999).
In many applications the interface between two fluids is not sharp; an
example is a breaking wave or a hydraulic jump, where a region exists in
which the water and air form a foamy mixture. In such a case it would be
necessary to add a model for the mixing of the two fluids, similar to the models
of turbulent transport in single-phase flows. Also, cavitation is an important
phenomenon which falls into the class of two-phase flows which require hybrid
methods for their simulation. The equation for the volume fraction of the gas
phase has to have both a diffusion term (to account for turbulent diffusion)
and a source term to account for the phase change; an example of such
a method is the one presented by Sauer (2000). Special treatment is also
required when computing bubble growth due to heat addition during boiling,
as well as in some other flows with free surfaces; it is beyond the scope of
this book to go into details of each particular application, but most of the
methods in use are related to one of the methods described above.
12.6 Meteorological and Oceanographic Applications
The atmosphere and the oceans are the sites of the largest scale flows on
Earth. The velocities may be tens of meters per second and the length scales
are enormous so the Reynolds numbers are huge. Due to the very large aspect ratios of these flows (thousands of kilometers horizontally and a few
kilometers of depth), the large-scale flow is almost two-dimensional (although
vertical motions are important) while the flow a t the small scales is threedimensional. The Earth's rotation is a major force on the large scales but is
less significant at the small scales. Stratification or a stable variation of density is important, mainly a t the smaller scales. The forces and phenomena
that play dominant roles are different on different scales.
Also, one needs predictions on different time scales. In the case of greatest
interest to the public, one wants to predict the state of the atmosphere or
ocean for a relatively short time in the future. In weather forecasting, the
time scale is a few days while in the ocean, which changes more slowly, the
scale is a few weeks to a few months. In either case, a method that is accurate
in time is required. At the other extreme are climate studies, which require
prediction of the average state of the atmosphere over a relatively long time
period. In this case, the short term time behavior can be averaged out and
the time accuracy requirement relaxed; however, it is essential to model the
ocean as well as the atmosphere in this case. Because the actual state of
the atmosphere or ocean is required, computations in these fields are nearly
always large-eddy simulations.
Computations are done on a wide range of different length scales. The
smallest region of interest is the atmospheric boundary layer or ocean mixed