1. Introduction
Mountain waves (MWs) have been the subject of numerous observational, modeling, and theoretical studies over the previous 100 years (Smith 2018). Examples of important physical effects include downslope winds, turbulence at flight altitudes, and transport and deposition of energy and momentum that have major roles in weather, climate, and atmospheric composition and structure. An extensive literature has addressed their dynamics and implications extending into the middle stratosphere and spawned many reviews and books. Only recently, however, were MWs first observed in the mesosphere over the central Andes (Smith et al. 2009), though modeling studies anticipated this potential (Schoeberl 1985; Bacmeister 1993; Sato et al. 2009) and motivated earlier measurement programs (Goldberg et al. 2006).
MWs have been understood to play major roles in atmospheric circulation, structure, and variability at lower altitudes for many years. As such, many efforts have addressed their parameterization at lower altitudes (see Palmer et al. 1986; Lott 1999) and as a component of more general gravity wave (GW) parameterizations throughout the atmosphere (Kim et al. 2003). Importantly, global measurements cannot resolve GW λh smaller than ~200–400 km (Geller et al. 2013), hence cannot include potentially significant contributions by GWs having λh ~ 30–200 km. In situ measurements, in contrast, emphasize the importance of intermittent MW contributions at typically much smaller λh (Hertzog et al. 2008). Observational studies performed to date, by MWs having λh ~ 30–100 km (Bossert et al. 2018; Fritts et al. 2018) and those specifically focused on MW momentum fluxes in the mesosphere and lower thermosphere (MLT), likewise suggest that the major momentum fluxes are contributed.
Since their discovery at high altitudes, increasing attention has focused on the conditions leading to MW responses in the MLT and their associated dynamics. The majority of recent studies resulted from the Deep Propagating Gravity Wave Experiment (DEEPWAVE) involving airborne measurements over and around the New Zealand South Island (SI) in June and July 2014. These were supported by extensive ground-based and radiosonde measurements on SI and Tasmania spanning a broader interval [see the DEEPWAVE overview by Fritts et al. (2016)]. DEEPWAVE was preformed in the Southern Hemisphere in order to avoid the potential for a sudden stratospheric warming, one of which induced a MW critical level that prevented propagation into the MLT during the January 2003 Mountain and Convective Waves Ascending Vertically (MaCWAVE) program in northern Sweden (Goldberg et al. 2006; Wang et al. 2006). The initial target was intended to be the southern Andes because of their dominant contributions to GW variances in the middle stratosphere (see Hendricks et al. 2014), but DEEPWAVE was moved to New Zealand due to an inability to identify a suitable wintertime aircraft base near the tip of South America.
The comprehensive DEEPWAVE dataset has enabled studies of multiple aspects of MW dynamics from their sources into the MLT to date. Observations in the upper troposphere and lower stratosphere employing flight-level in situ measurements revealed the character and diversity of MW responses spanning many research flights. These data were employed by Smith et al. (2016) and Fritts et al. (2018) to assess MW wavelengths, amplitudes, vertically propagating versus trapped lee wave character, and energy and momentum fluxes for variable forcing conditions. Kruse et al. (2016) and Bramberger et al. (2017) addressed the conditions enabling MW propagation into the stratosphere. Propagation conditions enabling MWs to penetrate to high altitudes were examined by Kaifler et al. (2015), Bramberger et al. (2017), and Fritts et al. (2018). Studies by Fritts et al. (2018) and Portele et al. (2018) identified the causes for sometimes significant delays between variable MW forcing and responses in the stratosphere and MLT. One such case in which MWs arose due to flow over the low terrain of the Auckland Islands was found to generate a lee “ship wave” response exhibiting MW breaking extending above 80 km (Eckermann et al. 2016; Pautet et al. 2016; Broutman et al. 2017). Secondary GWs (SGWs) in the stratosphere and MLT were observed at smaller scales and accompanied MW breaking at lower altitudes (Bossert et al. 2015, 2017). Large-amplitude MW breaking and large momentum fluxes in the mesosphere were seen to accompany weak forcing, but conducive propagation conditions at lower altitudes (Heale et al. 2017; Bossert et al. 2018; Fritts et al. 2018; Taylor et al. 2019). In addition, the radar studies of de Wit et al. (2017) suggest that the large eastward GW momentum flux observed above the stratospheric jet is likely due to secondary waves resulting from MW breaking over the southern Andes. DEEPWAVE airborne observations also provided evidence of trailing waves refracting into the polar vortex in the stratosphere (Jiang et al. 2019). Finally, ground-based measurements at the Andes Lidar Observatory at 30°S and during DEEPWAVE enabled identification of the instability dynamics accounting for MW breaking in the MLT in two events (Hecht et al. 2018; Fritts et al. 2019a).
Modeling and data analyses described in several of the DEEPWAVE studies cited above have revealed the complexity of MW responses to variable wind and temperature fields at all altitudes. None of the modeling efforts extended to the highest altitudes observed, however, nor did they resolve the instability dynamics accounting for MW breaking, dissipation, and SGW generation. As such, they were unable to describe the true variability of the responses, which likely include the intermittency and scales of SGWs, influences of instability dynamics on the variability of MW amplitudes in space and time, and details of their interactions with mean and tidal fields throughout the atmosphere. DEEPWAVE studies to date also provided no information on the potential impacts at higher altitudes in the thermosphere, though observations over New Zealand in March 2009 revealed SGWs penetrating to ~250 km (Smith et al. 2013).
