Gravity Waves

gwaveGravity waves are buoyancy oscillations that fill the atmosphere and ocean. They propogate long distances horizontally and vertically, have length scales from meters to thousands of kilometers, time scales from seconds to weeks, and release energy into turbulence by wave breaking. The wave breaking drives much of the mixing in the deep ocean and upper parts of the atmosphere, particularly the stratosphere and mesosphsere. In the troposphere, breaking gravity waves are the prime source of clear-air turbulence, a flight hazard that has injured passengers and damaged aircraft. In addition to mixing, breaking gravity waves in the stratosphere and mesosphere affect the speed and direction of the winds.

This influence on turbulent mixing and the winds is important enough that gravity waves need to be included in weather and climate models by parameterizations that are an active area of research. Most of these waves are too small and too fast to be resolved by models, but have a collective impact on the larger scale atmospheric circulation because they are a source of energy loss that must be parameterized. Similarly, ocean models include mixing parameterizations for the effects of breaking gravity waves.

Gravity waves are generated in the atmosphere by flow over mountains (called mountain waves) and by storms, and in the ocean by surface winds and by tidal flow over seamounts, among other sources. In rare moments, gravity waves can be visualized by the motion of clouds as shown in the video below from a Tama, Iowa KCCI-TV webcam on 6 May 2007.

A rare case where gravity waves can be visualized by the motion of clouds (Credit: akrherz)

CPI is developing gravity-wave models for basic and applied research, such as the simulation of long-wave / short-wave interactions in the ocean shown in the top left hand image of this web page. The objectives include understanding gravity-wave dynamics in the middle atmosphere, interpreting satellite observations and numerical model simulations, forecasting mountain waves and associated turbulence on Earth and Mars, and determining gravity-wave influences on infrasound propagation. Related models for the ocean predict the internal gravity wavefield generated by a submarine and its wake. These models are based on a computationally fast Fourier synthesis of ray solutions. They are run in combination with mesoscale circulation models for the atmosphere, and submarine hydrodynamic codes for the ocean. The work is in collaboration with teams at the Naval Research Laboratory (NRL) and at Science Applications International Corporation (SAIC). Two example projects are described below.

Ray Methods for Atmospheric Gravity Waves

The aim of this project is to develop computationally fast ray formulations for atmospheric gravity waves that account for full three-dimensional geometrical spreading from localized sources and that can be practically corrected for caustics and focal regions in three dimensions. The devised method uses a combination of Fourier and ray methods, and involves a new treatment of trapped waves. Typically 50,000 rays are traced simultaneously, with a computation time of 5-10 minutes on a standard processor. Shown below is a comparison of satellite observations (upper panel) and model simulations (lower panel) of gravity waves over Jan Mayen Island.

Gravity waves over Jan Mayen Island on Jan 25, 2000, 1635-1643 UTD: a) AVHRR image, b) Fourier-ray image reconstruction with radiosonde profiles.

Gravity waves over Jan Mayen Island on Jan 25, 2000, 1635-1643 UTD: a) AVHRR image, b) Fourier-ray image reconstruction with radiosonde profiles.

This project is sponsored by the National Science Foundation (NSF) and NRL.

Gravity Wave Scattering of Infrasound in the Atmosphere

Infrasound from sources at or near the Earth's surface can propagate high into the atmosphere, reaching the thermosphere above 100km altitude. The propagation paths are influenced by wind and temperature fields, including small-scale fluctuations induced by gravity waves. CPI has developed a new specification of the gravity wavefield for infrasound modeling. The resulting infrasound simulations give improved comparisons with measurements. Shown below is a sample infrasound simulation that includes the CPI specification of gravity waves.

Infrasound simulation from Ruffle Cyprus propogation analysis. The color bar shows the transmission loss in decibels. (Courtesy of Doug Drob, NRL.)

Infrasound simulation from Ruffle Cyprus propogation analysis. The color bar shows the transmission loss in decibels. (Courtesy of Doug Drob, NRL.)

This project is sponsored by the Office of Naval Research (ONR) and is a collaboration between CPI and NRL.

Internal waves generated by a submarine

Submarines generate internal waves in two ways: by flow over the body of the submarine and by turbulent motions in the wake of the submarine. CPI is developing computationally fast models of internal-wave production for body and wake generated internal waves, which also follow internal-wave propagation through a realistic ocean, from the submarine to the sea surface.

Submarine generated internal waves in a thermocline. The colorbar shows a non-dimensional vertical velocity that corresponds to a peak value of a few cm/sec under realistic coastal-ocean conditions.

Submarine generated internal waves in a thermocline. The colorbar shows a non-dimensional vertical velocity that corresponds to a peak value of a few cm/sec under realistic coastal-ocean conditions.

This project is sponsored by ONR and is a collaboration between CPI and SAIC.

Publications

Drob, D.P., D. Broutman, M. A. Hedlin, N. W. Winslow, and R. G. Gibson, A method for specifying atmospheric gravity wavefields for long-range infrasound propagation calculations, J. Geophys. Res. Atmos. 118, 3933–3943, doi:10.1029/2012JD018077 (2013).

Broutman, D., and S.D. Eckermann, Analysis of a ray-tracing model for gravity waves generated by tropospheric convection, J. Geophys. Res. 117, D05132, doi:10.1029/2011JD016975 (2012).

