The Frontal Width Problem

W. Blumen Program in Atmospheric and Oceanic Sciences, University of Colorado, Boulder, Colorado

Search for other papers by W. Blumen in
Current site
Google Scholar
PubMed
Close
and
M. Piper Program in Atmospheric and Oceanic Sciences, University of Colorado, Boulder, Colorado

Search for other papers by M. Piper in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Observations of two low-level frontal passages by a hot-wire anemometer placed at 3 m above the ground provide evidence that frontal zones and the postfrontal regions exhibit enhanced kinetic energy dissipation. These observations support a postulated linear relationship between turbulent kinetic energy dissipation rate ϵ and a characteristic frontal width L. A rigorous theoretical development is not available to verify the postulate that an equilibrated frontal width is determined by a balance between frontogenetical forcing and turbulent dissipation of kinetic energy. Instead, a simple construct, based on a model of inviscid frontogenesis, is introduced. This model exhibits downscale spectral energy transfer that decreases with horizontal scale during frontogenesis. This model is invalid in the dissipative range of fully turbulent small-scale motions. In those cases, however, when frontal equilibration occurs at scales close to the scales where dissipation just begins to become significant, the inviscid model provides some theoretical support for the postulated relationship between ϵ and L. The analysis is then extended to show how the vertical scale Lυ in a surface-based front is related to ϵ and N (N is the Brunt–Väisälä frequency) when the earth’s rotation is not a factor, but Lυ depends on ϵ, N, and f (f is the Coriolis parameter) when rotation is retained. Questions that remain unanswered by the present analysis concern the appropriate definition of a frontal scale, the role of precipitation in frontal scaling, and the equilibration of broad-scale fronts L ≥ 105 m, when turbulent dissipation of kinetic energy may not be the controlling factor in the equilibration of a front.

Corresponding author address: W. Blumen, CB 311, University of Colorado, Boulder, CO 80309-0311.

Email: blumen@paradox.colorado.edu

Abstract

Observations of two low-level frontal passages by a hot-wire anemometer placed at 3 m above the ground provide evidence that frontal zones and the postfrontal regions exhibit enhanced kinetic energy dissipation. These observations support a postulated linear relationship between turbulent kinetic energy dissipation rate ϵ and a characteristic frontal width L. A rigorous theoretical development is not available to verify the postulate that an equilibrated frontal width is determined by a balance between frontogenetical forcing and turbulent dissipation of kinetic energy. Instead, a simple construct, based on a model of inviscid frontogenesis, is introduced. This model exhibits downscale spectral energy transfer that decreases with horizontal scale during frontogenesis. This model is invalid in the dissipative range of fully turbulent small-scale motions. In those cases, however, when frontal equilibration occurs at scales close to the scales where dissipation just begins to become significant, the inviscid model provides some theoretical support for the postulated relationship between ϵ and L. The analysis is then extended to show how the vertical scale Lυ in a surface-based front is related to ϵ and N (N is the Brunt–Väisälä frequency) when the earth’s rotation is not a factor, but Lυ depends on ϵ, N, and f (f is the Coriolis parameter) when rotation is retained. Questions that remain unanswered by the present analysis concern the appropriate definition of a frontal scale, the role of precipitation in frontal scaling, and the equilibration of broad-scale fronts L ≥ 105 m, when turbulent dissipation of kinetic energy may not be the controlling factor in the equilibration of a front.

Corresponding author address: W. Blumen, CB 311, University of Colorado, Boulder, CO 80309-0311.

Email: blumen@paradox.colorado.edu

Save
  • Andrews, D. G., and B. J. Hoskins, 1978: Energy spectra predicted by semi-geostrophic theories of frontogenesis. J. Atmos. Sci.,35, 509–512.

  • Blumen, W., 1999: Inertial oscillations and frontogenesis in a zero potential vorticity model. J. Phys. Oceanogr., in press.

  • ——, N. Gamage, R. L. Grossman, M. A. LeMone, and L. J. Miller, 1996: The low-level structure and evolution of a dry arctic cold front over the central United States. Part II: Comparison with theory. Mon. Wea. Rev.,124, 1676–1692.

  • ——, R. L. Grossman, and M. Piper, 1999: Analysis of heat budget, dissipation and frontogenesis in a shallow density current. Bound.-Layer Meteor., in press.