To address these dynamics comprehensively, we have performed a numerical simulation of MW generation and responses extending to 200 km in a large computational domain, but having very high spatial resolution in the central portion where MW breaking and SGW generation are anticipated. Because the largest responses in the stratosphere accompany MW forcing over the southern Andes and the strongest polar vortex winds enabling deep MW penetration occur at higher southern latitudes, we chose to perform this initial simulation over the southern Andes rather than over New Zealand. We anticipate future simulations targeting New Zealand to allow comparisons with specific DEEPWAVE events.
Our goals in this paper are to describe the MW and related dynamics accompanying strong flow over the southern Andes extending into the MLT under winter conditions allowing deep MW propagation. Section 2 describes the model and the simulation configuration employed. The evolution of the MW field over ~4 h following a gradual ramp in cross-mountain flow is presented in section 3. Key elements of the response include 1) strong MW breaking extending from the stratosphere to the lower thermosphere, 2) excitation and evolution of SGWs and acoustic waves (AWs) penetrating to high altitudes, and 3) filtering and modulation of the MW and SGW field by tidal winds. Section 4 provides a discussion of these results relative to previous studies. Our summary and conclusions are presented in section 5. Companion papers by Fritts et al. (2019b, manuscript submitted to J. Atmos. Sci., hereafter F19b; D. C. Fritts et al. 2020, unpublished manuscript, hereafter F20) describe the momentum fluxes, mean-flow accelerations, and GW–tidal interactions and the MW instability dynamics and sources of SGWs and AWs, respectively.
2. Model description and setup
a. Governing equations
b. Finite-volume solution method
The governing equations are discretized using the finite-volume framework, in which each computational cell is considered to be a small control volume. Our method, known as the Complex Geometry Compressible Atmospheric Model (CGCAM) is designed for fully curvilinear meshes, which is necessary for our detailed terrain-following description of the Andes mountain ranges.
In CGCAM the solution variables are stored at the cell centroids and fluxes on the faces are constructed using a kinetic energy–conserving interpolation scheme similar to that discussed in Felten and Lund (2006) for the incompressible Navier–Stokes equations. Several similar compressible finite-volume algorithms can be found in the literature, e.g., Hou and Mahesh (2005), Shoeybi et al.(2010), Reiss and Sesterhenn (2014), and Coppola et al. (2019) and a more complete description of our scheme can be found in Dong et al. (2019).
The resulting scheme is globally conservative for mass, momentum, total energy, and kinetic energy. Time advancement is achieved via a low-storage, third-order accurate Runge–Kutta scheme with a fixed time step of Δt = 0.3 s.
c. Simulation domain and grid layout
The computational domain extends 2500 (2000) km in longitude (latitude) and 200 km in altitude. It is centered at 48.2°S, 73.5°W between the two major massifs of the southern Andes, each of which has maximum terrain height ~4 km. The high-resolution, central portion of the domain extends 250 (750) km in longitude (latitude), is centered 75 km east of the major massifs, and has horizontal resolution of 500 m and vertical resolution of 500 m below 144 km. Outside of the high-resolution region the horizontal grid spacing is increased gradually via a fixed 2% stretching rate in order to achieve ~22 km spacing at the zonal boundary and ~12 km at the meridional boundary. Although the mesh is considerably coarser near the horizontal boundaries, it is still sufficient to resolve the predominantly large-scale waves found in this region (see section 3). The vertical mesh is likewise stretched above 144 km to a resolution of 1.4 km at 200 km altitude. A total of 900 × 1840 × 352 mesh points are used in the zonal, meridional, and vertical directions, respectively.
A series of two-dimensional simulations at resolutions of 2000, 1000, 500, and 250 m for a cross-section passing over the South Peak was used to form a mesh-convergence study. As expected, the difference between successive solutions decreased with resolution and the changes between 500 and 250 m were sufficiently small that the 500 m spacing was deemed adequate for resolving the MW dynamics.
The southern Andes terrain is obtained from the NOAA Global Land One-km Base Elevation Project (GLOBE) dataset (Hastings et al. 1999). The terrain at the north end of the domain is artificially damped to sea level via a hyperbolic tangent function with characteristic width of 100 km, centered 300 km from the boundary. This modification eliminates surface forcing near the north boundary, making it possible to use a relatively simple boundary condition there (see discussion below). The terrain and the computational mesh in the horizontal are shown in Fig. 1a. While the mesh uses a Cartesian layout in the horizontal directions, it is distorted in the vertical direction in order to match the terrain at the lower boundary. The vertical mesh distortions are then gradually faded out with increasing grid level, becoming nonexistent at the 30th level (15 km altitude). The mesh is then purely Cartesian from this position to the top of the domain.
