Extratropical Rossby waves in the presence of buoyancy mixing
MetadataShow full item record
The propagation of Rossby waves on a midlatitude β plane is investigated in the presence of density diffusion with the aid of linear hydrostatic theory. The search for wave solutions in a vertically bounded medium subject to horizontal (vertical) diffusion leads to an eigenvalue problem of second (fourth) order. Exact solutions of the problem are obtained for uniform background stratification (N), and approximate solutions are constructed for variable N using the Wentzel–Kramers–Brillouin method. Roots of the eigenvalue relations for free waves are found and discussed. The barotropic wave of adiabatic theory is also a solution of the eigenvalue problem as this is augmented with density diffusion in the horizontal or vertical direction. The barotropic wave is undamped as fluid parcels in the wave move only horizontally and are therefore insensitive to the vortex stretching induced by mixing. On the other hand, density diffusion modifies the properties of baroclinic waves of adiabatic theory. In the presence of horizontal diffusion the baroclinic modes are damped but their vertical structure remains unaltered. The ability of horizontal diffusion to damp baroclinic waves stems from its tendency to counteract the deformation of isopycnal surfaces caused by the passage of these waves. The damping rate increases (i) linearly with horizontal diffusivity and (ii) nonlinearly with horizontal wavenumber and mode number. In the presence of vertical diffusion the baroclinic waves suffer both damping and a change in vertical structure. In the long-wave limit the damping is critical (wave decay rate numerically equal to wave frequency) and increases as the square roots of vertical diffusivity and zonal wavenumber. Density diffusion in the horizontal or vertical direction reduces the amplitude of the phase speed of westward-propagating waves. Observational estimates of eddy diffusivities suggest that horizontal and vertical mixing strongly attenuates baroclinic waves in the ocean but that vertical mixing is too weak to notably modify the vertical structure of the gravest modes.
Author Posting. © American Meteorological Society, 2009. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 39 (2009): 2910-2925, doi:10.1175/2009JPO4139.1.
Showing items related by title, author, creator and subject.
Tropical to extratropical : marine environmental changes associated with Superstorm Sandy prior to its landfall Zambon, Joseph B.; He, Ruoying; Warner, John C. (John Wiley & Sons, 2014-12-16)Superstorm Sandy was a massive storm that impacted the U.S. East Coast on 22–31 October 2012, generating large waves, record storm surges, and major damage. The Coupled Ocean-Atmosphere-Wave-Sediment Transport modeling ...
Chen, Changsheng; Beardsley, Robert C.; Luettich, Richard A.; Westerink, Joannes J.; Wang, Harry; Perrie, Will; Xu, Qichun; Donahue, Aaron S.; Qi, Jianhua; Lin, Huichan; Zhao, Liuzhi; Kerr, Patrick C.; Meng, Yanqiu; Toulany, Bash (John Wiley & Sons, 2013-10-07)The Integrated Ocean Observing System Super-regional Coastal Modeling Testbed had one objective to evaluate the capabilities of three unstructured-grid fully current-wave coupled ocean models (ADCIRC/SWAN, FVCOM/SWAVE, ...
Pan, L. L.; Randel, W. J.; Gary, B. L.; Mahoney, M. J.; Hintsa, Eric J. (American Geophysical Union, 2004-12-04)Definitions of the extratropical tropopause are examined from the perspective of chemical composition. Fine-scale measurements of temperature, ozone, carbon monoxide, and water vapor from approximately 70 aircraft flights, ...