  • Browning, K. A., T. W. Harrold, and J. R. Starr, 1970: Richardson number limited shear zones in the free atmosphere. Quart. J. Roy. Meteor. Soc.,96, 40–49.

  • Davies, H. C., and J. C. Müller, 1988: Detailed description of deformation-induced semigeostrophic frontogenesis. Quart. J. Roy. Meteor. Soc.,114, 1201–1219.

  • Dougherty, J. P., 1961: The anisotropy of turbulence at the meter level. J. Atmos. Terr. Phys.,21, 210–213.

  • Emanuel, K. A., 1985: What limits front formation? Nature,315, p. 99.

  • Gall, R. L., R. T. Williams, and T. L. Clark, 1987: On the minimum scale of surface fronts. J. Atmos. Sci.,44, 2562–2574.

  • Garner, S. T., 1989: Fully Lagrangian numerical solution of unbalanced frontogenesis and frontal collapse. J. Atmos. Sci.,46, 717–739.

  • Gill, A. E., 1982: Atmosphere–Ocean Dynamics. Academic, 662 pp.

  • Griffiths, R. W., and E. J. Hopfinger, 1984: The structure of mesoscale turbulence and horizontal spreading of ocean fronts. Deep-Sea Res.,31, 245–269.

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

  • Joint Organizing Committee, 1972: Parameterization of sub-grid scale processes. Global Atmospheric Research Program Publications Series 8, World Meteorological Organization, Geneva, 101 pp.

  • Kay, A., 1992: Frontogenesis in gravity-driven flows with nonuniform density gradients. J. Fluid Mech.,235, 529–556.

  • Lighthill, M. J., 1956: Viscosity effects in sound waves of finite amplitude. Surveys in Mechanics, G. K. Batchelor and R. M. Davies, Eds., Cambridge University Press, 250–351.

  • Lilly, D. K., 1983: Stratified turbulence and the mesoscale variability of the atmosphere. J. Atmos. Sci.,40, 749–761.

  • ——, 1989: Two-dimensional turbulence generated by energy sources at two scales. J. Atmos. Sci.,46, 2026–2030.

  • Miller, L. J., M. A. LeMone, W. Blumen, R. L. Grossman, N. Gamage, and R. J. Zamora, 1996: The low-level structure and evolution of a dry Arctic front over the central United States. Part I: Mesoscale observations. Mon. Wea. Rev.,124, 1648–1675.

  • Mory, M., and E. J. Hopfinger, 1985: Rotating turbulence evolving freely from an initial quasi-two-dimensional state. Macroscopic Modelling of Turbulent Flows, U. Frisch, Ed., Vol. 230, Lecture Notes in Physics, Springer-Verlag, 218–236.

  • Nielsen, J. W., 1992: In situ observations of Kelvin–Helmholtz waves along a frontal inversion. J. Atmos. Sci.,49, 369–386.

  • Oncley, S. P., C. A. Friehe, J. A. Businger, E. C. Itsweire, J. C. LaRue, and S. S. Chang, 1996: Surface-layer fluxes, profiles, and turbulence measurements over uniform terrain under near-neutral conditions. J. Atmos. Sci.,53, 1029–1044.

  • Orlanski, I., and B. B. Ross, 1984: The evolution of an observed cold front. Part II: Mesoscale dynamics. J. Atmos. Sci.,41, 1669–1703.

  • Ozmidov, R. V., 1965: On the turbulent exchange in a stably stratified ocean. Atmos. Ocean Phys.,8, 493–497.

  • Platzman, G. W., 1964: An exact integral of complete spectral equations for unsteady one-dimensional flow. Tellus,16, 422–431.

  • Rhines, P. B., 1975: Waves and turbulence on the beta plane. J. Fluid Mech.,69, 417–443.

  • Simpson, J. E., 1997: Gravity Currents in the Environment and the Laboratory. 2d ed. Cambridge University Press, 244 pp.

  • Snyder, C., W. C. Skamarock, and R. Rotunno, 1993: Frontal dynamics near and following frontal collapse. J. Atmos. Sci.,50, 3194–3211.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 81 26 0
PDF Downloads 29 12 0