(a) Southern Andes topography and CGCAM domain and mesh and (b) terrain elevations and (c) spectra over the north and south peaks. The 500-m mesh extends from −50 to 200 km in x and from ±400 km in y. The solid lines in (a) show the locations of the cross sections shown in the figures below, while the dashed rectangle shows the central region without sponge-layer damping.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
(a) Southern Andes topography and CGCAM domain and mesh and (b) terrain elevations and (c) spectra over the north and south peaks. The 500-m mesh extends from −50 to 200 km in x and from ±400 km in y. The solid lines in (a) show the locations of the cross sections shown in the figures below, while the dashed rectangle shows the central region without sponge-layer damping.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
(a) Southern Andes topography and CGCAM domain and mesh and (b) terrain elevations and (c) spectra over the north and south peaks. The 500-m mesh extends from −50 to 200 km in x and from ±400 km in y. The solid lines in (a) show the locations of the cross sections shown in the figures below, while the dashed rectangle shows the central region without sponge-layer damping.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
Terrain elevations and zonal wavelength spectra over the northern and southern massifs 120 km north (N) and 120 km south (S) of the domain center averaged over 30 km in latitude are shown in Figs. 1b and 1c. The spectra reveal power at zonal wavelengths λx ~ 25–200 km, with multiple peaks near 40, 80, and 160 km for the N Peak and a single broad peak near 70 km for the S Peak. As shown in section 3, the major GW responses at later times occur close to these values, mainly within the range λx ~ 30–200 km.
d. Boundary conditions
Conventional boundary conditions must also be used with the sponges and we use periodic conditions in the horizontal directions and a characteristic outflow condition at the upper boundary for this purpose. While periodic boundary conditions in the horizontal directions would seem to be a poor choice, the sponges effectively transform these into inflow/outflow/radiation conditions. To see that this is so, consider an advecting flow disturbance or a right-running GW approaching the downstream boundary. This disturbance will be attenuated to near extinction as it attempts to cross the sponge layer, leaving little or no disturbance at the downstream boundary. Due to the periodic boundary condition any small residual arriving at the boundary will of course reenter the domain on the left, but will then encounter the sponge layer on that side, diminishing its amplitude even further as it attempts to propagate across it. The net result is that outgoing waves simply appear to leave the domain permanently once they enter the sponge region. Similarly flow structures advecting toward an outflow boundary appear to leave the domain permanently while disturbance-free flow at the specified background conditions is supplied at the downstream end of the sponge region at an inflow boundary. We have found the sponge approach to be far superior at eliminating wave reflections as compared with even sophisticated radiation conditions that act strictly at the boundary.
The only downside of the sponge layers is that they increase the cost of the simulation. Since the sponge terms are nonphysical, the solution cannot be used anywhere within the sponge regions. This reality means that the effective position of the boundaries must be moved inward by the thickness of the sponge, thereby reducing the valid flow region. In our case, this requirement leads to an effective domain that extends from −1050 to 1050 km in the zonal direction, from −900 to 900 km in the meridional direction, and from 0 to 185 km in z. We respect these restricted domain limits for all analysis of our results and never display data taken from within a sponge region.
e. Initial conditions and forcing
Background fields for the Andes MW simulation were obtained from a Whole Atmosphere Community Climate Model (WACCM) simulation for July conditions. This WACCM version is based on a spectral element (SE) dynamical core solved on a cubed sphere, with a global quasi-uniform horizontal resolution of ~25 km. The vertical domain extends from the ground to ~145 km, with vertical resolution of 0.1 scale height above the middle stratosphere and higher below. The model can resolve GWs having λx ~ 200 km and larger. A detailed description of WACCM and the simulation employed here can be found in Liu et al. (2014) and Liu (2016). The wind and temperature fields at 50°S, 65°W at the time selected had a strong eastward jet at ~50 km and significant tidal influences at higher altitudes. Above 120 km, the winds were specified to approximate tidal winds asymptotically approaching U0 = 0 and V0 = 70 m s−1 above 200 km to allow exploration of SGWs and AWs arising from MW dynamics at lower altitudes without constraints by large zonal wind shears at higher altitudes. Initial profiles of U0, V0, temperature T0(z), and the corresponding
Initial profiles of T0, U0 and V0, time,
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
Initial profiles of T0, U0 and V0, time,
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
Initial profiles of T0, U0 and V0, time,
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
These fields were assumed to be uniform over the domain, as the major responses of interest are confined to about ±5° in longitude and latitude around the domain center. They were also assumed to be constant in time, apart from departures driven by MW forcing. This is because MW propagation from ~10 to 80 km occurs on short time scales because strong zonal winds cause the dominant MW λx ~ 30–80 km to have λz ~ 15–60 km or larger, and hence to be nonhydrostatic and have large vertical group velocities cgz. As a result, the dynamics of interest occur on time scales significantly shorter than tidal periods.
Because the imposed mean and tidal wind and stability profiles are highly structured in altitude, the initial mean Richardson number,
f. Subgrid-scale turbulence model
While our 500 m grid spacing is sufficient to resolve both the dominant GW instability structures and the large-scale inertial range turbulent structures it is insufficient to resolve the smaller-scale, mainly dissipative turbulent motions. We account for this reality by incorporating the dynamic Smagorinsky subgrid-scale model (Germano et al. 1991; Moin et al. 1991) in order to mimic the energy drain due to the unresolved turbulent motions. The equations for the eddy viscosity, eddy conductivity, and turbulent kinetic energy coefficients are averaged over limited horizontal planes (x = [−200: 400], y = [−600, 600] km) that contain just the turbulent flow. This is standard treatment and results in well conditioned equations for the model coefficients. The dynamic subgrid-scale model is self-calibrating and thus will only result in enhanced dissipation in actively turbulent regions. Thus the model does not interfere with molecular dissipation that occurs in the largely nonturbulent region above 140 km.
