• Achatz, U., R. Klein, and F. Senf, 2010: Gravity waves, scale asymptotics and the pseudo-incompressible equations. J. Fluid Mech., 663, 120147, https://doi.org/10.1017/S0022112010003411.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Alexander, M. J., and Coauthors, 2010: Recent developments in gravity-wave effects in climate models and the global distribution of gravity-wave momentum flux from observations and models. Quart. J. Roy. Meteor. Soc., 136, 11031124, https://doi.org/10.1002/qj.637.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Andrews, D. G., and M. E. Mcintyre, 1978: An exact theory of nonlinear waves on a Lagrangian-mean flow. J. Fluid Mech., 89, 609646, https://doi.org/10.1017/S0022112078002773.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bölöni, G., B. Ribstein, J. Muraschko, C. Sgoff, J. Wei, and U. Achatz, 2016: The interaction between atmospheric gravity waves and large-scale flows: An efficient description beyond the nonacceleration paradigm. J. Atmos. Sci., 73, 48334852, https://doi.org/10.1175/JAS-D-16-0069.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bretherton, F. P., 1969: Momentum transport by gravity waves. Quart. J. Roy. Meteor. Soc., 95, 213243, https://doi.org/10.1002/qj.49709540402.

  • Broutman, D., J. W. Rottman, and S. D. Eckermann, 2002: Maslov’s method for stationary hydrostatic mountain waves. Quart. J. Roy. Meteor. Soc., 128, 11591171, https://doi.org/10.1256/003590002320373247.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Broutman, D., J. Ma, S. D. Eckermann, and J. Lindeman, 2006: Fourier-ray modeling of transient trapped lee waves. Mon. Wea. Rev., 134, 28492856, https://doi.org/10.1175/MWR3232.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bühler, O., 2009: Waves and Mean Flows. Cambridge University Press, 341 pp.

    • Crossref
    • Export Citation
  • Bühler, O., and M. E. McIntyre, 2003: Remote recoil: A new wave-mean interaction effect. J. Fluid Mech., 492, 207230, https://doi.org/10.1017/S0022112003005639.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bühler, O., and M. E. McIntyre, 2005: Wave capture and wave-vortex duality. J. Fluid Mech., 534, 6795, https://doi.org/10.1017/S0022112005004374.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, C.-C., D. R. Durran, and G. J. Hakim, 2005: Mountain-wave momentum flux in an evolving synoptic-scale flow. J. Atmos. Sci., 62, 32133231, https://doi.org/10.1175/JAS3543.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, C.-C., G. J. Hakim, and D. R. Durran, 2007: Transient mountain waves and their interaction with large scales. J. Atmos. Sci., 64, 23782400, https://doi.org/10.1175/JAS3972.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dosser, H., and B. Sutherland, 2011: Weakly nonlinear non-Boussinesq internal gravity wavepackets. Physica D, 240, 346356, https://doi.org/10.1016/j.physd.2010.09.008.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Durran, D. R., 1995: Do breaking mountain waves deceierate the local mean flow? J. Atmos. Sci., 52, 40104032, https://doi.org/10.1175/1520-0469(1995)052<4010:DBMWDT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Eckermann, S. D., J. Ma, and D. Broutman, 2015: Effects of horizontal geometrical spreading on the parameterization of orographic gravity wave drag. Part I: Numerical transform solutions. J. Atmos. Sci., 72, 23302347, https://doi.org/10.1175/JAS-D-14-0147.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Eckermann, S. D., and Coauthors, 2016: Dynamics of orographic gravity waves observed in the mesosphere over the Auckland Islands during the Deep Propagating Gravity Wave Experiment (DEEPWAVE). J. Atmos. Sci., 73, 38553876, https://doi.org/10.1175/JAS-D-16-0059.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Eliassen, A., and E. Palm, 1960: On the transfer of energy in stationary mountain waves. Geofys. Publ., 22 (3), 123.

