• Buizza, R., 1995: Optimal perturbation time evolution and sensitivity of ensemble prediction to perturbation amplitude. Quart. J. Roy. Meteor. Soc., 121 , 17051738.

    • Search Google Scholar
    • Export Citation
  • Buizza, R., , and T. N. Palmer, 1995: The singular-vector structure of the atmospheric global circulation. J. Atmos. Sci., 52 , 14341456.

    • Search Google Scholar
    • Export Citation
  • Chelton, D. B., , M. H. Freilich, , J. M. Sienkiewicz, , and J. M. Von Ahn, 2006: On the use of QuikSCAT scatterometer measurements of surface winds for marine weather prediction. Mon. Wea. Rev., 134 , 20552071.

    • Search Google Scholar
    • Export Citation
  • Doyle, J., , and T. Warner, 1990: Mesoscale coastal processes during GALE IOP 2. Mon. Wea. Rev., 118 , 283308.

  • Farrell, B. F., 1988: Optimal excitation of neutral Rossby waves. J. Atmos. Sci., 45 , 163172.

  • Farrell, B. F., 1989: Optimal excitation of baroclinic waves. J. Atmos. Sci., 46 , 11931206.

  • Farrell, B. F., , and P. J. Ioannou, 1996: Generalized stability theory. Part I: Autonomous operators. J. Atmos. Sci., 53 , 20252040.

  • Feliks, Y., 2004: Nonlinear dynamics and chaos in the sea and land breeze. J. Atmos. Sci., 61 , 21692187.

  • Feliks, Y., , M. Ghil, , and E. Simonnet, 2004: Low-frequency variability in the midlatitude atmosphere induced by an oceanic thermal front. J. Atmos. Sci., 61 , 961981.

    • Search Google Scholar
    • Export Citation
  • Feliks, Y., , M. Ghil, , and E. Simonnet, 2007: Low-frequency variability in the midlatitude baroclinic atmosphere induced by an oceanic thermal front. J. Atmos. Sci., 64 , 97116.

    • Search Google Scholar
    • Export Citation
  • Giordani, H., , and S. Planton, 2000: Modeling and analysis of ageostrophic circulation over the Azores oceanic front during the SEMAPHORE experiment. Mon. Wea. Rev., 128 , 22702287.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B., 1975: The geostrophic momentum approximation and the semi-geostrophic equations. J. Atmos. Sci., 32 , 233242.

  • Hoskins, B., , and F. Bretherton, 1972: Atmospheric frontogenesis models: Mathematical formulation and solution. J. Atmos. Sci., 29 , 1137.

    • Search Google Scholar
    • Export Citation
  • Hsu, S., 1984: Sea-breeze-like winds across the north wall of the Gulf Stream: An analytical model. J. Geophys. Res., 89 , 20252028.

  • Huang, C-Y., , and S. Raman, 1988: A numerical modeling study of the marine boundary layer over the Gulf Stream during cold air advection. Bound.-Layer Meteor., 45 , 251290.

    • Search Google Scholar
    • Export Citation
  • Joly, A., 1995: The stability of steady fronts and the adjoint method: Nonmodal frontal waves. J. Atmos. Sci., 52 , 30823108.

  • Lohmann, G., , and J. Schneider, 1999: Dynamics and predictability of Stommel’s box model. A phase-space perspective with implications for decadal climate variability. Tellus, 51A , 326336.

    • Search Google Scholar
    • Export Citation
  • Marchuk, G. I., 1975: Methods of Numerical Mathematics. Springer, 316 pp.

  • Minobe, S., , A. Kuwano-Yoshida, , N. Komori, , S-P. Xie, , and R. J. Small, 2008: Influence of the Gulf Stream on the troposphere. Nature, 452 , 206209. doi:10.1038/nature06690.

    • Search Google Scholar
    • Export Citation
  • Moore, A. M., 1999: Wind-induced variability of ocean gyres. Dyn. Atmos. Oceans, 29 , 335364.

  • Moore, A. M., , and R. Kleeman, 1997: The singular vectors of a coupled ocean–atmosphere model of ENSO. I. Thermodynamics, energetics and error growth. Quart. J. Roy. Meteor. Soc., 123 , 953981.

    • Search Google Scholar
    • Export Citation
  • O’Neill, L., , D. Chelton, , and S. Esbensen, 2003: Observations of SST-induced perturbations of the wind stress field over the Southern Ocean on seasonal time scales. J. Climate, 16 , 23402354.

    • Search Google Scholar
    • Export Citation
  • O’Neill, L., , D. Chelton, , S. Esbensen, , and F. Wentz, 2005: High-resolution satellite measurements of the atmospheric boundary layer response to SST variations along the Agulhas Return Current. J. Climate, 18 , 27062723.

    • Search Google Scholar
    • Export Citation
  • Park, K., , P. Cornillon, , and D. Codiga, 2006: Modification of surface winds near ocean fronts: Effects of Gulf Stream rings on scatterometer (QuikSCAT, NSCAT) wind observations. J. Geophys. Res., 111 , C03021. doi:10.1029/2005JC003016.