3. Mountain wave evolutions and dynamics
a. Mountain wave and secondary wave evolution in the (x, z) plane at y = −120 km
We begin with an overview of the major features of the MW and secondary wave evolution from t = 7.5 to 12 h, where the lower altitude winds increase from 82% to 100% of their maximum values (see Fig. 2c). Figures 3–6 show streamwise-vertical cross sections of u(x, z), w(x, z), T′/T0(x, z), and spanwise vorticity ζy(x, z), respectively, over the southern peak (y = −120 km, hereafter S Peak) at 7.5, 8, 8.5, 9, 10, and 12 h. Movies of the evolutions of these fields, others over N Peak at y = 120 km, and in (x, y) planes over both peaks are included for reference in the accompanying support materials.
Cross sections of u (x, z) over the south peak from z = 0–180 km and 7.5–12 h (note the expanding streamwise domain at the earlier times).
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
Cross sections of u (x, z) over the south peak from z = 0–180 km and 7.5–12 h (note the expanding streamwise domain at the earlier times).
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
Cross sections of u (x, z) over the south peak from z = 0–180 km and 7.5–12 h (note the expanding streamwise domain at the earlier times).
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
As in Fig. 3, but for w.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
As in Fig. 3, but for w.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
As in Fig. 3, but for w.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
As in Fig. 3, but for T′/T0.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
As in Fig. 3, but for T′/T0.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
As in Fig. 3, but for T′/T0.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
As in Fig. 3, but for ζy. (bottom) The dashed box shows the region depicted in Fig. 7.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
As in Fig. 3, but for ζy. (bottom) The dashed box shows the region depicted in Fig. 7.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
As in Fig. 3, but for ζy. (bottom) The dashed box shows the region depicted in Fig. 7.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
The earliest responses at 7.5 h extend from lower altitudes into the MLT. Wave reflection, identified by opposite phase slope, is visible below ~40 km and downstream of x = 60 km (see the u, T′/T0, and ζy fields). Evidence of the anticipated nonhydrostatic behavior in the strong U0 from ~30 to 80 km for λx ~ 30 km is seen most clearly in w. At higher altitudes, very weak MWs are seen in the temperature and vorticity fields at altitudes close to the MW critical level at ~115 km. This fact indicates that the near critical level (U0 ~ 10 m s−1) at ~85 km does not act as a barrier for all wave scales. It does, however, locally compress the vertical wave scale and locally increase the wave amplitude to the extent that it becomes the site for the primary instability.
Increasing cross-mountain flow and especially the rapid nonhydrostatic MW vertical propagation result in much stronger MW and secondary wave responses at 8 h. Strong MW responses and associated instabilities accompanying breaking now extend from the Andes to ~150 km eastward. The dominant MW scale has increased to λx ~ 50–60 km, and there are now two strong breaking regions. Initial instabilities arise in the upward and westward phases of the MW, initiate vortex dynamics comprising a succession of vortices having large, negative ζy along the MW phase below having negative ζy, opposite maxima above and westward, that decouple from the unstable MW phase and are swept downstream (to the east) thereafter while undergoing vortex dynamics driving a rapid cascade to smaller turbulence scales. They now extend from below 60 to above 90 km, and their scales decrease with increasing altitude due to decreasing MW λz in decreasing |c − U0| approaching the U0 minimum at ~85 km.
Additionally, there is now evidence for initial SGW and AW excitation in the MW breaking regions. SGWs having amplitudes of T′/T0 ~ 0.1–0.3 are seen extending more than 100 km upstream of the Andes and to altitudes well above 120 km (see the T′/T0 and ζy fields). Initial, roughly spherical AWs are also seen above the stronger instabilities from x ~ 40–150 km. These are most conspicuous in w, but are also seen in u and T′/T0. They exhibit rapid transitions from warm, rising phases to cooler, descending phases with increasing altitude and have w as large as ~50–100 m s−1 at this stage of the evolution. The positive correlation of w and T′/T0 for the AWs is distinct from the quadrature relations anticipated, and seen, for MWs and SGWs.
The MW field and its associated instabilities, SGWs, and AWs continue to intensify to 8.5 and 9 h as cross-mountain winds achieve 95% of their final magnitudes. Stronger forcing is seen to yield a further increase in the dominant MW scale to λx ~ 70 km, an upstream extension over the Andes at ~80–115 km including initial instabilities at z ~ 80 and 100 km, and instabilities and turbulence extending further downstream with increasing time at altitudes ~50–80 km.
