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			<titleStmt><title level='a'>Observations and Modeling of Gravity Wave-Kelvin Helmholtz Instability (GW-KHI) Interactions in the Mesosphere and Lower Thermosphere: KHI Localization and Modulation by the GW Field</title></titleStmt>
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				<publisher>ESS Open Archive</publisher>
				<date>01/08/2026</date>
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				<bibl> 
					<idno type="par_id">10663766</idno>
					<idno type="doi">10.22541/essoar.176789041.12396308/v1</idno>
					
					<author>Tyler S Mixa</author><author>David C Fritts</author><author>Thomas S Lund</author><author>Pierre-Dominique Pautet</author>
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			<abstract><ab><![CDATA[Not Available]]></ab></abstract>
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<div xmlns="http://www.tei-c.org/ns/1.0"><p>manuscript submitted to JGR: Atmospheres <ref type="bibr">Hendricks et al., 2014;</ref><ref type="bibr">Jiang et al., 2003;</ref><ref type="bibr">Wu &amp; Eckermann, 2008)</ref>. Some of these GWs are primary orographic waves that reach the MLT under favorable wind conditions <ref type="bibr">(Fritts et al., 2019;</ref><ref type="bibr">Kaifler et al., 2020)</ref> or by tunneling through the PNJ <ref type="bibr">(Mixa et al., 2021)</ref>.</p><p>Others are higher order waves generated by multistep coupling or body forces from local shear turbulence <ref type="bibr">(Vadas et al., 2003</ref><ref type="bibr">(Vadas et al., , 2018))</ref>. The duration of MLT wave activity from these sources depends on the source duration and vertical group velocities, lasting from minutes to hours. Such localized temporal and spatial GW scales are parameterized in general circulation models (GCMs) of the MLT, and their absence contributes to mixing deficits of up to 50% in WACCM-X relative to satellite observations <ref type="bibr">(Liu, 2021)</ref>. Consequently, studies of small scale transport dynamics are essential to improve mixing parameterizations by GCMs in the MLT.</p><p>GWs encounter sharp wind and temperature gradients throughout the atmosphere.</p><p>The compounded e!ects of local instabilities, GW propagation, and GW breaking in a continuously evolving atmosphere create near ubiquitous sheet and layer structures that influence and interact with propagating GWs (e.g., <ref type="bibr">Kantha et al., 2017;</ref><ref type="bibr">Doddi et al., 2021;</ref><ref type="bibr">Barat, 1982;</ref><ref type="bibr">Sato &amp; Woodman, 1982;</ref><ref type="bibr">Lehmacher et al., 2011;</ref><ref type="bibr">Mesquita et al., 2020)</ref>. Unstable layers with Richardson numbers Ri &lt; 0.25 promote the formation of Kelvin-Helmholtz instabilities (KHI) that rapidly deposit energy and reshape the background environment. KHI support a range of secondary and tertiary instabilities that vary with Ri and the local Reynolds number (Re), including secondary KHI, secondary convective instabilities (CI), crankshaft instabilities, and mode 1 and 2 twist waves. Many of these features form as a consequence of KHI tube and knot dynamics (T&amp;K) where KHI reconnect across non-uniform shear or reorient away from the primary shear direction within a layer <ref type="bibr">(Thorpe, 1987;</ref><ref type="bibr">Fritts, Wang, Lund, &amp; Thorpe, 2022;</ref><ref type="bibr">Fritts, Wang, Thorpe, &amp; Lund, 2022;</ref><ref type="bibr">Mixa et al., 2023, and others)</ref>. KHI T&amp;K have been shown to amplify mixing by locally accelerating or extending dissipation relative to simulated KHI breakdown in hypothetically idealized layers with uniform shear <ref type="bibr">(Mixa et al., 2023</ref><ref type="bibr">(Mixa et al., , 2025))</ref>. This suggests that KHI forming in a layer distorted by GW propagation could promote elevated local mixing from T&amp;K dynamics. KHI have been readily observed in atmospheric environments showing strong GW influence. KHI observations in thin tropospheric clouds date back to the 1950s (e.g., R. S. <ref type="bibr">Scorer, 1951;</ref><ref type="bibr">R. Scorer, 1969;</ref><ref type="bibr">R. Scorer &amp; Wexler, 2013)</ref>, and KHI forming perpendicular to GW phases can be regularly observed in lenticular clouds east of the Rocky Mountains (see