Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-24T09:42:15.227Z Has data issue: false hasContentIssue false
  • English
  • Français

The spontaneous generation of inertia–gravity waves during frontogenesis forced by large strain: theory

Published online by Cambridge University Press:  26 September 2014

Callum J. Shakespeare  and
J. R. Taylor
Callum J. Shakespeare
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
J. R. Taylor*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: J.R.Taylor@damtp.cam.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

Density fronts are common features of ocean and atmosphere boundary layers. Field observations and numerical simulations have shown that the sharpening of frontal gradients, or frontogenesis, can spontaneously generate inertia–gravity waves (IGWs). Although significant progress has been made in describing frontogenesis using approximations such as quasi-geostrophy (Stone, J. Atmos. Sci., vol. 23, 1966, pp. 455–565, Williams & Plotkin J. Atmos. Sci., vol. 25, 1968, pp. 201–206) semi-geostrophy (Hoskins, Annu. Rev. Fluid Mech., vol. 14, 1982, pp. 131–151), these models omit waves. Here, we further develop the analytical model of Shakespeare & Taylor (J. Fluid Mech., vol. 736, 2013, pp. 366–413) to describe the spontaneous emission of IGWs from an initially geostrophically balanced front subjected to a time-varying horizontal strain. The model uses the idealised configuration of an infinitely long, straight front and uniform potential vorticity (PV) fluid, with a uniform imposed convergent strain across the front, similar to Hoskins & Bretherton (J. Atmos. Sci., vol. 29, 1972, pp. 11–37). Inertia–gravity waves are generated via two distinct mechanisms: acceleration of the large-scale flow and frontal collapse. Wave emission via frontal collapse is predicted to be exponentially small for small values of strain but significant for larger strains. Time-varying strain can also generate finite-amplitude waves by accelerating the cross-front flow and disrupting geostrophic balance. In both cases waves are trapped by the oncoming strain flow and can only propagate away from the frontal zone when the strain field weakens sufficiently, leading to wave emission that is strongly localised in both time and space.