SGWs increase in amplitude and propagate to the highest altitudes and far upstream and downstream in some cases at these times. Those propagating westward have λx ~ 70–150 km and phase speeds of ~80–200 m s−1. The slower of these approach critical levels where |c − U| and λz decrease with increasing altitude below ~130 km and undergo instabilities and dissipation where |u′| ~ |c − U|=Nλz/(2π). Those having larger negative c outrun the westward tidal wind peak at ~130 km and refract to larger λz where |c − U| increases at higher altitudes. SGWs are also seen propagating eastward, but these have very different character because of the large-scale U and T fields. The primary eastward-propagating SGW at these times has λx ~ 65 km and c ~ 220 m s−1, and exhibits ducting at ~90–110 km, an increasing amplitude in time, evolving instabilities accompanying the eastward u′ maxima and ζy minima, and additional laminar maxima that are in quadrature due to evanescence above ~120 km [see the movies of this evolution in the (x, z) plane in the accompanying materials]. The features enabling these eastward-propagating ducted SGWs are the m2 maxima seen for the gray line (for λx = 65 km and c = 220 m s−1) in Fig. 2f at ~105 and 110 km. This m2 maximum, and the negative m2 above and below, comprise a duct that occurs due to −Uzz/U > 0 at ~100 km and large N2/U2 at ~108 km; see the first two terms on the right-hand side of Eq. (11).
AWs likewise become much stronger by 9 h and arise at ~2–3 min intervals in the strong MW breaking regions at lower altitudes. These have phase speeds cAW ~ 500 m s−1 at higher altitudes, velocities normal to their phase surfaces, and continue to exhibit roughly spherical phase fronts suggesting very localized sources. Their phase fronts are not strictly spherical because T(z) and cAW ~ T1/2 increase strongly between their source altitudes and ~150 km. AW amplitude increases with increasing altitude drive their evolution to shock waves having very sharp transitions from warm rising phases to cold descending phases in many cases. As when first seen, they appear to be strongly correlated with the regions of most intense instability dynamics accompanying MW breaking from ~50 to 80 km (see F20).
The subsequent evolution of the MW field is shown at 10 and 12 h in the bottom two panels of Figs. 3–6. These reveal significant reductions in the strength of MW instability dynamics from ~45 to 115 km, of SGW and AW amplitudes above ~85 km, and of SGW instabilities in the lee of the Andes that were prominent at 9 h. This is despite the cross-mountain flow reaching its peak amplitude during this interval. Also seen at 10 and 12 h is a continuation of the increase in the dominant MW scale λx over and upstream of the Andes. Stationary MWs have λx ~ 150–200 km at z ~ 75 km over and ~200 km upstream of the Andes at 10 h, and this shifts to somewhat larger λx, higher altitudes, and further upstream by 12 h, revealing increasing relative roles for the larger MW λx seen in the terrain k spectral power in Fig. 1c at later times.
We now explore the apparent causes for decreasing smaller-λx MWs and their associated SGW, AW, and instability responses over S Peak after 9 h. Shown at left in Fig. 7 are cross sections of ζy in a subdomain at x = 0–100 km and z = 0–30 km from 7.5 to 12 h (see dashed box at 9 h in Fig. 6). MW forcing has achieved ~70% of its peak amplitude by 7 h, and the MW amplitude in the lower stratosphere has achieved ~70% of its peak amplitude by ~7.5 h, based on the scales seen in Fig. 2 and inferred cgz. Dominant MW responses are seen at λx ~ 50–80 km over and in the lee of S Peak. However, there are also transient responses apparently arising from temporally variable flow over the mountain peak. These appear to contribute to modulation of the MWs and to other GWs propagating upward to the E up to ~9 h.
As in Fig. 3, but for ζy in subdomains covering x = 0–100 km and z = 0–30 km at 30-min intervals from 9 to 12 h over the (left) south peak and (right) north peak.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
As in Fig. 3, but for ζy in subdomains covering x = 0–100 km and z = 0–30 km at 30-min intervals from 9 to 12 h over the (left) south peak and (right) north peak.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
As in Fig. 3, but for ζy in subdomains covering x = 0–100 km and z = 0–30 km at 30-min intervals from 9 to 12 h over the (left) south peak and (right) north peak.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
The MWs at x ~ 0–60 km exhibit instabilities beginning prior to 8 h and extending throughout this interval. Specifically, strong, small-scale vorticity dynamics begin prior to 8 h, modulate the MW amplitude at ~20 km initially, then more aggressively and extending to lower altitudes at ~10 h and thereafter. Characteristic scales of these instability dynamics are ~3–4 km, consistent with expectations for λz ~ 10–15 km and strong breaking (Fritts et al. 2009), and they necessarily reduce MW amplitudes at higher altitudes thereafter. These dynamics have the same character and scales seen over S Peak from ~80 and 100 km at 8.5 and 9 h in Fig. 6, where U and the MW λz are comparable to those in the lower stratosphere. They are also similar to the instabilities from ~50 to 70 km from 8 to 9 h, where the MW instability scales are larger due to larger λz > 2πU/N, and which strongly reduce MW amplitudes due to breaking. MW instability dynamics, momentum fluxes, tidal interactions, and their influences are examined in greater detail by F19b and F20.
b. Comparison of MW and secondary wave evolutions over and around S Peak and N Peak
The N and S Peak have roughly linear N–S Peak terrain extending ~60 and 150 km, respectively, but very different east–west terrain. To compare the responses to the different terrain, and explore the broader responses to the southern Andes massifs, we show u(x, z) cross sections over N Peak from 7.5 to 9 h in the upper panels of Fig. 8 for comparison with those over S Peak at these times in Fig. 3, with the (x, z) cross sections at y = ±120 km; Fig. 7 shows ζy(x, z) cross sections over N Peak from 7.5 to 12 h at right for comparison with those over S Peak at left; Fig. 9 provides more extended (y, z) cross sections of u′, υ′, w′, and T′/T0 at x = 50 km and 9 h; finally, Figs. 10–12 show (x, y) cross sections of u, w′ and T′/T0, respectively, at 8, 9, and 10 h (left to right) at altitudes of 70, 100, 120, and 180 km (top to bottom).