sample author photos in Figure <ref type="figure">1</ref>). KHI in the MLT have also been observed in polar mesospheric clouds (PMCs) in the presence of large amplitude GWs <ref type="bibr">(Witt, 1962)</ref>. PMC images from <ref type="bibr">Fritts et al. (2014)</ref> and <ref type="bibr">Baumgarten and Fritts (2014)</ref> document widespread KHI events with regions of amplified and attenuated responses suggesting KHI are influenced by the background GW field; in addition to evidence of KHI forming in specific GW phase locations where the PMC layer is advected up/down, they found regions of KHI rapidly expanding within 10 minute cycles roughly matching the local GW period, suggesting that cyclical GW evolutions contributed to elevated local shear to reduce the Richardson number (Ri) and promote instabilities. Advanced mesospheric temperature mapper (AMTM) OH airglow imagery in <ref type="bibr">Fritts et al. (2023)</ref> also shows a range of KHI orientations and scales in close spatial proximity, implying a multiscale environment of superposed inertial GWs <ref type="bibr">(Lelong &amp; Dunkerton, 1998)</ref>. Such GW-shear superpositions have been shown to drive T&amp;K dynamics in KHI observed by rocketsonde chemical tracers <ref type="bibr">(Mesquita et al., 2020;</ref><ref type="bibr">Mixa et al., 2023)</ref> and stratospheric radiosonde profiles <ref type="bibr">(Mixa et al., 2025)</ref>. <ref type="bibr">Hecht et al. (2021)</ref> provides some of the clearest evidence to-date of GW modulation of KHI. High fidelity airglow imagery from Aerospace Corporation's legacy near-IR camera (ANI) reveals a clear GW phase structure with perpendicular KHI. The KHI initially form with extended axial coherence and uniform billows that span several GW horizontal wavelengths (&#969; x ). As they pass through the GW field, KHI appear to exhibit manuscript submitted to JGR: Atmospheres weaker amplitudes and distorted billow structure within negative GW temperature perturbations that roughly correlate with reduced OH brightness, suggesting that variations in GW-induced shear promote KHI billow amplification and attenuation. Billow discontinuities form in these regions that then exhibit T&amp;K as they reconnect. The associated modeling study from <ref type="bibr">Fritts et al. (2021)</ref> identified the potential for T&amp;K dynamics in su"ciently "wide" shear layers where KHI can exhibit axial deformations. This study and other T&amp;K studies to-date have shown KHI evolutionary characteristics in uniform shear, but they have not identified or diagnosed GW-specific responses like phase-localized shear layer modulation, vertical advection cycles that intensify and localize shear responses with each GW period, or oscillations over time due to horizontal advection through successive GW phases. These GW-modulated KHI dynamics merit further study to assess the impact of their resulting instability characteristics and mixing contributions.</p><p>Here we present AMTM observations and modeling results of KHI advecting through a stationary GW field on 18 July 2018 over Tierra del Fuego, Argentina. KHI form orthogonal to the GW and exhibit a range of horizontal extents -some localized to a single GW &#969; x with others spanning multiple GW &#969; x . High resolution numerical modeling studies reproduce the underlying GW-KHI environment observed in the AMTM data and explore the impact of Ri and layer depth on KHI deformation by the GW. Numerical results of the baseline Case 1 with Ri min = 0.15 and layer depth d = 600 m reveal how the underlying GW field perturbs the shear layer and promotes horizontally localized KHI where shear attenuation yields gaps in subcritical Ri. Decreasing Ri min in Trial 1 increases axial billow extents and promotes billow undulations that yield T&amp;K.</p><p>Trial 2 shows how reducing d from 600 m to 300 m with Ri min = 0.05 produces more localized billows with fewer undulations that reduce the formation of T&amp;K. The results of this study reveal the impact of di!erent KHI scales and shear intensities to explain how GW-KHI interactions promote mixing in di!erent atmospheric environments.