Cover Journal of the Atmospheric Sciences
Journal of the Atmospheric Sciences

  • Blumen, W., 1980: A comparison between the Hoskins-Bretherton model of frontogenesis and the analysis of an intense surface frontal zone. J. Atmos. Sci.,37, 64–77.

  • Bretherton, F. P., 1966: Critical layer instability in baroclinic flows. Quart. J. Roy. Meteor. Soc.,92, 335–345.

  • Cho, H.-R., and J. N. Koshyk, 1989: Dynamics of frontal discontinuities in the semigeostrophic theory. J. Atmos. Sci.,46, 2166–2177.

  • Cooper, I. M., A. J. Thorpe, and C. H. Bishop, 1992: The role of diffusive effects on potential vorticity in fronts. Quart. J. Roy. Meteor. Soc.,118, 629–647.

  • Cullen, M. J. P., and R. J. Purser, 1984: An extended Lagrangian theory of semigeostrophic frontogenesis. J. Atmos. Sci.,41, 1477–1497.

  • Garner, S. T., I. M. Held, and N. Nakamura, 1992: Nonlinear equilibration of two-dimensional Eady waves: A new perspective. J. Atmos. Sci.,49, 1984–1996.

  • Haynes, P. H., and M. E. McIntyre, 1987: On the evolution of vorticity and potential vorticity in the presence of diabatic heating and friction or other forces. J. Atmos. Sci.,44, 828–841.

  • Hoskins, B. J., 1975: The geostrophic momentum approximation and the semigeostrophic equations. J. Atmos. Sci.,32, 233–242.

  • ——, and F. P. Bretherton, 1972: Atmospheric frontogenesis models:Mathematical formulation and solution. J. Atmos. Sci.,29, 11–37.

  • ——, M. E. McIntyre, and A. W. Robertson, 1985: On the use and significance of isentropic potential vorticity maps. Quart. J. Roy. Meteor. Soc.,111, 877–946.

  • Keyser, D., and R. A. Anthes, 1982: The influence of planetary boundary layer physics on frontal structure in the Hoskins-Bretherton deformation model. J. Atmos. Sci.,39, 1783–1802.

  • Koshyk, J. N., and H.-R. Cho, 1992: Dynamics of mature front in a uniform potential vorticity semigeostrophic model. J. Atmos. Sci.,49, 497–510.

  • Nakamura, N., 1994: Nonlinear equilibration of two-dimensional Eady waves: Simulations with viscous geostrophic momentum equations. J. Atmos. Sci.,51, 1023–1035.

  • ——, and I. M. Held, 1989: Nonlinear equilibration of two-dimensional Eady waves. J. Atmos. Sci.,46, 3055–3064.

  • Purser, R. J., and M. J. P. Cullen, 1987: A duality principle in semigeostrophic theory. J. Atmos. Sci.,44, 3449–3468.

  • Wu, R., and W. Blumen, 1982: An analysis of Ekman boundary layer dynamics incorporating the geostrophic momentum approximation. J. Atmos. Sci.,39, 1774–1782.

  • Xu, Q., 1988: Baroclinic waves and frontogenesis with an embedded zone of small moist symmetric stability. Quart. J. Roy. Meteor. Soc.,114, 1221–1251.

  • ——, 1989: Extended Sawyer–Eliassen equation for frontal circulations in the presence of small viscous moist symmetric stability. J. Atmos. Sci.,46, 2671–2683.

  • ——, 1990: Cold and warm frontal circulations in an idealized moist semigeostrophic baroclinic wave. J. Atmos. Sci.,47, 2337–2352.

  • ——, 1992: Formation and evolution of frontal rainbands and geostrophic potential vorticity anomalies. J. Atmos. Sci.,49, 629–648.