Contours of u and u′ over the north peak at the times indicated. The top three rows are streamwise–vertical views of u, whereas the bottom three are spanwise–vertical views of u′ at x = 50 km. The black triangles near the ground in the latter are approximations to the mountain peaks, projected onto the downstream view.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
Contours of u and u′ over the north peak at the times indicated. The top three rows are streamwise–vertical views of u, whereas the bottom three are spanwise–vertical views of u′ at x = 50 km. The black triangles near the ground in the latter are approximations to the mountain peaks, projected onto the downstream view.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
Contours of u and u′ over the north peak at the times indicated. The top three rows are streamwise–vertical views of u, whereas the bottom three are spanwise–vertical views of u′ at x = 50 km. The black triangles near the ground in the latter are approximations to the mountain peaks, projected onto the downstream view.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
(y, z) cross sections of u′, υ′, w′, and T′/T0 at x = 50 km and 9 h.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
(y, z) cross sections of u′, υ′, w′, and T′/T0 at x = 50 km and 9 h.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
(y, z) cross sections of u′, υ′, w′, and T′/T0 at x = 50 km and 9 h.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
(top to bottom) Cross sections of u′(x, y) at 70, 100, 120, and 180 km and (left to right) times of 8, 9, and 10. The positions of the north and south peaks are shown with plus signs.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
(top to bottom) Cross sections of u′(x, y) at 70, 100, 120, and 180 km and (left to right) times of 8, 9, and 10. The positions of the north and south peaks are shown with plus signs.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
(top to bottom) Cross sections of u′(x, y) at 70, 100, 120, and 180 km and (left to right) times of 8, 9, and 10. The positions of the north and south peaks are shown with plus signs.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
As in Fig. 10, but for w′.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
As in Fig. 10, but for w′.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
As in Fig. 10, but for w′.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
As in Fig. 10, but for T′/T0.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
As in Fig. 10, but for T′/T0.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
As in Fig. 10, but for T′/T0.
Citation: Journal of the Atmospheric Sciences 77, 12; 10.1175/JAS-D-19-0356.1
As seen in u(x, z) over S Peak (Fig. 3), N Peak (Fig. 8, top panels) yields emerging MW breaking downstream and generation of SGWs and AWs having similar scales and character that readily propagate to higher altitudes. Compared to S Peak, however, N Peak exhibits weaker lee MW overturning, less significant trailing turbulence from ~40 to 100 km, much less upstream MW penetration above ~70 km, and weaker SGW and AW responses everywhere. The cross sections at y = ±120 km do not provide a complete picture, however, because the responses include expanding strong MW breaking, turbulence, and their consequences much further N and S along the southern Andes at later times. The u′(y, z) cross sections at the bottom in Fig. 8 show the breaking regions in the lee of each massif to dip below z = 50 km at x = 50 km, and to extend significantly N and S at z ~ 60–80 and ~100 km at 9 and 10 h, with the strongest instability dynamics where u′ is most negative. Alternating bands of u′ > 0 and <0 at adjacent altitudes reveal the local MW λz, its variations in altitude with varying U(z), and the modulation of the MW phase along y. The downward extensions indicate where MW breaking is nearer the spine of the Andes because of the upward and westward MW phase slopes, suggesting that MWs having smaller λx contribute preferentially to stronger breaking (also see Figs. 10–12 below).
A broader perspective of the responses to strong MW forcing over the southern Andes is provided in the perturbation fields in Fig. 9 showing (y, z) cross sections extending 1800 km in y and in Figs. 10–12 showing horizontal cross sections spanning 1200–1800 km in x and y at z = 70, 100, 120, and 180 km. Considering first the u′, w′, and T′/T0 fields in Fig. 9 and at 70 km in Figs. 10–12, we see that strong MW responses and breaking occur over the highest terrain at |y| < 300 km (Figs. 9–12 at top), but that strong flow over lower terrain yields significant MWs extending to |y| > 500 km at 9 h. Strong MW breaking also expands E–W and to higher altitudes at 9 and 10 h (approaching the MW critical level at z ~ 114 km, as seen above). These fields, especially the υ′ and T′/T0(y, z) cross sections and the (x, y) cross sections, reveal SGWs and AWs extending to ~120–180 km and laterally to the edges of the computational domain.
The plots of u′(y, z) in Fig. 10 at 8 h exhibits large MW amplitudes and strong zonal decelerations at 70 km that are localized in y in the lee of N Peak and S Peak, but extend multiple MW λx (~200 km) downstream. Similar responses are seen at 100 km, but with MW propagation toward N of W due to influences of V < 0 below, which favors propagation in the direction of largest ci = (c − Uh). Specifically, these reveal |u′| exceeding |c − U| in the evolving local mean wind, U(x, y, z, t), where c may acquire westward values (e.g., westward self acceleration) due to local dU/dt < 0 accompanying MW momentum deposition. This is confirmed by |T′/T0| exceeding an overturning threshold for the relevant λz. These dynamics advance the MW phases westward at the locations of strongest dU/dt < 0, as seen in Fig. 10 at 70 and 100 km at 8 h.