</p><p>The remainder of the paper is organized as follows: The observational methods are presented in Section 2. Section 2.1 provides a description of the AMTM instrument capturing the GW-KHI events and the associated background conditions for GW propagation at Tierra del Fuego. GW and KHI identification methods are shown in Section 2.2, including descriptions of the 2D FFT approach used to isolate the GW and the spatial derivative approach for identifying KHI billow cores. The observational results are presented in Section 3, including the observed GW and KHI characteristics in Section 3.1 and observed GW-KHI interactions in Section 3.2. Section 4 presents a description of the numerical methods, including the governing equations, solution method, and simulation parameters employed by the Complex Geometry Compressible Atmospheric Model (CGCAM) for our numerical analysis; and the initial conditions and layer parameters that define the simulation environment. Section 5 shows the numerical results: the shear layer evolution of the baseline CGCAM simulation (d = 600 m, Ri min = 0.15) is presented in Section 5.1; the results of Trial 1 (d = 600 m, varying Ri min ) are presented in Section 5.2; and the results of Trial 2 (Ri min = 0.05, varying d) are presented in Section 5.3. A summary of our results and conclusions is found in Section 4. A companion paper published at a later date will include assessments of the turbulence characteristics and competing mixing influences of KHI and GWs in a more generalized MLT environment.  temperatures from the rotation-vibration OH (3,1) band that is located at 86.8 &#177; 2.6 km with a full width at half maximum (FWHM) extent of &#8594; 8 km <ref type="bibr">(Baker &amp; Stair, 1988;</ref><ref type="bibr">She &amp; Lowe, 1998)</ref>. Figure <ref type="figure">2</ref> shows the AMTM location and field of view in panel a and the OH layer altitude from the nearest SABER overpass in panel b. An indium-galliumarsenide camera captures the spectral peaks produced by the dominant OH vibrational modes, using their ratio to calculate temperature via the method of <ref type="bibr">Makhlouf et al. (1995)</ref>.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="2">Observational Methods</head></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="2.1">Instrument Descriptions and Event Observations Overview</head><p>The resulting 2D images show temperatures accurate to &#177;2&#8593;4 K over a 160 km x 200 km field with horizontal resolution of 0.625 km. Temperature measurements are produced every 35 s, and data are line-of-sight integrated over the vertical depth of the OH layer.</p><p>The brightness of the P 1 (2) and P 1 (4) lines of the OH (3,1) band show variations in the OH layer roughly analogous with scaled temperature perturbations. Though AMTM P 1 (2) and temperature data capture the same features (see e.g., Figure <ref type="figure">5a</ref> and <ref type="figure">5c</ref>), P 1 (2) data has less noise, making it easier to discern KHI and other small amplitude features close to the instrument's signal to noise ratio. Hence, we utilize P 1 (2) brightness data from the AMTM for GW and KHI analysis in this study.</p><p>A sample P 1 (2) brightness intensity image from the AMTM in Figure <ref type="figure">2c</ref> shows a superposition of SW-NE aligned, smaller scale &#8594; 10 km KHI advecting through a background field comprised of a larger scale, &#8594; 30 km GW aligned NW-SE. KHI features appear prominently at &#8594; 4:10 UTC with an approximate duration of 10-15 min. The variable phase and amplitude structure of the KHI along the SW-NE GW propagation direction suggests the potential for T&amp;K dynamics influenced by the GW. The SAAMER winds are shown in Figure <ref type="figure">2d</ref> as the wind components parallel (&#8595;) and perpendicular (&#8596;) to the GW vector. Wind components are weighted with a vertical gaussian function centered at 87 km to mimic the OH weighting of the AMTM. Weighted wind components show a background inertial GW with a period of &#8594; 12 hours. The KHI events occur near 4 UTC, when u &#8595; GW &#8594; 33 m s &#8594;1 from the SW. The GW orientation and sign of u &#8595; GW suggest that Cordillera Darwin, a prominent subrange of the Andes SW of Tierra del Fuego, is the most likely terrain source of the GW. Though the quasi-stationary GW field in the AMTM suggests an orographic source, it is not known if the wave observed in the AMTM