Gravity Waves

Gravity waves represent an important problem of subgrid-scale modeling and parameterization for atmosphere and ocean. Our research strives for a better understanding of the dynamics of these waves, and for a more reliable representation of their effects in weather and climate modeling.



Achatz, U., Alexander, M.J., Becker, E., Chun, H.-Y., Dörnbrack, A., Holt, L., PLougonven, R., Polichtchouk, I., Sato, K., Sheshadri, A., Stephan, C., van Niekerk, A., und Wright, C. (2023). Atmospheric Gravity Waves: Processes and Parameterization. J. Atmos. Sci., doi: 10.1175/JAS-D-23-0210.1

Achatz, U., Kim, Y.-H., und Voelker, G. S. (2023). Multi-scale dynamics of the interaction between waves and mean flows: From nonlinear WKB theory to gravity-wave parameterizations in weather and climate models. J. Math. Phys., 64(11) (

Dolaptchiev, S., Spichtinger, P., Baumgartner, M., und Achatz, U. (2023). Interactions between gravity waves and cirrus clouds: asymptotic modeling of wave induced ice nucleation. J. Atmos. Sci., doi:10.1175/JAS-D-22-0234.1


Schmid, F., Gagarina, E., Klein, R., and U. Achatz, 2021:  Towards a numerical laboratory for investigations of gravity-wave mean-flow interactions in the atmosphere. Mon. Wea. Rev. accepted

Kim, Y.-H., and U. Achatz, 2021: Interaction between stratospheric Kelvin waves and gravity waves in the easterly QBO phase. Geophys. Res. Lett., accepted.

Bölöni, G., Kim, Y.-H., Borchert, S., and U. Achatz, 2021: Toward transient subgrid-scale gravity wave representation in atmospheric models. Part I: Propagation model including non-dissipative direct wave-mean-flow interactions. J. Atmos. Sci., accepted. (pdf)


Schlutow, M.and G.S. Voelker, 2020: On strongly nonlinear gravity waves in a vertically sheared atmosphere. Math. Clim. Weather Forecasting, accepted

Kim, Y., G. Bölöni, S. Borchert, H. Chun, and U. Achatz, 2020: Towards transient subgrid-scale gravity wave representation in atmospheric models. Part II: Wave intermittency simulated with convective sources. J. Atmos. Sci., doi:

Rodda, C.,  Hien, S.,  Achatz, U., and  U. Harlander, 2019: A new atmospheric-like differentially heated rotating annulus configuration to study gravity wave emission from jets and fronts. Exp. Fluids, 61, 2 (pdf)


Wei, J., Bölöni, G. and U Achatz, 2019: Efficient modelling of the interaction of mesoscale gravity waves with unbalanced large-scale flows: Pseudomomentum-flux convergence versus direct approach. J. Atmos Sci., 76(9): 2715–2738 (pdf)

Sutherland, B.R., Achatz, U., Caulfield, C.P., and J.M. Klymak 2019: Recent Progress in Modelling Imbalance in the Atmosphere and Ocean. Phys. Rev.  Fluids, 44:010501. (pdf).


Wilhem, J., Akylas, T.R., Bölöni, G., Wei, J., Ribstein, B., Klein, R., and U. Achatz 2018: Interactions between Meso- and Sub-Mesoscale Gravity Waves and their Efficient Representation in Mesoscale-Resolving Models, J. Atmos. Sci., 75, 2257-2280 (pdf)

Hien, S., Rolland, J., Borchert, S., Schoon, L., Zülicke, C., and U. Achatz, 2018: Spontaneous inertia-gravity wave emission in the differentially heated rotating annulus experiment. J. Fluid Mech., 838, 5-41. (pdf)


Achatz, U., Ribstein, B., Senf, F., and R. Klein 2017: The interaction between synoptic-scale balanced flow and a finite-amplitude mesoscale wave field throughout all atmospheric layers: Weak and moderately strong stratification. Quart. J. Roy. Met. Soc., 143, 342–361


Bölöni, G.,  Ribstein, B., Muraschko, J., Sgoff, C., Wei, J. and U. Achatz 2016: The interaction between atmospheric gravity waves and large-scale flows: an efficient description beyond the non-acceleration paradigm. J. Atmos. Sci., 73, 4833-4852   (pdf)