  • ——, 1994: Semi-balance model—Connection between geostrophic-type and balanced-type intermediate models. J. Atmos. Sci.,51, 953–970.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 165 21 4
PDF Downloads 52 13 3
Editorial Type:
Article
Article Type:
Research Article

Baroclinic Eady Wave and Fronts. Part I: Viscous Semigeostrophy and the Impact of Boundary Condition

Qin XuNaval Research Laboratory, Monterey, California

Search for other papers by Qin Xu in
Current site
Google Scholar
PubMedClose
,
Wei GuDepartment of Atmospheric Sciences, Nanjing University, Nanjing, China, and CIMMS, University of Oklahoma, Norman, Oklahoma

Search for other papers by Wei Gu in
Current site
Google Scholar
PubMedClose
, and
Jidong GaoCAPS, University of Oklahoma, Norman, Oklahoma

Search for other papers by Jidong Gao in
Current site
Google Scholar
PubMedClose
Print Publication:
01 Dec 1998
DOI:
https://doi.org/10.1175/1520-0469(1998)055<3598:BEWAFP>2.0.CO;2
Page(s):
3598–3615
Restricted access

Abstract

A two-dimensional viscous semigeostrophic model is developed to study the evolution of the baroclinic Eady wave and fronts with two types (free-slip and nonslip) of boundary conditions. With the free-slip boundary condition, the solution is very similar to the inviscid one but the frontal collapse is prevented by the diffusive effect. When the fronts become sharp in the mature stage, strong horizontal diffusions of momentum and potential temperature cause strong inward fluxes of geostrophic potential vorticity (GPV) at the surface fronts, so high GPV anomalies are generated at the surface fronts and advected into the interior, forming two backward-tilted plumes along the upper and lower fronts. The wave and front development can be interpreted by the interaction between the lower- and upper-level GPV anomalies in terms of GPV thinking similarly to that in the inviscid case.

When the boundary condition is nonslip, the initial growth and subsequent nonlinear evolution of the solution are significantly slower than the inviscid one, but the associated boundary layer processes allow the model to produce realistic features in the vicinity of the front. Diffusive GPV fluxes at the boundaries are caused mainly by vertical diffusions of momentum and potential temperature, so GPV anomalies are produced over broad regions behind and ahead of the front. As the GPV anomalies are transported from the boundary layer into the interior, they evolve into two mushroom clouds. The shallow boundary layer circulation, driven by the inverted geostrophic flow through Ekman pumping, produces a positive feedback to the horizontal spreading of the interior GPV anomalies. This explains why and how the GPV anomalies grow into two mushroom clouds.

Corresponding author’s address: Dr. Qin Xu, Naval Research Laboratory, Monterey, CA 93943-5502.

Email: xuq@nrlmry.navy.mil

Abstract

A two-dimensional viscous semigeostrophic model is developed to study the evolution of the baroclinic Eady wave and fronts with two types (free-slip and nonslip) of boundary conditions. With the free-slip boundary condition, the solution is very similar to the inviscid one but the frontal collapse is prevented by the diffusive effect. When the fronts become sharp in the mature stage, strong horizontal diffusions of momentum and potential temperature cause strong inward fluxes of geostrophic potential vorticity (GPV) at the surface fronts, so high GPV anomalies are generated at the surface fronts and advected into the interior, forming two backward-tilted plumes along the upper and lower fronts. The wave and front development can be interpreted by the interaction between the lower- and upper-level GPV anomalies in terms of GPV thinking similarly to that in the inviscid case.

When the boundary condition is nonslip, the initial growth and subsequent nonlinear evolution of the solution are significantly slower than the inviscid one, but the associated boundary layer processes allow the model to produce realistic features in the vicinity of the front. Diffusive GPV fluxes at the boundaries are caused mainly by vertical diffusions of momentum and potential temperature, so GPV anomalies are produced over broad regions behind and ahead of the front. As the GPV anomalies are transported from the boundary layer into the interior, they evolve into two mushroom clouds. The shallow boundary layer circulation, driven by the inverted geostrophic flow through Ekman pumping, produces a positive feedback to the horizontal spreading of the interior GPV anomalies. This explains why and how the GPV anomalies grow into two mushroom clouds.

Corresponding author’s address: Dr. Qin Xu, Naval Research Laboratory, Monterey, CA 93943-5502.

Email: xuq@nrlmry.navy.mil

Save