Recent progress in modeling imbalance in the atmosphere and ocean

Imbalance refers to the departure from the large-scale primarily vortical flows in the atmosphere and ocean whose motion is governed by a balance of Coriolis, pressure-gradient, and buoyancy forces and can be described approximately by quasigeostrophic theory or similar balance models. Imbalanced motions are manifest either as fully nonlinear turbulence or as internal gravity waves which can extract energy from these geophysical flows but which can also feed energy back into the flows. Capturing the physics underlying these mechanisms is essential to understanding how energy is transported from large geophysical scales ultimately to microscopic scales, where it is dissipated. In the atmosphere, it is also necessary for understanding momentum transport and its impact upon the mean wind and current speeds. During a February 2018 workshop at the Banff International Research Station (BIRS), atmospheric scientists, physical oceanographers, physicists, and mathematicians gathered to discuss recent progress in understanding these processes through interpretation of observations, numerical simulations, and mathematical modeling. The outcome of this meeting is reported upon here.

Figure 1

Schematics illustrating the myriad processes that generate internal waves and which ultimately lead to breaking in (a) the atmosphere and (b) the ocean (the latter, copyright © American Meteorological Society, is used with permission from Fig. 1 of MacKinnon et al. [8]).

Figure 2

Images acquired from the Moderate Resolution Imaging Spectroradiometer on NASA's Terra satellite showing (left) atmospheric cyclones between Iceland and Scotland visualized by clouds on November 20, 2006 [NASA image by Jesse Allen, Earth Observatory], and (right) anticyclonic and cyclonic eddies interacting with the Gulf Stream on May 8, 2000, and visualized by sea surface temperature [created at the University of Miami using the 11- and 12-$\mu \mathrm{m}$ bands, by Evans, Minnett, and coworkers]. The horizontal white bar to the lower right in the left image indicates a length of 250 km. The vertical white bar to the upper left of the right image indicates a length of 222 km.

Figure 3

(a) Spectra of along-track and across-track velocities determined from a collection of aircraft flights in the lower stratosphere, (b) Helmholtz decomposition of the spectra into rotational and divergent components, and (c) adjustment for spectra accounting for internal gravity wave polarization relations. (Reproduced with permission from Fig. 1 of Callies et al. [23].)

Figure 4

Composite of temperature observed by lidar below 60 km altitude and sodium ion density in upper mesosphere measured during the DEEPWAVE campaign on July 13, 2014, above Lauder, New Zealand. (Copyright © American Meteorological Society. Used with permission from Fig. 9 of Fritts et al. [74].)

Figure 5

Comparison between simulations (left) and radiosonde balloon observations (right) of 5-month time-averaged momentum fluxes at 19 km altitude in the Southern Hemisphere. The simulations from ECMWF have had their spatial resolution downgraded to correspond to that of the balloon data and their values have been multiplied by 5. Although the spatial pattern of the fluxes is similar, the simulation underpredicts observations by a factor of 5. (Copyright © American Meteorological Society. Used with permission from Figs. 1(c) and 1(d) of Jewtoukoff et al. [121].)

Figure 6

Estimates of global ocean energy flux inferred from observations. Colors represent a log scale from ${10}^{-4}$ (white) to ${10}^{-1}\text{W}/{\text{m}}^2$ (dark red). The spidery dark red features correspond to internal modes launched by tidal flow over bottom topography; the remaining light-red zones represent inertia gravity waves launched by wind stress in the ocean. (Copyright © American Meteorological Society. Used with permission from Fig. 2 of Waterhouse et al. [134]).

Figure 7

Global estimates of dissipation in the top 1 km of the ocean. (Copyright © American Meteorological Society. Used with permission, adapted from Fig. 1 of Waterhouse et al. [134]).