    • Search Google Scholar
    • Export Citation
  • Penland, C., , and P. D. Sardeshmukh, 1995: The optimal growth of tropical sea surface temperature anomalies. J. Climate, 8 , 19992024.

  • Sikora, T., , G. Young, , R. Beal, , and J. Edson, 1995: Use of spaceborne synthetic aperture radar imagery of the sea surface in detecting the presence and structure of the convective marine atmospheric boundary layer. Mon. Wea. Rev., 123 , 36233632.

    • Search Google Scholar
    • Export Citation
  • Small, R. J., and Coauthors, 2008: Air–sea interaction over ocean fronts and eddies. Dyn. Atmos. Oceans, 45 , 274319. doi:10.1016/j.dynatmoce.2008.01.001.

    • Search Google Scholar
    • Export Citation
  • Sublette, M., , and G. Young, 1996: Warm-season effects of the Gulf Stream on mesoscale characteristics of the atmospheric boundary layer. Mon. Wea. Rev., 124 , 653667.

    • Search Google Scholar
    • Export Citation
  • Sweet, W., , R. Fett, , J. Kerling, , and P. LaViolette, 1981: Air–sea interaction effects in the lower troposphere across the north wall of the Gulf Stream. Mon. Wea. Rev., 109 , 10421052.

    • Search Google Scholar
    • Export Citation
  • Tokinaga, H., , Y. Tanimoto, , and S. Xie, 2005: SST-induced surface wind variations over the Brazil–Malvinas confluence: Satellite and in situ observations. J. Climate, 18 , 34703482.

    • Search Google Scholar
    • Export Citation
  • Tziperman, E., , and P. J. Ioannou, 2002: Transient growth and optimal excitation of thermohaline variability. J. Phys. Oceanogr., 32 , 34273435.

    • Search Google Scholar
    • Export Citation
  • Wai, M., , and S. Stage, 1989: Dynamical analyses of marine atmospheric boundary layer structure near the Gulf Stream oceanic front. Quart. J. Roy. Meteor. Soc., 115 , 2944.

    • Search Google Scholar
    • Export Citation
  • Warner, T., , M. Lakhtakia, , J. Doyle, , and R. Pearson, 1990: Marine atmospheric boundary layer circulations forced by Gulf Stream sea surface temperature gradients. Mon. Wea. Rev., 118 , 309323.

    • Search Google Scholar
    • Export Citation
  • Weissman, D., , T. Thompson, , and R. Legeckis, 1980: Modulation of sea surface radar cross section by surface stress: Wind speed and temperature effects across the Gulf Stream. J. Geophys. Res., 85 , 50325042.

    • Search Google Scholar
    • Export Citation
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Nonnormal Frontal Dynamics

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  • 1 Department of Mathematics, Israel Institute for Biological Research, Ness-Ziona, Israel
  • 2 Department of Earth and Planetary Sciences, and School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts
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Abstract

The generalized stability of the secondary atmospheric circulation over strong SST fronts is studied using a hydrostatic, Boussinesq, two-dimensional f-plane model. It is shown that even in a parameter regime in which these circulations are stable to small perturbations, significant nonnormal growth of optimal initial perturbations occurs. The maximum growth factor in perturbation total energy is 250 and is dominated by the potential energy, which obtains a growth factor of 219 two to five hours after the beginning of the integration. This domination of potential energy growth is consistent with the observation that the available potential energy (APE) of the secondary circulation is larger by two orders of magnitude than the kinetic energy as well as with the transfer of kinetic to potential perturbation energy at the beginning of the growth of the perturbations.

The norm kernel is found to significantly influence the structure of the optimal initial perturbation as well as the energy obtained by the mature perturbations, but the physical mechanism of growth and the structure of the mature perturbations are robust.

Corresponding author address: Yizhak Feliks, Dept. of Mathematics, Israel Institute for Biological Research, P.O. Box 19, Ness-Ziona, 70450 Israel. Email: feliks@iibr.gov.il

Abstract

The generalized stability of the secondary atmospheric circulation over strong SST fronts is studied using a hydrostatic, Boussinesq, two-dimensional f-plane model. It is shown that even in a parameter regime in which these circulations are stable to small perturbations, significant nonnormal growth of optimal initial perturbations occurs. The maximum growth factor in perturbation total energy is 250 and is dominated by the potential energy, which obtains a growth factor of 219 two to five hours after the beginning of the integration. This domination of potential energy growth is consistent with the observation that the available potential energy (APE) of the secondary circulation is larger by two orders of magnitude than the kinetic energy as well as with the transfer of kinetic to potential perturbation energy at the beginning of the growth of the perturbations.

The norm kernel is found to significantly influence the structure of the optimal initial perturbation as well as the energy obtained by the mature perturbations, but the physical mechanism of growth and the structure of the mature perturbations are robust.

Corresponding author address: Yizhak Feliks, Dept. of Mathematics, Israel Institute for Biological Research, P.O. Box 19, Ness-Ziona, 70450 Israel. Email: feliks@iibr.gov.il

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