is the primary orographic GW or a higher order GW reaching the MLT through a multi-step coupling process below the field of observation. GW and KHI features in the AMTM data are roughly orthogonal and have distinct scale ranges, so we utilize a 2D fast Fourier transform (FFT) decomposition to isolate the GW response from the KHI modes in the P 1 (2) field. The GW can then be reconstructed to determine the wave parameters and assess the GW influence on KHI behavior. A sample FFT decomposition is shown in Figure <ref type="figure">3</ref>, where the GW is identified as NE/SW propagating modes with &#969; x = 30&#8593;90 km and the KHI is identified as NW/SE propagating modes with &#969; x = 5 &#8593; 30 km. This method is suitable for identifying the GW due to its sinusoidal composition and temperature (T ) phase alignment with P 1 (2) perturbations (&#8599; scaled T &#8593; ), but there are several challenges to using FFT decomposition to identify KHI.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="2.2">GW and KHI Identification Methods</head><p>Raw P 1 (2) brightness or T fields from the AMTM show clear responses to the presence of KH billows. It is tempting to identify the brightest regions (or analogously, warmest T &#8593; perturbations) as the KHI billow cores themselves, as was done by <ref type="bibr">Hecht et al. (2021)</ref>; <ref type="bibr">Fritts et al. (2021)</ref>, but KHI simulations reveal that this is not the case (see Figure <ref type="figure">4</ref> discussion below). KH billow cores in the vorticity fields occur directly between positive (+) and negative (&#8593;) weighted T &#8593; , making the precise billow evolution di"cult to discern from the visible evolution of &#177;T &#8593; . In addition, billow misalignments and T&amp;K features do not align with the primary KHI propagation direction, so they can be masked by 2D FFT reconstruction due to the filtering direction.</p><p>Figure <ref type="figure">4</ref> shows cross-sections of simulated KHI to identify the most appropriate method to track KH billow evolution in weighted brightness or temperature fields. KH billow cores rotate in the spanwise vertical (y &#8593; z) plane and are clearly visible in the temperature field in panel a: billow cores are marked by rising (&#8593;) T &#8593; and descending (+) T &#8593; . The vorticity component that captures the yz field of KHI rotation, &#949; x = &#977;w/&#977;y&#8593; &#977;v/&#977;z, is strongly negative in the billow core and weakly elsewhere (for this example with clockwise yz billow rotation and &#977;v/&#977;z &gt; &#977;w/&#977;y). This is also the case for the vertically weighted &#949; y field in panel b, which clearly identifies the billow cores from T &#8593; as the locations with strongest (-) &#949; x . In the vertically weighted T &#8593; field (panel c, roughly equivalent to the P 1 (2) in the AMTM), weighted T &#8593; goes from (&#8593;) to (+) where the &#949; x billow cores are located in panels a and b. Thus, we can utilize the spatial derivative &#977;(weighted T )/&#977;y projected in the KHI propagation direction to correctly identify billow cores (+) from billow gaps (&#8593;). This is shown in panel d for &#977;(weighted T )/&#977;y &gt; 0.</p><p>&#977;/&#977;y (T or brightness) suitably captures the location of KH billow cores where they are indicated by the &#949; y field. &#977;(weighted T )/&#977;y or &#977;(weighted P 1 (2))/&#977;y can be computed from the raw AMTM data because KHI are roughly perpendicular to GWs and contain negligible contributions from &#977;T /&#977;y along the GW phases. KH billow cores have positive &#977;/&#977;y in the direction of propagation, whereas gaps between billow cores have negative &#977;/&#977;y. This allows for a clearer assessment of where the billow cores are located relative to visual temperature perturbations to better analyze Ri and billow evolution features without misidentification. UTC exhibits &#177;1&#8593;2 K OH-weighted T &#8593; and a propagation direction of 237 &#8595; (SW). The keogram in panel e along the wave vector shows sustained presence of near-stationary phase structure before/after the KHI observations from 4 &#8593; 5 UTC. Horizontal wavelengths range from &#969; x &#8594; 30 &#8593; 50 km, with 30 km GWs observed prominently near 