## 1. Introduction

[2] Observations, theory, and modeling spanning many years have suggested gravity wave (GW) penetration and potentially significant effects extending well into the thermosphere. Early observations of ionospheric irregularities motivated the initial theoretical studies of GWs at high altitudes [see *Hines*, 1960, 1974], while more recent observations, primarily employing incoherent scatter radars, provided more quantitative descriptions of the vertical scales and frequencies of these motions extending to high altitudes [e.g., *Oliver et al.*, 1997; *Djuth et al.*, 1997, 2004; *Nicolls et al.*, 2004; *Vadas and Nicolls*, 2008, 2009; *Abdu et al.*, 2009]. Initial linear steady state and ray-tracing models and theory have examined responses to various sources, including convection, body forcing accompanying GW dissipation, and tsunamis, the influences of various wind and temperature fields on GW penetration, and their heating and cooling of the thermosphere [e.g.,*Hickey and Cole*, 1988; *Vadas and Fritts*, 2004, 2005, 2006, 2009; *Vadas*, 2007; *Fritts and Vadas*, 2008; *Fritts et al.*, 2008; *Hickey et al.*, 2009, 2011; *Vadas and Liu*, 2009, 2011; *Vadas and Crowley*, 2010]. The source studies, in particular, suggest that large-scale GWs may achieve large amplitudes extending well into the thermosphere (∼200 to 500 km or higher), despite having nearly undetectable amplitudes in the MLT. Large anticipated GW scales can invalidate the WKB assumption since this approach requires negligible variation in the background state over one vertical wavelength. As discussed by*Vadas and Fritts* [2005] and *Vadas* [2007], this fact has important implications for the validity of ray tracing methods applied at higher altitudes, while large implied GW amplitudes suggest a potential for similar instability dynamics to those observed and simulated in the MLT and at lower altitudes [see [*Fritts and Alexander*, 2003; *Hecht*, 2004, and references therein], and for significant induced mean flows that are not accounted for by linear theory. Finally, the nonlinear GW parameterization initially developed for the atmosphere from the ground to the mesosphere and lower thermosphere region [*Medvedev and Klaassen*, 1995; *Medvedev et al.*, 1998; *Medvedev and Klaassen*, 2000] has been extended to the upper thermosphere in attempts to account for broader spectral GW responses at altitudes above the turbopause [*Yiğit et al.*, 2008, 2009; *Yiğit and Medvedev*, 2009, 2010; *Yiğit et al.*, 2012].

[3] Despite the theoretical potential for large GW amplitudes to contribute instability and neutral turbulence well into the thermosphere, there is no direct observational evidence for such at present. Indeed, the dynamics occurring throughout the lower atmosphere and the MLT have been recognized to lead to turbulence occurring on many scales and extending into the lower thermosphere for many years [*Roper*, 1966, 1977; *Justus*, 1967; *Bishop et al.*, 2004]. But these measurements have also yielded indications of a “turbopause” above which “.. molecular diffusion rates are much greater than the wind-induced mixing rates”, with most data suggesting only laminar diffusion occurring above ∼105 and 110 km [*Roper*, 1977]. We note, however, that this apparent discrepancy between observations and theory may be a matter of the spatial scales on which turbulence is assumed to occur: turbulence at low Reynolds numbers and high altitudes should likely be expected at dramatically larger spatial scales (by ∼1 to 2 orders of magnitude) than observed at lower altitudes, given that the smallest turbulence scales vary as , where *ν* is the kinematic viscosity and *ε* is the kinetic energy dissipation rate.

[4] Linear models of GW saturation do not capture nonlinear dynamics of GW processes in the whole atmosphere system. The extended nonlinear parameterization by *Yiğit et al.*, [2008] based on the work by *Medvedev and Klaassen* [1995]successfully accounts for scale-dependent nonlinear diffusion. In the present work, a finite-volume numerical model solving the anelastic equations described by*Lipps and Hemler* [1982], which yield the dispersion relation appropriate for deep GWs, has been developed in order to shed light into detailed theoretical understanding of nonlinear GW dynamics. The model is applied in direct numerical simulations (DNS) to describe the three-dimensional (3D) evolution of a GW having a high intrinsic frequency,*ω*_{i} = *N*/3.72, a large vertical wavelength, *λ*_{z} ≃ 20 km, and exhibiting strong instability dynamics approximately 50 km above the generally accepted “turbopause” altitude. Two cases are considered, one in which the mean flow does not change (yielding instability dynamics accompanying a GW having the specified scales) and a second in which the mean flow is allowed to evolve due to GW momentum transport and deposition.

[5] A brief description of the numerical model is provided in Section 2. Sections 3 and 4 present results from the two cases exhibiting GW breaking and turbulence generation extending to 170 and 140 km, respectively, and Section 5 provides a discussion of the implications of these results and our conclusions.