  • Fritts, D. C., and T. J. Dunkerton, 1984: A quasi-linear study of gravity-wave saturation and self-acceleration. J. Atmos. Sci., 41, 32723289, https://doi.org/10.1175/1520-0469(1984)041<3272:AQLSOG>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fritts, D. C., B. Laughman, T. S. Lund, and J. B. Snively, 2015: Self-acceleration and instability of gravity wave packets: 1. Effects of temporal localization. J. Geophys. Res. Atmos., 120, 87838803, https://doi.org/10.1002/2015JD023363.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Garcia, R. R., and S. Solomon, 1985: The effect of breaking gravity waves on the dynamics and chemical composition of the mesosphere and lower thermosphere. J. Geophys. Res., 90, 38503868, https://doi.org/10.1029/JD090iD02p03850.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gregory, D., G. J. Shutts, and J. R. Mitchell, 1998: A new gravity-wave-drag scheme incorporating anisotropic orography and low-level wave breaking: Impact upon the climate of the UK Meteorological Office Unified Model. Quart. J. Roy. Meteor. Soc., 124, 463493, https://doi.org/10.1002/qj.49712454606.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hasha, A., O. Bühler, and J. Scinocca, 2008: Gravity wave refraction by three-dimensionally varying winds and the global transport of angular momentum. J. Atmos. Sci., 65, 28922906, https://doi.org/10.1175/2007JAS2561.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Holton, J. R., 1983: The influence of gravity wave breaking on the general circulation of the middle atmosphere. J. Atmos. Sci., 40, 24972507, https://doi.org/10.1175/1520-0469(1983)040<2497:TIOGWB>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kim, Y.-J., and A. Arakawa, 1995: Improvement of orographic gravity wave parameterization using a mesoscale gravity wave model. J. Atmos. Sci., 52, 18751902, https://doi.org/10.1175/1520-0469(1995)052<1875:IOOGWP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kim, Y.-J., and J. D. Doyle, 2005: Extension of an orographic-drag parametrization scheme to incorporate orographic anisotropy and flow blocking. Quart. J. Roy. Meteor. Soc., 131, 18931921, https://doi.org/10.1256/qj.04.160.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kruse, C. G., R. B. Smith, and S. D. Eckermann, 2016: The midlatitude lower-stratospheric mountain wave valve layer. J. Atmos. Sci., 73, 50815100, https://doi.org/10.1175/JAS-D-16-0173.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lindzen, R. S., 1981: Turbulence and stress owing to gravity wave and tidal breakdown. J. Geophys. Res., 86, 97079714, https://doi.org/10.1029/JC086iC10p09707.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lott, F., and H. Tietelbaum, 1993: Linear unsteady mountain waves. Tellus, 45, 201220, https://doi.org/10.3402/tellusa.v45i3.14871.

  • Lott, F., and M. J. Miller, 1997: A new subgrid-scale orographic drag parametrization: Its formulation and testing. Quart. J. Roy. Meteor. Soc., 123, 101127, https://doi.org/10.1002/qj.49712353704.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McFarlane, N. A., 1987: The effect of orographically excited gravity wave drag on the general circulation of the lower stratosphere and troposphere. J. Atmos. Sci., 44, 17751800, https://doi.org/10.1175/1520-0469(1987)044<1775:TEOOEG>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McLandress, C., 1998: On the importance of gravity waves in the middle atmosphere and their parameterization in general circulation models. J. Atmos. Sol.-Terr. Phys., 60, 13571383, https://doi.org/10.1016/S1364-6826(98)00061-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Miles, J. W., 1969: Waves and wave drag in stratified flows. Applied Mechanics: Proceedings of the Twelfth International Congress of Applied Mechanics, M. Hetényi and W. G. Vincenti, Eds, IUTAM Series, Springer, 50–75, https://doi.org/10.1007/978-3-642-85640-2_4.

    • Crossref
    • Export Citation
  • Miller, M. J., T. N. Palmer, and R. Swinbank, 1989: Parameterization and influence of subgridscale orography in general circulation model and weather prediction models. Meteor. Atmos. Phys., 40, 84209, https://doi.org/10.1007/BF01027469.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Palmer, T. N., G. J. Shutts, and R. Swinbank, 1986: Alleviation of a systematic westerly bias in general circulation and numerical weather prediction models through an orographic gravity wave drag parametrization. Quart. J. Roy. Meteor. Soc., 112, 10011039, https://doi.org/10.1002/qj.49711247406.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Portele, T. C., A. Dörnbrack, J. S. Wagner, S. Gisinger, B. Ehard, P.-D. Pautet, and M. Rapp, 2018: Mountain-wave propagation under transient tropospheric forcing: A DEEPWAVE case study. Mon. Wea. Rev., 146, 18611888, https://doi.org/10.1175/MWR-D-17-0080.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rieper, F., U. Achatz, and R. Klein, 2013: Range of validity of an extended WKB theory for atmospheric gravity waves: One-dimensional and two-dimensional case. J. Fluid Mech., 729, 330363, https://doi.org/10.1017/jfm.2013.307.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Scinocca, J. F., and T. G. Shepherd, 1992: Nonlinear wave-activity conservation laws and Hamiltonian structure for the two-dimensional anelastic equations. J. Atmos. Sci., 49, 528, https://doi.org/10.1175/1520-0469(1992)049<0005:NWACLA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., and Coauthors, 2008: A description of the Advanced Research WRF version 3. NCAR Tech. Note NCAR/TN-475+STR, 113 pp., http://dx.doi.org/10.5065/D68S4MVH.