4 UTC. Using the observed &#969; x and the intrinsic phase speed of the GW (&#8599; &#8593;u &#8595; GW), the remaining GW properties can be calculated from the dispersion relation <ref type="bibr">(Fritts &amp; Alexander, 2003)</ref>. A representative Brunt-Vaisala frequency of N = 0.02 s &#8594;1 yields the following GW parameters: &#982; i = 0.0076 s &#8594;1 &#8599; 0.4N , GW period &#1009; GW &#8599; 14 min, and</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="3">Observational Results</head></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="3.1">GW and KHI Characteristics</head><p>Figure <ref type="figure">6</ref> shows the KHI characteristics of the two KHI events, including P 1 (2) fields and their associated KHI reconstructions using &#977;/&#977;x (weighted P 1 (2)). KHI signatures in P 1 (2) have a propagation direction of &#8599; 337 &#8595; in rough alignment with u &#8596; GW. &#977;/&#977;x (P 1 (2)) projected to 337 &#8595; exhibits clear billow cores with 7-8 km &#969; x at both times, implying an underlying shear layer depth of d &#8594; &#969; x /4&#962; &#8599; 600 m. This thin shear layer is too small to detect with SAAMER winds and strongly localized within the OH layer, suggesting that KH amplitudes will be severely underestimated. Frame-by frame analysis of KHI at 4 UTC reveals an advection speed of roughly 28 m s &#8594;1 NE that nearly matches u &#8595; GW; that is, KHI at 4 UTC do not appear to advect in the u &#8596; GW direction in which they are oriented, only along u &#8595; GW. This implies an underlying shear layer with a central velocity of u &#8596; GW = 0 m s &#8594;1 .  </p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="3.2">Observed GW-KHI interactions</head><p>Figure <ref type="figure">7</ref> shows overplots of the reconstructed GW and KHI for the two events depicted in Figure <ref type="figure">6</ref>, utilizing the same GW and KHI colormaps as in Figures <ref type="figure">5</ref> and <ref type="figure">6</ref>, respectively. KHI in both events exhibit a range of coherence lengths from &#8594; 0.5&#8593;2 GW &#969; x . In event 1 (panels a-c), localized KHI identified in the boxed region form angled billow regions that connect to adjacent, misaligned billows as they advect along the GW  -12-manuscript submitted to JGR: Atmospheres initial conditions, and simulation trial characteristics are described in the Section 4 (Numerical Methods), and the results and analysis follow in Section 5 (Numerical Results).</p><p>4 Numerical Methods</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="4.1">CGCAM Model Architecture</head><p>Simulations herein are conducted using the Complex Geometry Compressible Atmosphere Model (CGCAM). CGCAM solves the nonlinear, compressible Navier-Stokes equations, written in divergence form as:</p><p>where &#8637; ij and q j are the viscous stress and thermal conduction, defined as</p><p>Here &#181; is the dynamic viscosity, &#8640; is the thermal conductivity, and &#8636; ij is the Kronecker delta. &#181; and &#8640; depend on the temperature through Sutherland's Law <ref type="bibr">(White, 1974)</ref>. The solution variables are the air density &#966;, the local total energy per unit mass E, and the momentum per unit volume &#966;u i with velocity components u i = (u, v, w) along (x, y, z).</p><p>We assess the evolution of instability features via the vorticity magnitude</p><p>and the intermediate eigenvalue &#969; 2 of the tensor</p><p>(see e.g., <ref type="bibr">Jeong &amp; Hussain, 1995)</ref>, where S and R are the strain and rotation rate tensors, with components defined as </p><p>where v 0 is the magnitude of the tanh function, z 0 is the layer altitude, and d is the shear layer half depth. The Richardson number is calculated from from the squared vertical shear of the total velocity profile (&#977;U/&#977;z) 2 and the Brunt-Vaisala frequency N as</p><p>and the Reynolds number is calculated as</p><p>where #U is the velocity di!erence over the shear layer and &#181; is the dynamic viscosity.</p><p>&#181; is calculated via Sutherlands Law <ref type="bibr">(White, 1974)</ref>   GW-KHI interactions. Simulation parameters are summarized in Table <ref type="table">1</ref>. In Trial 1, v 0 scaled such that all cases in both trials have Re = 5000 at the shear layer.