Varying dU(x, y, z)/dt due to MW momentum deposition contributes advection of the MW phases (e.g., self acceleration) that varies with MW amplitude along the MW phase, compresses the MW λx upstream of the strongest dU/dt, and accounts for the phase variations seen in the lower panels of Fig. 8 and the smaller (larger) λx at the upstream (downstream) edges of the regions of strongest breaking. These dynamics account for the “ship wave” patterns centered over each peak and having MW phases to the N and S of each further downstream at 8 h, implying outward (partial N–S) MW propagation from localized sources at lower altitudes. Strong zonal decelerations apparent over N Peak and S Peak at 8 h and 70 km are seen to have compensating (eastward) U(x, y) accelerations between, and N and S of, N Peak and S Peak, to satisfy continuity in the larger-scale flow. The local decelerations seen at 8 h and 70 km are seen to merge in latitude at later times as the large-scale mean flow, (U, V, W)(x, y, z, t), adjusts to the localized and variable 3D MW momentum deposition in space and time. This causes an evolution to a larger ship-wave response over both peaks, weaker at 70 km and much stronger at 100 km, seen in Figs. 10–12 at 9 and 10 h.
The (x, y) cross sections also reveal more clearly the emerging SGW scales, typically λx ~ 200 km and larger, and roughly circular, outward phase propagation beginning at z ~ 100 km and extending with increasing scales and amplitudes to higher altitudes. Additionally, (x, y) cross sections from 100 to 180 km, especially w′ and T′/T0 at smaller radii, reveal nearly circular features beginning to emerge at 8 h that intensify with altitude and time to 9 h, but have large amplitudes and gradients only within ~200 km of the regions of strong MW breaking at lower altitudes. These are the AWs seen in the vertical cross sections above, and are clearly stronger over the more intense MW breaking over S Peak. See especially Figs. 11 and 12 at 8 and 9 h.
SGW and AW responses at 10 h in Figs. 3–5 and 10–12 exhibit significantly reduced amplitudes compared to those at 9 h over N Peak and S Peak, despite continuing increases in MW forcing at the lowest altitudes. MW, and associated SGW and AW, amplitude reductions over S Peak after 9 h are attributed above to emerging MW breaking below 30 km over S Peak, and associated decreasing small-λx amplitudes extending to higher altitudes as a result of the approach to the strongest cross-mountain flow at low altitudes. We see, for example, that MWs having small λx and large ωi, hence large cgz, exhibit somewhat weaker amplitudes and instabilities at 70 and 100 km at 10 h. This is because influences of decreasing forcing for these MWs due to instabilities at ~30 km and below are quickly communicated to higher altitudes. The most rapid reductions of SGW amplitudes above ~100 km accompany smaller λh, hence larger ωi and cgz, enabling them to propagate most quickly to higher altitudes. By comparison, SGWs excited by larger-scale MWs and having larger λh, hence smaller ωi and cgz, are seen to persist to 10 h at 120 and 180 km at greater distances from their sources (see especially Figs. 10 and 12), and even exhibit increasing amplitudes again by 12 h (see Figs. 3–5).
In contrast, MWs having λh ~ 200–300 km propagate vertically much more slowly, requiring multiple hours to penetrate the weak zonal winds in the troposphere, lower stratosphere, and near 85 km. Hence the λx ~ 150–300 km MWs excited prior to 9 h continue to propagate upward, grow in amplitude with altitude, exhibit increasing responses to ~10 h and beyond, and excite SGWs arising from these dynamics in the stratosphere and MLT that persist to 10–12 h. As examples, see the larger MW amplitudes and accompanying instabilities at ~50–115 km in Figs. 3–6 at 10 and 12 h and the larger-scale MW instabilities at 100 km at 10 h in Figs. 10 and 12.
As noted in the discussion of the ζy fields over S Peak, unsteady flow occurs over N Peak prior to ~7.5 h, but subsides by 10 h (see Fig. 7 at right). MW instabilities also occur over N Peak and impact MW amplitudes prior to 9 h, again after 10 h, and perhaps between at nearby latitudes. These dynamics appear to have somewhat lesser roles over N Peak compared to S Peak, as suggested by the SGW and AW responses at higher altitudes discussed above. However, they do not prevent similar MW and instability features over both peaks and extending over significant distances N and S spanning multiple hours.
c. Impacts of MW dynamics and momentum transport and deposition on large-scale winds
Induced mean wind changes accompanying strong MW breaking were noted in the discussion of the u′(x, y) fields at 70 km in Fig. 10. Evidence of such changes are also seen in Fig. 3 beginning at 8.5 h and increasing to later times. These were not discussed above because stationary MWs having large λx can yield varying u(x, z) that could be confused with mean wind variations due to local momentum deposition. With the knowledge that U(z = 70 km) varies in x and y, we can return to Fig. 3 to explore variations in z as well. The u′(x, y) field in Fig. 10 at 70 km and 8 h reveals strong, eastward U deficits localized over N and S Peaks. Responses at 70 km have weakened, merged along y, and extended >500 km downstream by 9 h. By 10 h, they have further expanded downstream, significantly northward, somewhat southward, and another ~100 km westward. Compensating U enhancements in all of these fields occur between and/or at the edges of the U deficits at these times.
