Nonlinear Stratified Flows: High-Resolution Simulation of Breaking Gravity Waves in the Earth's Atmosphere

J. M. Prusa, Iowa State University
P. K. Smolarkiewicz, National Center for Atmospheric Research
A. A. Wyszogrodzki, University of Warsaw

Research Objectives

Gravity waves (GWs) are generated in the Earth's atmosphere whenever a parcel of air is disturbed from its hydrostatic equilibrium position. In turn, wave-wave interactions (WWI) and turbulence generated by gravity wave breaking (GWB) force the atmosphere at many scales. At planetary scales, GWB makes a dominant contribution towards reversing the meridional temperature gradient at mesopause altitudes-compared to what would occur due to radiative balance alone. Wave drag induced by GWs is considered to be important in improving subgrid parameterizations for global climate models. At mesoscales, GWs may be a key component in determining the spectral energy of the atmosphere. By using the 512-PE Cray T3E at NERSC, we were able to generate the detailed dynamics of GWB from the mesoscale down to the Kolmogorov scale. These results are being used to detail the mechanisms by which GWs actually influence the mean state of the atmosphere.

Computational Approach

We developed a multiplatform fluid-flow application that runs efficiently on massively parallel machines like the T3E or on scalar processor machines. It solves the anelastic equations of motion in nonorthogonal terrain-following coordinates. The resulting elliptic pressure equation is solved using a conjugate-residual method. Our application has several sets of options to choose from, such as semi-Lagrangian or Eulerian solver, dry or moist model, grid types, turbulence parameterizations, and monotonicity (nonoscillatory) constraints.

Accomplishments

Using all 512 processors on the T3E for approximately ten hours, we simulated three hours of GW dynamics on a computational grid of 544 x 80 x 291 points, corresponding to a physical domain of 200 km (zonal) x 30 km (meridional) x 110 km (vertical). This simulation captured approximately 50 minutes of intense turbulence generated by GWB that was nonstationary, inhomogeneous, and anisotropic. A good idea of this inhomogeneity and anisotropy can be gained from the figure, which shows the zonal (), meridional (), and vertical () velocity derivative skewness. For isotropic turbulence, = = ~ 0.5.

Significance

Power spectra reveal three distinct subranges in the evolution of GWB: (1) an inertial range turbulence at the highest wavenumbers, (2) a buoyancy range turbulence at midscales, and (3) a WWI subrange at the lowest wavenumbers. The last subrange has properties that are consistent with two-dimensional waves that are forcing the basic state. We have conjectured that WWI of two-dimensional GWs (known to be common by direct observation) may be a key dynamical mechanism forcing the atmosphere at the mesoscale. Current efforts are focused on trying to find supporting evidence for this conjecture through direct computation of the turbulent fluxes and structure function statistics.

Contour density plot of velocity derivative skewnesses in horizontal xy plane at 100 km altitude and t = 155 minutes. The averaging blocks for the computations were 10 x 5 x 7.5 km in zonal x spanwise x vertical extent. The region of vigorous wavebreaking/broken waves is -70 x 10 km. Contours are shown at = -1.0, -0.35, 0.0, 0.35 (bold), 0.65, and 1.0, with redder hues corresponding to larger values of .

Assumptions of isotropy and stationarity are often used in turbulent flow problems. The present work is helping to illuminate the more complex dynamics at work when these assumptions are not valid, and ultimately may allow us to better understand the physics of real turbulence.

Publications

J. Prusa, P. K. Smolarkiewicz, and W. W. Wyszogrodzki, "Simulations of gravity wave induced turbulence using 512 PE CRAY T3E," Proc. 2nd International Workshop on Software Engineering and Code Design in Parallel Meteorological and Oceanographic Applications (Preprint Vol. NASA GSFC/CP-1998-206860, Scottsdale, Arizona, June 15-18, 1998), pp. 139-151.

J. Prusa, P. K. Smolarkiewicz, and W. W. Wyszogrodzki, "Massively parallel computation of gravity wave turbulence in the Earth's atmosphere," SIAM News, Applications on Advanced Architecture Computers (submitted, 1998).

J. Prusa, P. K. Smolarkiewicz, R. R. Garcia, and W. W. Wyszogrodzki, "Evolution of gravity wave spectra at mesopause altitudes," presented at IUTAM Developments in Geophysical Turbulence, National Center for Atmospheric Research, Boulder, Colorado, June 16-19, 1998.