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Junhong Wei, Gergely Bölöni, and Ulrich Achatz

in a Lagrangian-mean reference frame the effect of GWs on the large-scale flow only appears in the momentum equation ( Andrews and McIntyre 1978 ). Application of this theory to an Eulerian-mean reference frame leads to a pseudomomentum-flux convergence by which the large-scale momentum is to be forced ( Andrews and McIntyre 1976 , 1978 ). As will be shown below this is at least justified if the large-scale flow is in geostrophic and hydrostatic balance. The direct scheme does not rely on any

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Jannik Wilhelm, T. R. Akylas, Gergely Bölöni, Junhong Wei, Bruno Ribstein, Rupert Klein, and Ulrich Achatz

is described by a quasigeostrophic potential vorticity that is affected by the GWs via pseudomomentum-flux convergence. For efficiency reasons, parameterizations use these theoretical results with drastic simplifications: (i) lateral GW propagation and the impact of horizontal mean flow gradients are ignored, and (ii) the time-dependent transient wave–mean flow interaction is replaced by an equilibrium picture where, because of the nonacceleration paradigm, GWs can only modify the resolved flow

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Claudia Christine Stephan, Cornelia Strube, Daniel Klocke, Manfred Ern, Lars Hoffmann, Peter Preusse, and Hauke Schmidt

2004 , Plougonven and Zhang 2014 ) and flow over orography (e.g., Lilly and Kennedy 1973 ; Dörnbrack et al. 1999 ; Eckermann and Preusse 1999 ; Jiang et al. 2004 ; Fritts et al. 2016 ). We here present the first intercomparison of GW pseudomomentum fluxes (GWMFs) in global convection-permitting simulations of three different state-of-the-art GCMs and those derived from satellite observations. Two simulations are performed with each model. The horizontal resolutions between each pair of

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Gergely Bölöni, Bruno Ribstein, Jewgenija Muraschko, Christine Sgoff, Junhong Wei, and Ulrich Achatz

again statically stable. Following Lindzen (1981) and Becker (2004) , the turbulent fluxes are modeled by eddy viscosity and diffusivity so that small scales are damped more strongly than larger scales. The buoyancy equation, for example, is supplemented by a diffusion term with the turbulent eddy diffusivity coefficient . By Fourier transformation in space and integration over a short time interval , one obtains the following as change of the buoyancy amplitude: Employing identical eddy

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Tyler Mixa, Andreas Dörnbrack, and Markus Rapp

from the Advanced Mesospheric Temperature Mapper (AMTM), which remained stationary for several hours ( Pautet et al. 2016 ). Simultaneous lidar measurements of sodium mixing ratios in the mesosphere and lower thermosphere (MLT) indicate peak gravity wave amplitudes of ≈±10 K at z ≈ 83 km and λ x ≈ 40 km. Later flight legs show strong indications of gravity wave breaking, with apparent vortex ring formation and momentum fluxes estimated over 320 m 2 s −2 ( Pautet et al. 2016 ). Eckermann et al

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Mark Schlutow

vector form: (12) ∂ y ∂ t + ∂ F ⁡ ( y ) ∂ z = G ⁡ ( y ) , with a flux F and an inhomogeneity G where y = ( k z , a , u ) T is the prognostic vector. 4. General stationary solutions of the modulation equations In this section we will explore general stationary solutions before we focus on particular solutions for which we will present stability analysis in the upcoming sections. In the inviscid limit (i.e., Λ → 0), the modulation equations assume stationary solutions where ∂ p /∂ x = 0

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Mahnoosh Haghighatnasab, Mohammad Mirzaei, Ali R. Mohebalhojeh, Christoph Zülicke, and Riwal Plougonven

forcing mechanism. The spectrum of IGWs generated by convection depends on the latent heat released, properties of convection in the lower troposphere and the environmental wind ( Beres and Alexander 2004 ; Beres et al. 2005 ). There have been many studies devoted to finding a suitable method for parameterization of convectively generated IGWs in the GCMs mainly following two main approaches, based on either the momentum flux (e.g., Song et al. 2003 ; Beres and Alexander 2004 ) or the energy (e

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