C. Listowski, C. C. Stephan, A. Le Pichon, A. Hauchecorne, Y.-H. Kim, U. Achatz, and G. Bölöni, 2024: Stratospheric gravity waves impact on infrasound transmission losses across the International Monitoring System. Pure and Applied Geophysics, accepted


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

Masur, G.T., Mohamad, H., and M. Oliver, 2023: Quasi-convergence of an implementation of optimal balance by backward-forward nudging. Multiscale Model Simul., 21, 624 - 640 (

A. K. Barua, R. Chew, S. Li, J. Lowengrub, A. Münch, and B. Wagner. (2023). Sharp-interface problem of the Ohta-Kawasaki model for symmetric diblock copolymers. Journal of Computational Physics, vol. 481, p. 112032. doi:10.1016/ [link]

R. Chew, M. Schlutow, and R. Klein. (2023). An unstable mode of the stratified atmosphere under the non-traditional Coriolis acceleration. Journal of Fluid Mechanics, vol. 967, A21. doi:10.1017/jfm.2023.474 [link]


Achatz, U., 2022: Atmospheric Dynamics. Springer, Berlin (

Achatz, U., 2022: Atmosphärendynamik. Springer, Berlin (


Polichtchouk, I., Wedi, N., and Kim, Y.-H., 2022: Resolved gravity waves in the tropical stratosphere: Impact of horizontal resolution and deep convection parametrization. Quart. J. Roy. Met. Soc., 148(742), 233–251.

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. 149, 4005 - 4026

Kim, Y.-H., and U. Achatz, 2021: Interaction between stratospheric Kelvin waves and gravity waves in the easterly QBO phase. Geophys. Res. Lett., 48, e2021GL095226.

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., 78, 1317 - 1338. (pdf)

Völker, G.S., Akylas T.R. and U. Achatz, 2021: An Application of WKBJ Theory for Triad Interactions of Internal GravityWaves in Varying Background Flows. Quart. J. Roy. Met. Soc., 147, 1112–1134


Schlutow, M.and G.S. Voelker, 2020: On strongly nonlinear gravity waves in a vertically sheared atmosphere. Math. Clim. Weather Forecasting, 6, 63-74

Baumgartner, M., Weigel, R., Harvey, A.H., Plöger, F., Achatz, U., and P. Spichtinger, 2020: Reappraising the appropriate calculation of a common meteorological quantity: Potential Temperature. Atmos. Chem. Phys., 20, 15585–15616

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, 2020: A new atmospheric-like differentially heated rotating annulus configuration to study gravity wave emission from jets and fronts. Exp. Fluids, 61, 2 (pdf)


Dolaptchiev, S.I., Achatz, U. and Th. Reitz, 2019: Planetary geostrophic Boussinesq dynamics: barotropic flow, baroclinic instability and forced stationary waves. Quart. J. Roy. Met. Soc., 145, 3751 – 3765 (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)


Pieroth, M., Dolaptchiev, S.I., Zacharuk, M., Heppelmann, T., Gritsun, A., Achatz, U. 2018: Climate-Dependence in Empirical Parameters of Subgrid-Scale Parameterizations using the Fluctuation-Dissipation Theorem. J. Atmos. Sci., 75(11):3843–3860 (pdf)

Zacharuk, M., Dolaptchiev, S.I., Achatz, U. and Timofeyev, I. 2018: Stochastic subgrid-scale parameterization for one-dimensional shallow water dynamics using stochastic mode reduction. Quart. J. Roy. Met. Soc., 144:1975–1990 (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)


Schlutow, M., Klein, R., and U. Achatz 2017: Finite-amplitude gravity waves in the atmosphere: traveling wave solutions, J. Fluid Mech., 826, 1034-1065 (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 (pdf)

Berner J., Achatz U., Batte L., Bengtsson L., de la Cámara A., Christensen H., Colangeli M, Coleman D., Crommelin D., Dolaptchiev S.I., Franzke C., Friederichs P., Imkeller P., Järvinen H., Juricke S., Kitsios V., Lott F., Lucarini V.; Mahajan S., Palmer T., Penland C.,  Sakradzija M., von Storch J.-S., Weisheimer A., Weniger M., Williams P.,  and J.-I. Yano 2017: Stochastic parameterization: Towards a new view of weather and climate models. Bull. Am. Met. Soc., 98, 565 - 587 (pdf)