Similar responses are also seen at 100 km in Fig. 10, but with interesting differences. As this altitude is above the primary wave breaking zone, we are observing a combination of primary and secondary waves, with the later becoming dominant as time progresses. Larger-λh MWs play a larger role at 100 km. At 8 h, they extend ~200 km farther upstream and have distinct ship-wave responses over N and S Peaks oriented somewhat N of W. This pattern evolves to a larger ship-wave response to an apparent single, larger obstacle at lower altitudes from 8 to 10 h, imposes a U deficit spanning a significantly larger area than at 70 km, and is likewise oriented slightly N of W. The response also now exhibits a U deceleration (acceleration) at the N (S) center that exhibits a bias in y that is opposite to that seen at 70 km at 9 and 10 h.
The rotation of the response at 100 km can be traced to the contribution of the meridional wind to favorable MW penetration to higher altitudes, but having a WNW orientation, as noted above. Referring to Fig. 2b, we see that MWs oriented somewhat N of W have a larger headwind below 100 km than those oriented S of W. This favors attainment of larger MW amplitudes inclined N of W seen at 8 h, and implies larger |c − Uh| and stronger decelerations at and below 100 km to the N of the response center at 9 and 10 h by these MWs. Those oriented S of W to the S of the response center encounter decreasing headwinds, smaller |c − Uh|, experience stronger amplitude constraints, and impose weaker forcing, consistent with the observed U deficits or enhancements at 9 and 10 h.
Referring to Figs. 3 and 8, we see that there are significant U deficits in the lee of N and S Peaks beginning at 70 km and expanding up to ~80 and down to ~50 km from 8 to 10 h that span several MW cycles and are thus not due to a larger-scale MW. In the same manner, the u′(x, y) fields at 100 km in Fig. 10 reveal a lack of a significant U deficit in the lee of S Peak and a weaker deficit associated largely with a larger-λx MW imposing u′ < 0 extending farther upstream at later times, which are consistent with inferences from the (x, y) fields discussed above.
4. Discussion
We have presented the first large-scale compressible simulation of MW dynamics arising from increasing near-surface winds blowing over realistic high terrain. High resolution in the central domain enabled realistic descriptions of initial instability dynamics and realistic MW dissipation, momentum deposition, and secondary wave generation extending into the MLT. A slow ramp of the cross-mountain flow avoided nonphysical transients, revealed the initial occurrence of MW breaking and instability dynamics in the mesosphere under linear MW propagation conditions at lower altitudes, and demonstrated the weakening of MLT responses following MW breaking at lower altitudes. Responses in the MLT included 1) instability and wave breaking at the near critical level at z = 85 km (where Uh ~ 10 m s−1) 2) generation of SGWs able to propagate to higher altitudes and upstream, downstream, and laterally from the forcing terrain, 3) generation of AWs able to achieve shock wave character in the MLT and penetrate quickly to higher altitudes, and 4) large-scale ship-wave responses and local flow decelerations extending into the thermosphere.
Our results validate the initial studies by Schoeberl (1985) and Bacmeister (1993) suggesting MW influences extending into the MLT. They confirm the potential noted in previous studies for smaller- and larger-scale MWs to penetrate into the MLT and exhibit strong breaking and/or SGW generation over the Andes (Smith et al. 2009; de Wit et al. 2017; Becker and Vadas 2018; Hecht et al. 2018) and New Zealand (Smith et al. 2013; Bossert et al. 2015, 2017, 2018; Kaifler et al. 2015; Eckermann et al. 2016; Fritts et al. 2016, 2018; Pautet et al. 2016; Bramberger et al. 2017; Broutman et al. 2017). They also suggest the potential for such responses to accompany MW generation over other large- and small-scale terrain at middle and high latitudes and to extend well into the thermosphere under suitable propagation conditions. Other implications of this simulation addressing MW and SGW momentum deposition, mean forcing, tidal interactions, and instability dynamics in the lower atmosphere and MLT are discussed in the companion papers F19a and F19b.
5. Conclusions
Our results demonstrate the complex interworking of GW generation, propagation, refraction, and instability accompanying MW dynamics. Furthermore, we have shown that wave breaking and the attendant momentum deposition provides sources for both SGWs and AWs that propagate freely into the lower thermosphere. Since the secondary waves have nonzero ground-based frequency, they are unaffected by the MW critical level at 115 km. The secondary waves carry sufficient momentum and energy to measurably alter the mean state as they are ultimately dissipated at altitudes above our model top.
It should be noted that nearly all of these complicated physical processes cannot be described with linear theory. We have shown that even refraction of the primary waves is not well predicted by the theory, presumably due to a failure of the WKB approximation required to account for the highly variable background environments. This situation provides a challenge for GW parameterization schemes required in low- to medium-resolution numerical models. Simple saturation schemes would predict that all of the primary wave momentum is deposited at the critical level at 115 km and a more sophisticated ray tracing approach would predict that most of the wave energy is reflected at lower levels. Our numerical simulation database provides a unique tool for constructing improved parameterizations and we are currently working on producing such a product.
Acknowledgments
The research described here was performed under National Science Foundation and National Aeronautics and Space Administration, grants cited in the Grant Electronic Management System. We thank the Department of Defense High Performance Computing Modernization Program for access to computational resources that enabled this modeling study.
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