Pautet, P.-D., J. Stegman, C. M. Wrasse, K. Nielsen, H. Takahashi, M. J. Taylor, K. W. Hoppel, and S. D. Eckermann, Analysis of gravity wave structures visible in noctilucent cloud images, J. Atmos. Terr. Phys. 73, 2082-2090, doi:10.1016/j.jastp.2010.06.001, (2011).

Taylor, M. J., P.-D. Pautet, Y. Zhao, C. E. Randall, J. D. Lumpe, S. M. Bailey, J. Carstens, K. Nielsen, J. M. Russell III, and J. Stegman, High-latitude gravity wave measurements in noctilucent clouds and polar mesospheric clouds, in Aeronomy of the Earth's Atmosphere and Ionosphere, IAGA Special Sopron Book Series, Volume 2, Part 1, 93-105, doi:10.1007/978-94-007-0326-1_7 (2011).

Eckermann, S. D., J. Lindeman, D. Broutman, J. Ma, and Z. Boybeyi, Momentum fluxes of gravity waves generated by variable Froude number flow over three-dimensional obstacles, J. Atmos. Sci. 67, 2260-2278 (2010).

Eckermann, S. D., J. Ma, and X. Zhu, Scale-dependent infrared radiative damping rates on Mars and their role in the deposition of gravity-wave momentum flux, Icarus 211, doi:10.1016/j.icarus.2010.10.029 (2010).

Lindeman, J., D. Broutman, S. D. Eckermann, J. Ma, and Z. Boybeyi, A coupled mesoscale-model Fourier-method for idealized mountain-wave simulations over Hawaii, Meteorol. Atmos. Phys. 108, 71-81 (2010).

Alexander, M. J., S. D. Eckermann, D. Broutman, and J. Ma, Momentum flux estimates for South Georgia Island mountain waves in the stratosphere observed via satellite, Geophys. Res. Lett. 36, L12816, doi:10.1029/2009GL038587 (2009).

Broutman, D., S. D. Eckermann, and J. Rottman, Practical application of two turning-point theory to mountain wave transmission through a wind jet, J. Atmos. Sci. 66, 481-494 (2009).

Lindeman, J., D. Broutman, S. D. Eckermann, J. Ma, J. W. Rottman, Z. Boybeyi, Mesoscale model initialization of the Fourier transform method for mountain waves, J. Atmos. Sci. 65, 2749-2756 (2008).

Eckermann, S. D., J. Ma, D. L. Wu, and D. Broutman, A three-dimensional mountain wave imaged in satellite radiance throughout the stratosphere: Evidence of the effects of directional wind shear, Quart. J. Roy. Meteorol. Soc. 133, 1959-1975 (2007).

Broutman, D., J. Ma, S. D. Eckermann, and J. Lindeman, Fourier-ray modeling of transient trapped lee waves, Mon. Wea. Rev. 134(10), 2849-2856, DOI:10.1175/MWR3232.1 (2006).

Eckermann, S. D., D. Broutman, J. Ma and J. Lindeman, Fourier-ray modeling of short wavelength trapped lee waves observed in satellite imagery near Jan Mayen, Mon. Wea. Rev.134, 2830-2848 (2006).

Hopfner, M., N. Larsen, R. Spang, B. P. Luo, J. Ma, S. H. Svendsen, S. D. Eckermann, B. Knudsen, P. Massoli, F. Cairo, G. Stiller, T. V. Clarmann, and H. Fischer, MIPAS detects Antarctic stratospheric belt of NAT PSCs caused by mountain waves, Atmos. Chem. Phys. 6, 1221-1230 (2006).

Nielsen, K., M. J. Taylor, P.-D. Pautet, D. C. Fritts, N. Mitchell, C. Beldon, B. P. Williams, W. Singer, F. J. Schmidlin, and R. A. Goldberg, Propagation of shot-period gravity waves at high-latitudes during the MaCWAVE winter campaign, Ann. Geophys. 24, 1227-1243, Sref-ID:1432-0576/ag/2006-24-1227 (2006).

Stockwell, R. G., M. J. Taylor, K. Nielsen, and M. J. Jarvis (2006), A novel joint spacewavenumber analysis of an unusual Antarctic gravity wave event, Geophys. Res. Lett. 33, L08805, doi:10.1029/2005GL025660 (2006).

Broutman, D., and J. W. Rottman, A simplified Fourier method for computing the internal wavefield generated by an oscillating source in a horizontally moving, depth-dependent background, Phys. Fluids 16, 3682-3689 (2004).

Broutman, D., R. Grimshaw, and S. D. Eckermann, Internal Waves in a Lagrangian Reference Frame, J. Atmos. Sci. 61, 1308 - 1313 (2004).

Broutman, D., J. W. Rottman, and S. D. Eckermann, Ray models for internal waves in the atmosphere and ocean, Ann. Rev. Fluid Mech. 36, 233-253, (2004).

Jiang, J. H., S. D. Eckermann, D. L. Wu, and J. Ma,, A search for mountain waves in MLS stratospheric limb radiance from the Northern Hemisphere: data analysis and global mountain wave modeling, J. Geophys. Res. 109, D03107, doi:10.1029/2003JD003974 (2004).

Jiang, J. H., D. L. Wu, S. D. Eckermann, and J. Ma,, Mountain waves in the middle atmosphere: Microwave Limb Sounder observations and analyses, Adv. Space Res. 32, 801, doi:10.1029/2003JD003756 (2004).