    • Crossref
    • Export Citation
  • Smith, R. B., 1977: The steepening of hydrostatic mountain waves. J. Atmos. Sci., 34, 16341654, https://doi.org/10.1175/1520-0469(1977)034<1634:TSOHMW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smith, R. B., 1979: The influence of mountains on the atmosphere. Advances in Geophysics, B. Saltzman, Ed., Vol. 21, Academic Press, 87–230, https://doi.org/10.1016/S0065-2687(08)60262-9.

    • Crossref
    • Export Citation
  • Smith, R. B., and C. G. Kruse, 2017: Broad-spectrum mountain waves. J. Atmos. Sci., 74, 13811402, https://doi.org/10.1175/JAS-D-16-0297.1.

  • Smith, R. B., and C. G. Kruse, 2018: A gravity wave drag matrix for complex terrain. J. Atmos. Sci., https://doi.org/10.1175/JAS-D-17-0380.1, in press.

    • Crossref
    • Export Citation
  • van den Bremer, T. S., and B. R. Sutherland, 2014: The mean flow and long waves induced by two-dimensional internal gravity wavepackets. Phys. Fluids, 26, 106601, https://doi.org/10.1063/1.4899262.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Webster, S., A. R. Brown, D. R. Cameron, and C. P. Jones, 2003: Improvements to the representation of orography in the Met Office Unified Model. Quart. J. Roy. Meteor. Soc., 129, 19892010, https://doi.org/10.1256/qj.02.133.

    • Crossref
    • Search Google Scholar
    • Export Citation
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Nondissipative and Dissipative Momentum Deposition by Mountain Wave Events in Sheared Environments

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  • 1 Yale University, New Haven, Connecticut
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Abstract

Mountain waves (MWs) are generated during episodic cross-barrier flow over broad-spectrum terrain. However, most MW drag parameterizations neglect transient, broad-spectrum dynamics. Here, the influences of these dynamics on both nondissipative and dissipative momentum deposition by MW events are quantified in a 2D, horizontally periodic idealized framework. The influences of the MW spectrum, vertical wind shear, and forcing duration are investigated. MW events are studied using three numerical models—the nonlinear, transient WRF Model; a linear, quasi-transient Fourier-ray model; and an optimally tuned Lindzen-type saturation parameterization—allowing quantification of total, nondissipative, and dissipative MW-induced decelerations, respectively. Additionally, a pseudomomentum diagnostic is used to estimate nondissipative decelerations within the WRF solutions. For broad-spectrum MWs, vertical dispersion controls spectrum evolution aloft. Short MWs propagate upward quickly and break first at the highest altitudes. Subsequently, the arrival of additional longer MWs allows breaking at lower altitudes because of their greater contribution to u variance. As a result, minimum breaking levels descend with time and event duration. In zero- and positive-shear environments, this descent is not smooth but proceeds downward in steps as a result of vertically recurring steepening levels. Nondissipative decelerations are nonnegligible and influence an MW’s approach to breaking, but breaking and dissipative decelerations quickly develop and dominate the subsequent evolution. Comparison of the three model solutions suggests that the conventional instant propagation and monochromatic parameterization assumptions lead to too much MW drag at too low an altitude.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Christopher G. Kruse, christopher.kruse@yale.edu

Abstract

Mountain waves (MWs) are generated during episodic cross-barrier flow over broad-spectrum terrain. However, most MW drag parameterizations neglect transient, broad-spectrum dynamics. Here, the influences of these dynamics on both nondissipative and dissipative momentum deposition by MW events are quantified in a 2D, horizontally periodic idealized framework. The influences of the MW spectrum, vertical wind shear, and forcing duration are investigated. MW events are studied using three numerical models—the nonlinear, transient WRF Model; a linear, quasi-transient Fourier-ray model; and an optimally tuned Lindzen-type saturation parameterization—allowing quantification of total, nondissipative, and dissipative MW-induced decelerations, respectively. Additionally, a pseudomomentum diagnostic is used to estimate nondissipative decelerations within the WRF solutions. For broad-spectrum MWs, vertical dispersion controls spectrum evolution aloft. Short MWs propagate upward quickly and break first at the highest altitudes. Subsequently, the arrival of additional longer MWs allows breaking at lower altitudes because of their greater contribution to u variance. As a result, minimum breaking levels descend with time and event duration. In zero- and positive-shear environments, this descent is not smooth but proceeds downward in steps as a result of vertically recurring steepening levels. Nondissipative decelerations are nonnegligible and influence an MW’s approach to breaking, but breaking and dissipative decelerations quickly develop and dominate the subsequent evolution. Comparison of the three model solutions suggests that the conventional instant propagation and monochromatic parameterization assumptions lead to too much MW drag at too low an altitude.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Christopher G. Kruse, christopher.kruse@yale.edu
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