Ribstein, B. and  U. Achatz 2016: The interaction between gravity waves and solar tides in a linear tidal model with a 4D ray-tracing gravity-wave parameterization. J. Geophys. Res., doi:10.1002/2016JA022478  (pdf)


Ribstein, B., Achatz, U., and F. Senf, 2015: The interaction between Gravity Waves and Solar Tides: Results from 4D Ray Tracing coupled to a Linear Tidal Model, J. Geophys. Res., doi:10.1002/2015JA021349 (pdf)

Remmler, S., Hickel, S., Fruman, M.D., and U. Achatz, 2015: Validation of Large-Eddy Simulation Methods for Gravity-Wave Breaking. J. Atmos. Sci., 72, 3537-3562 (pdf)

Remmler, S., Fruman, M.D., Achatz, U. and S. Hickel, 2015: Numerical simulation of breaking gravity waves. In "Direct and Large-Eddy Simulation IX", eds. Fröhlich, J., Kuerten, H., Geurts, B.J. and V. Armenio, Springer, 413-418

Remmler, S., Hickel, S., Fruman, M.D. and U. Achatz, 2015: Direct numerical simulation of breaking atmospheric gravity waves, in "High Performance Computing in Science and Engineering ‘14", Eds. Nagel, W.E., Kröner, D.H., and M.M. Resch, Springer, 593-607 

Muraschko, J. , Fruman, M. D. , Achatz, U. , Hickel, S., and Y. Toledo, 2015: On the application of WKB theory for the simulation of the weakly nonlinear dynamics of gravity waves. Q. J. Roy. Meteorol. Soc., 141, 676–697 (pdf)


Fruman, M.D., Remmler, S., Achatz, U. und S. Hickel, 2014: On the construction of a direct numerical simulation of a breaking inertia-gravity wave in the upper mesosphere. J. Geophys. Res., 119, 11,613--11,640 (pdf)

Borchert, S., U. Achatz and M.D. Fruman, 2014: Gravity Wave Emission in an Atmosphere-like Configuration of the Differentially Heated Rotating Annulus Experiment. J. Fluid Mech., 758, 287-311 (pdf)


Rieper, F., Achatz, U. und Klein, R., Range of validity of an extended WKB theory for atmospheric gravity waves: one-dimensional and two-dimensional case. J. Fluid Mech., 729, 330-363 

S. Remmler, M.D. Fruman, S. Hickel (2013) Direct numerical simulation of a breaking inertia-gravity wave. Journal of Fluid Mechanics., 722, 424-436.


Fruman, M. D., U. Achatz , Secondary instabilities in breaking inertia-gravity waves. J. Atmos. Sci. 69, 303-322 (pdf)


Senf, F. and Achatz, U. On the impact of middle-atmosphere thermal tides on the propagation and dissipation of gravity waves. J. Geophys. Res. 116, D24110, doi:10.1029/2011JD015794 (pdf)


Klein, R., Achatz, U., Bresch, D Knio, O. M., Smolarkiewicz, P. K., Regime of Validity of Soundproof Atmospheric Flow Models. J. Atmos. Sci., 67, 3226–3237 

Achatz, U., Klein, R.,Senf, F., Gravity waves, scale asymptotics and the pseudo-incompressible equations. J. Fluid Mech., 663, 120-147


Fruman, M. D., Hua, B. L., Schopp, R., Equatorial zonal jet formation through the barotropic instability of low-frequency mixed Rossby-gravity waves, equilibration by inertial instability, and transition to super-rotation. J. Atmos. Sci., 66, 2600-2619


Achatz, U., Gravity-wave breaking: Linear and primary nonlinear dynamics. Adv. Space Res., 40, 719-733  (pdf)

Achatz, U., Modal and nonmodal perturbations of monochromatic high-frequency gravity waves: Primary nonlinear dynamics. J. Atmos. Sci., 64, 1977- 1994 (pdf)

Achatz, U., The primary nonlinear dynamics of modal and nonmodal perturbations of monochromatic inertia-gravity waves. J. Atmos. Sci., 64, 74-95 (pdf)