viscosity and diffusivity with constant coefficients 1 cm
2 s
−1 and 0.1 cm
2 s
−1 ,
respectively. The AO modeling experience shows that these coefficients should be
at least 10 times smaller in the most parts of the Central Arctic to maintain the
observed vertical stratification. This conclusion agrees with the theoretical
assumptions that the internal waves are generally weak in the central parts of the
AO under the pack ice, but it seems to be oversimplified taking into account the
recent observational data.
The important research of internal waves both theoretical and observational in
the World Ocean [15] and especially in the high-latitude regions were carried out by
E.G. Morozov and his coauthors. In a series of papers [13, 14, 16–19] they showed
the importance of internal waves not only for the Arctic Ocean mixing, but also for
the sea ice formation [20].
The understanding of the role of internal waves in large-scale or climatic Arctic
Ocean state formation is still beyond the scope of ocean climate modeling, but it is
likely that it will be demanded soon, as the spatial resolution of the models will be
fine enough and the requirements to the accuracy will rise due to the improvements
in the observing systems in the AO. One may detect that in the models of the
general atmosphere circulation and weather forecast there are comprehensive
parameterizations employed for a long time both for orographic [22] and
non-orographic internal waves (induced by vertical shift of the wind or by convection [5]), which proved to be important for the mean stratosphere wind formation. The experience of ocean modeling shows that it lags behind the atmosphere
modeling approximately by 15–20 years, therefore, now we at the very moment to
take comprehensive parameterizations of internal waves into account in the ocean
models as well. The obvious problem for the parameterization of the internal waves
and tides in the AO is that their lengths are close to the scales of mesoscale and
submesoscale eddies; hence we again get into the “gray zone” in Fig. 1 and should
be aware of double describing the processes.
Summary
Numerical modeling in the Arctic Ocean exhibited an impressive progress in the
last 20 years. It happened mostly with the assistance of the ocean general circulation models based on the “traditional” approximations of incompressibility,
Boussinesq, and hydrostatics. These models were designed initially for the conditions of low- and mid-latitudes, in which the horizontal scale of mesoscale eddies is
large, and the vertical stratification is generally stable. The progress was provided
mainly by the evolution of the program codes towards higher horizontal resolution.
Now, at the resolution of the order of a few kilometers accessible even for the
global setups, the revolution is at hand. The bunch of mutually interacting processes
like mesoscale and submesoscale eddies, internal waves and vertical convection, all
approximately of the same horizontal scale, demand the new approaches to model
formulation, new parameterizations, and new numerical design. This work may be
Arctic Ocean Modeling: The Consistent Physics on the Path …
565
2 s
−1 and 0.1 cm
2 s
−1 ,
respectively. The AO modeling experience shows that these coefficients should be
at least 10 times smaller in the most parts of the Central Arctic to maintain the
observed vertical stratification. This conclusion agrees with the theoretical
assumptions that the internal waves are generally weak in the central parts of the
AO under the pack ice, but it seems to be oversimplified taking into account the
recent observational data.
The important research of internal waves both theoretical and observational in
the World Ocean [15] and especially in the high-latitude regions were carried out by
E.G. Morozov and his coauthors. In a series of papers [13, 14, 16–19] they showed
the importance of internal waves not only for the Arctic Ocean mixing, but also for
the sea ice formation [20].
The understanding of the role of internal waves in large-scale or climatic Arctic
Ocean state formation is still beyond the scope of ocean climate modeling, but it is
likely that it will be demanded soon, as the spatial resolution of the models will be
fine enough and the requirements to the accuracy will rise due to the improvements
in the observing systems in the AO. One may detect that in the models of the
general atmosphere circulation and weather forecast there are comprehensive
parameterizations employed for a long time both for orographic [22] and
non-orographic internal waves (induced by vertical shift of the wind or by convection [5]), which proved to be important for the mean stratosphere wind formation. The experience of ocean modeling shows that it lags behind the atmosphere
modeling approximately by 15–20 years, therefore, now we at the very moment to
take comprehensive parameterizations of internal waves into account in the ocean
models as well. The obvious problem for the parameterization of the internal waves
and tides in the AO is that their lengths are close to the scales of mesoscale and
submesoscale eddies; hence we again get into the “gray zone” in Fig. 1 and should
be aware of double describing the processes.
Summary
Numerical modeling in the Arctic Ocean exhibited an impressive progress in the
last 20 years. It happened mostly with the assistance of the ocean general circulation models based on the “traditional” approximations of incompressibility,
Boussinesq, and hydrostatics. These models were designed initially for the conditions of low- and mid-latitudes, in which the horizontal scale of mesoscale eddies is
large, and the vertical stratification is generally stable. The progress was provided
mainly by the evolution of the program codes towards higher horizontal resolution.
Now, at the resolution of the order of a few kilometers accessible even for the
global setups, the revolution is at hand. The bunch of mutually interacting processes
like mesoscale and submesoscale eddies, internal waves and vertical convection, all
approximately of the same horizontal scale, demand the new approaches to model
formulation, new parameterizations, and new numerical design. This work may be
Arctic Ocean Modeling: The Consistent Physics on the Path …
565