## 1. Introduction

[2] Turbulence plays a central, but not fully quantified or understood, role in defining the evolution and structure of the atmosphere from the Earth's surface to the turbopause. At larger scales, convective heat transports largely offset radiative tendencies in accounting for the negative mean thermal gradient in the troposphere [*Holton*, 1979; *Gill*, 1982]. Similarly, turbulent transport of heat accompanying gravity-wave breaking is credited with driving the mesosphere toward an adiabatic lapse rate [*Garcia and Solomon*, 1985], though its efficiency in heat and constituent transport has been challenged on both modeling and theoretical grounds [*Strobel et al.*, 1985, 1987; *Fritts and Dunkerton*, 1985; *Coy and Fritts*, 1988; *McIntyre*, 1989]. Turbulence is known to contribute mixing and transport under more strongly stratified conditions as well, for example in the stable nocturnal boundary layer, the stratosphere, and the lower thermosphere. In all stably stratified environments, turbulence often occurs in layers of limited depth, with the turbulence extent determined initially by the scale of shear instability or wave breaking and thereafter confined vertically by stratification.

[3] Because of the importance of turbulence in atmospheric dynamics on many scales, considerable efforts have been expended to define its roles under statically stable conditions. Applications range from constituent dispersal and surface temperature prediction (and energy consumption, etc.) near the earth's surface, to vertical mixing and transport throughout the atmosphere, to aircraft safety, laser propagation, radio communications, and astronomical observations. Field programs have employed extensive instrumentation to quantify turbulence effects throughout the lower and middle atmosphere, and these efforts have contributed greatly to our knowledge of turbulence influences statistically [*Wyngaard*, 1983; *Hocking*, 1985; *Lübken*, 1997; *Poulos et al.*, 2002]. Likewise, theoretical studies have explored turbulence structure and effects under isotropic and anisotropic (stratified and/or sheared) conditions [*Kolmogorov*, 1941; *Onsager*, 1945; *Bolgiano*, 1959; *Hill*, 1978; *Weinstock*, 1978]. Yet none of these studies have fully characterized turbulence influences because of the inherent limitations of, or assumptions underlying, these methodologies.

[4] For our purposes here, the most significant indications of turbulence effects in the atmosphere have come from observations of turbulence generation, layering, and confinement by mean stratification. Early aircraft, rocket, and balloon measurements by *Lilly and Lester* [1974], *Rosenberg and Dewan* [1975], and *Cadet* [1977] addressed the diffusion associated with discrete turbulent layers in the lower stratosphere. Radar observations by *Sato and Woodman* [1982a, 1982b] and *Woodman and Rastogi* [1984] provided indications of persistent layers of strong backscatter associated with inertia-gravity wave shears in the lower stratosphere and suggested turbulence as the source of backscatter. Similar results and interpretations were offered at mesospheric altitudes by *Yamamoto et al.* [1988], *Reid* [1990], and *Stitt and Kudeki* [1991]. Other studies at higher spatial resolution have revealed that enhanced backscatter is associated preferentially with the edges of turbulent layers [*Gossard et al.*, 1971; *Browning*, 1979; *Röttger and Schmidt*, 1979; *Eaton et al.*, 1995]. In all of these cases, large *C*_{N}^{2} (and radar backscatter) was interpreted as evidence of turbulence. Significant insights were also provided by high-resolution balloon measurements describing both the mean thermal structure and the turbulence temperature structure parameter, *C*_{T}^{2}, which correlates closely with radar backscatter [*Coulman et al.*, 1995]. These observations revealed a series of nearly adiabatic layers having sharp temperature gradients and *C*_{T}^{2} maxima at the edges of each. Importantly, *C*_{T}^{2} was usually extremely small within the turbulent layers themselves.

[5] A complete quantification of turbulence dynamics and effects requires direct numerical simulation, or DNS, of the evolution of a turbulent process in three spatial dimensions and time because such processes are episodic and spatially localized in nature and dependent on initial and environmental conditions. It is also necessary to resolve not only the source scales, the transition to turbulence, and the inertial range, but also a significant viscous range. This is because interactions between inertial-range and viscous-range scales can impact turbulence dynamics at larger scales if the dissipation scales are not accurately represented [*Jimenez*, 1994]. Indeed, it has only recently become possible to achieve Reynolds numbers representative of the mesopause region in numerical simulations of geophysical processes because of the extreme resolution requirements when turbulence is intense [*Werne and Fritts*, 1999, 2001; *Hill et al.*, 1999]. Initial applications of these results to calculations of radar backscatter yielded results in close agreement with observations and important insights into the interpretation of radar data [*Gibson-Wilde et al.*, 2000]. Indeed, these results have highlighted the importance of layering accompanying turbulence in stably stratified fluids for flow evolution and measurement interpretation.

[6] Our purposes in this paper are to describe and contrast the implications for layering and layered structures in the middle atmosphere of turbulence arising due to Kelvin-Helmholtz (KH) shear instability and gravity-wave (GW) breaking. These processes are believed to be the two dominant mechanisms for turbulence generation in the free atmosphere. KH instability is most often associated with strong shears of the mean wind or accompanying low-frequency gravity waves having small vertical group velocities and slowly evolving amplitudes and shears. Gravity-wave breaking is the more common means of turbulence generation for GWs having high intrinsic frequencies and large vertical group velocities because of their more rapid amplitude growth with time. Essentially, GWs having high intrinsic frequencies rush past the necessary (but not sufficient) condition for dynamical instability of a plane parallel shear flow (a Richardson number *Ri* < 1/4, see below) and quickly become convectively unstable (*Ri* < 0), though this is not strictly the condition for GW instability of a “convective” type [see *Fritts and Alexander*, 2003]. KH shear instability appears to be more common at lower altitudes, the troposphere and lower stratosphere, where vertical wavelengths and vertical group velocities tend to be small. GW breaking becomes increasingly important at higher altitudes where wave scales and group velocities are larger and is likely the dominant source of turbulence in the mesosphere and lower thermosphere.

[7] We begin in section 2 by describing briefly the numerical methods employed for these studies. An idealized KH instability evolution and turbulence transition, and its implications for layering, are described in section 3. The evolution of a breaking GW, its turbulence morphology, and implications for layering are discussed in section 4. Section 5 compares and contrasts the influences of turbulence arising due to these two very different sources. Our conclusions are presented in section 6.