Wouters, J., Dolaptchiev, S.I., Lucarini. V., and U. Achatz 2016: Parametrization of stochastic multiscale triads. Nonlin. Processes Geophys., 23, 435–445 (pdf)

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)

Tort M., Ribstein B., and V. Zeitlin 2016: Symmetric and asymmetric inertial instability of zonal jets on the f -plane with complete Coriolis force. J. Fluid Mech., 788, 274-302


Düben, P. and Dolaptchiev, S. I., 2015: Rounding errors may be benecial for simulations of
atmospheric  flow: Results from the forced 1D Burgers equation. Theor. Comp. Fluid Dyn., 29, 311-328. (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)


Borchert, S., Achatz. U., Remmler, S., Hickel, S., Harlander, U., Vincze, M., Alexandrov, K.D., Rieper, F., Heppelmann, T. and S.I. Dolaptchiev, 2014: Finite-volume models with implicit subgrid-scale parameterization for the differentially heated rotating annulus. Met. Zeitschr., 23, 561–580 (pdf)

Vinzce. M.,  Borchert, S., Achatz, U. , von Larcher, T., Baumann, M., Liersch, C., Remmler, S., Beck, T., Alexandrov, K., Egbers, C., Fröhlich, J., Heuveline, V., Hickel, S., and Harlander, U., 2014: Benchmarking in a rotating annulus: a comparative experimental and numerical study of baroclinic wave dynamics. Met. Zeitschr., 23, 611–635 (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)

B. Ribstein, V. Zeitlin and A-S Tissier. "Barotropic, baroclinic, and inertial instabilities of the easterly Gaussian jet on the equatorial -plane in rotating shallow water model". Phys. Fluids, 26, 056605 (2014)


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

Rieper, F., Hickel, S., and U. Achatz , A conservative integration of the pseudo-incompressible equations with implicit turbulence parameterization. Mon. Wea. Rev., 141, 861-886 (pdf) 

Dolaptchiev, S.I., Achatz U. and I. Timofeyev , Stochastic closure for local averages in the finite-difference discretization of the forced Burgers equation. Theor. Comput. Fluid Dyn. 27, 297-317 (pdf)

Dolaptchiev, S.~I., Timofeyev, I. and Achatz, U., Subgrid-scale closure for the inviscid Burgers-Hopf equation, Commun. Math. Sci., 11, 757–777 (pdf)

Dolaptchiev, S. I. and Klein, R., A multi-scale model for the planetary and synoptic motions in the atmosphere, J. Atmos. Sci., 70, 2963-2981 (pdf)

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

Achatz, U., U. Löbl, S. Dolaptchiev and A. Gritsun, Fluctuation-Dissipation Supplemented by Nonlinearity: A Climate-Dependent Sub-Grid-Scale Parameterization in Low-Order Climate Models. J. Atmos Sci., 70, 1833-1846 (pdf)


Achatz, U., F. Senf and N. Grieger, Solar diurnal tides in the middle atmosphere: Interactions with the zonal mean flow, planetary waves and gravity waves. In Climate and weather 
of the sun-earth system (CAWSES):Highlights from a priority program. Ed. F.-J. Lübken. Springer: Dordrecht.

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)

Rieper, F., A low Mach number fix for Roe's approximate Riemann solver. Journal of Computational Physics, Volume 230, Issue 13, 10 June 2011, Pages 5263-5287


Dellacherie S., Omnes P., Rieper, F., The influence of cell geometry on the Godunov scheme applied to the linear wave equation. J. Comp. Phys. 229 (2) (2010) 221-232

Rieper, F., On the dissipation mechanism of upwind-schemes in the low Mach number regime: a comparison between Roe and HLL. J. Comp. Phys. 229 (2) (2010) 221-232

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 (pdf)


Ménesguen, C., Hua, B. L., Fruman, M. D., Schopp, R., Intermittent layering in the Atlantic Equatorial Deep Jets. J. Mar. Res., 67, 347-360

Ménesguen, C., Hua, B. L., Fruman, M. D., Schopp, R., Dynamics of the combined Extra-Equatorial and Equatorial Deep Jets in the Atlantic. J. Mar. Res., 67, 323-346

Fruman, M. D., Equatorially bounded zonally propagating linear waves on a generalized β plane. J. Atmos. Sci., 66, 2937–2945

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., Grieger, N., Schmidt, H., Mechanisms controlling the diurnal solar tide: Analysis using a GCM and a linear model. J. Geophys. Res.,113, A08303, doi:10.1029/2007JA012967 (pdf)


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)