JFM classification

Geophysical and Geological Flows: Atmospheric flows Geophysical and Geological Flows: Ocean processes Geophysical and Geological Flows: Waves in rotating fluids
Type
Papers
Information
Journal of Fluid Mechanics , Volume 757 , 25 October 2014 , pp. 817 - 853
Copyright
© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alford, M. H., Shcherbina, A. Y. & Gregg, M. C. 2013 Observations of near-inertial internal gravity waves radiating from a frontal jet. J. Phys. Oceanogr. 43, 1225–1239.Google Scholar
Blumen, W. 1972 Geostrophic adjustment. Rev. Geophys. Space Phys. 10, 485–528.Google Scholar
Blumen, W. 2000 Inertial oscillations and frontogenesis in a zero potential vorticity model. J. Phys. Oceanogr. 30, 31–39.Google Scholar
Blumen, W. & Wu, R. 1995 Geostrophic adjustment: frontogenesis and energy conversion. J. Phys. Oceanogr. 25, 428–438.2.0.CO;2>CrossRefGoogle Scholar
Buhler, O. & McIntyre, M. E. 2005 Wave capture and wave-vortex duality. J. Fluid Mech. 534, 67–95.Google Scholar
Danioux, E., Vanneste, J., Klein, P. & Sasaki, H. 2012 Spontaneous inertia–gravity-wave generation by surface-intensifed turbulence. J. Fluid Mech. 699, 153–1732.Google Scholar
Ford, R., McIntyre, M. E. & Norton, W. A. 2000 Balance and the slow quasimanifold: some explicit results. J. Atmos. Sci. 57, 1236–1254.Google Scholar
Garner, S. T. 1989 Fully Lagrangian numerical solutions of unbalanced frontogensis and frontal collapse. J. Atmos. Sci. 46, 717–739.Google Scholar
Gill, A. E. 1976 Adjustment under gravity in a rotating channel. J. Fluid Mech. 77, 603–621.Google Scholar
Griffiths, M. & Reeder, M. J. 1996 Stratospheric inertia–gravity waves generated in a numerical model of frontogenesis. I: model solutions. Q. J. R. Meteorol. Soc. 122, 1153–1174.Google Scholar
Hoskins, B. J. 1982 The mathematical theory of frontogenesis. Annu. Rev. Fluid Mech. 14, 131–151.Google Scholar
Hoskins, B. J. & Bretherton, F. P. 1972 Atmospheric frontogenesis models: mathematical formulation and solution. J. Atmos. Sci. 29, 11–37.2.0.CO;2>CrossRefGoogle Scholar
Jones, W. L. 1969 Ray tracing for internal gravity waves. J. Geophys. Res. 74 (8), 2028–2033.Google Scholar
Juckes, M. 1994 Quasigeostrophic dynamics of the tropopause. J. Atmos. Sci. 51, 2756–2768.Google Scholar
Karan, H., Fitzpatrick, P. J., Hill, C. M., Li, Y., Xiao, Q. & Lim, E. 2010 The formation of multiple squall lines and the impacts of WSR-88D radial winds in a WRF simulation. J. Atmos. Sci. 25, 242–262.Google Scholar
Kuo, A. C. & Polvani, L. M. 1997 Time-dependent fully nonlinear geostrophic adjustment. J. Phys. Oceanogr. 27, 1614–1634.Google Scholar
Ley, B. E. & Peltier, W. R. 1978 Wave generation and frontal collapse. J. Atmos. Sci. 35, 3–17.2.0.CO;2>CrossRefGoogle Scholar
McIntyre, M. E. 2009 Spontaneous imbalance and hybrid vortex-gravity structures. J. Atmos. Sci. 66, 1315–1326.CrossRefGoogle Scholar
Ou, H. W. 1984 Geostrophic adjustment: a mechanism for frontogenesis. J. Phys. Oceanogr. 14, 994–1000.Google Scholar
Plougonven, R. & Snyder, C. 2005 Gravity waves excited by jets: propagation versus generation. Geophys. Res. Lett. 32, L18802.CrossRefGoogle Scholar
Plougonven, R. & Zhang, F. 2007 On the forcing of inertia–gravity waves by synoptic-scale flows. J. Atmos. Sci. 64, 1737–1742.Google Scholar
Plougonven, R. & Zhang, F. 2014 Internal gravity waves from jets and fronts. Rev. Geophys. 52, 33–76.Google Scholar
Polzin, K. L. 2010 Mesoscale eddy-internal wave coupling. Part II: energetics and results from PolyMode. J. Phys. Oceanogr. 40, 789–801.CrossRefGoogle Scholar
Reeder, M. J. & Griffiths, M. 1996 Stratospheric inertia–gravity waves generated in a numerical model of frontogenesis. II: wave sources, generation mechanisms and momentum fluxes. Q. J. R. Meteorol. Soc. 122, 1175–1195.Google Scholar
Rossby, C. G. 1938 On the mutual adjustment of pressure and velocity distributions in certain simple current systems, II. J. Mar. Res. 1, 239–263.Google Scholar
Shakespeare, C. J. & Taylor, J. R. 2013 A generalised mathematical model of geostrophic adjustment and frontogenesis: uniform potential vorticity. J. Fluid Mech. 736, 366–413.Google Scholar
Shcherbina, A. Y., D’Asaro, E. A., Lee, C. M., Klymak, J. M., Molemaker, M. J. & McWilliams, J. C. 2013 Statistics of vertical vorticity, divergence, and strain in a developed submesoscale turbulence field. Geophys. Res. Lett. 40, 4706–4711.Google Scholar
Snyder, C., Skamarock, W. & Rotunno, R. 1993 Frontal dynamics near and following frontal collapse. J. Atmos. Sci. 50, 3194–3211.Google Scholar
Stone, P. H. 1966 Frontogenesis by horizontal wind deformation fields. J. Atmos. Sci. 23, 455–565.Google Scholar
Tandon, A. & Garrett, C. 1994 Mixed layer restratification due to a horizontal density gradient. J. Phys. Oceanogr. 24 (6), 1419–1424.Google Scholar
Thomas, L. N., Tandon, A. & Mahadevan, A. 2008 Submesoscale processes and dynamics. In Ocean Modelling in an Eddying Regime, Geophysical Monograph Series, vol. 177. American Geophysical Union.Google Scholar
Vanneste, J. 2008 Exponential smallness of inertia–gravity wave generation at small Rossby number. J. Atmos. Sci. 65, 1622–1637.CrossRefGoogle Scholar
Vanneste, J. 2013 Balance and spontaneous wave generation in geophysical flows. Annu. Rev. Fluid Mech. 45, 147–172.CrossRefGoogle Scholar
Viudez, A. 2007 The origin of the stationary frontal wavepacket spontaneously generated in rotating stratified vortex dipoles. J. Fluid Mech. 593, 359–383.Google Scholar
Viudez, A. & Dritschel, D. G. 2006 Spontaneous generation of inertia–gravity wave packets by balanced geophysical flows. J. Fluid Mech. 553, 107–117.CrossRefGoogle Scholar
Williams, P. D., Haine, T. W. N. & Read, P. L. 2008 Inertia–gravity waves emitted from balanced flow: observations, properties, and consequences. J. Atmos. Sci. 65, 3543–3556.Google Scholar
Williams, R. T. & Plotkin, J. 1968 Quasi-geostrophic frontogenesis. J. Atmos. Sci. 25, 201–206.2.0.CO;2>CrossRefGoogle Scholar
Wunsch, C. & Ferrari, R. 2004 Vertical mixing, energy and the general circulation of the oceans. Annu. Rev. Fluid Mech. 36, 281–314.Google Scholar
Zhang, F. 2004 Generation of mesoscale gravity waves in upper-tropospheric jet-front systems. J. Atmos. Sci. 61, 440–457.Google Scholar