</p><p>To conserve numerical resources and enable a large number of simulations within the two trials, full DNS resolution is not utilized in these studies. The primary objective is to assess the initial layer evolution, development of KHI, and initial higher order instability features, all of which (1) precede the elevated dissipation associated with the flow transition to turbulence and (2) occur at larger, fully-resolved spatial scales. Due to this resolution constraint, a full assessment of turbulent mixing falls outside the scope of this study.  5 Numerical Results 5.1 Shear Layer and KHI Evolution with (Ri min , d) = (0.15, 600 m)</p><p>The initial layer evolution of Case 1 is shown in Figure <ref type="figure">9</ref>, including streamwisevertical xz plots of total squared shear (&#977;U/&#977;z) 2 in panels a-c and Ri in panels d-f overlaid on the GW T &#8593; field. Layers are plotted after the completion of the wind ramp at t 0 = 17.5 min and shown over several GW periods &#1009; GW . As the layer advects horizontally along u, (&#977;U/&#977;z) 2 is vertically advected &#8594; 0.5 km and back to its initial altitude by the path-integrated e!ects of GW w' once per &#1009; GW . From reference time t 0 to t 0 + 1 &#1009; GW , plots of (&#977;U/&#977;z) 2 in panels a-c reveal an initially flat layer at t 0 with periodic amplitude variations. At t 0 + 0.5 &#1009; GW (panel b), peak upward (downward) vertical deflection and shear amplification occur at negative (positive) T &#8593; phase centers, while peak shear attenuation occurs between deflected regions at the adjacent T &#8593; phase boundaries.</p><p>After 1 &#1009; GW (panel c), the shear layer returns to its initial altitude while retaining the streamwise regions of reduced and enhanced amplitude. This cycle continues and compounds the shear amplitude variations with each successive &#1009; GW .</p><p>Variations in (&#977;U/&#977;z) 2 amplitude produce corresponding changes to the associated Ri, plotted from t 0 to t 0 +2 &#1009; GW with color and opacity maps showing only Ri &lt; 0.3.</p><p>At t 0 (panel d), Ri is below 0.25 (i.e. subcritical) across the whole layer and could theoretically sustain KHI across the full spanwise extent of the simulation domain. How-ever, after 1 &#1009; GW (panel e), gaps in subcritical Ri form where (&#977;U/&#977;z) 2 is attenuated, and the gaps grow by t 0 +2 &#1009; GW (panel f) as the adjacent minimum Ri drops below 0.1. Gaps in sub-critical Ri limit the extent of KHI forming from the shear layer. and their associated Ri (xz cross sections) at t 0 +1.5&#1009; GW and t 0 +3&#1009; GW . At t 0 +1.5&#1009; GW (panels a and b), KHI visible in &#977;T /&#977;y initially form in warm T &#8593; phases where the layer is deflected downward and (&#977;U/&#977;z) 2 and Ri min are both locally enhanced. Because gaps in critical Ri separate the upward and downward deflected regions of the shear layer, the lateral extent of the KHI is initially limited to roughly 0.5 GW &#969; x . As KHI continue to intensify at t 0 +3&#1009; GW (panels c and d), the lateral extent of Ri &lt; 0.25 increases slightly as Ri decreases at the KHI, but gaps in subcritical Ri remain that bound the KHI lateral extent to less than GW &#969; x . Thus for an initial 600 m layer prescribed with a minimum Ri of 0.15, both the lateral extent of the KHI and gap locations between adjacent billows are determined by the GW &#969; x .</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="5.2">Trial 1: KHI Evolution with Decreasing Minimum Ri</head><p>Reducing the minimum Ri of the initial shear layer from 0.15 to 0.05 accelerates the formation of KHI, with billow rollup occurring in fewer &#1009; GW with reduced or eliminated lateral billow gaps. Figure <ref type="figure">11</ref> presents the KHI evolution for all three cases of Trial 1, showing the initial formation of KHI in &#977;T /&#977;y in panels a-c and the associated thickness of the Ri-unstable region in panels d-f. Each decrease in Ri accelerates the initial formation of KHI by &#8594; 0.7 &#8593; 0.8 &#1009; GW , with the Ri min = 0.05 case forming initial KHI before t 0 . Initial KHI in each case form at roughly the midpoint in the GW advection cycle when the shear layer is deflected farthest (&#8599; 0.5 km) from z 0 . Stronger initial KHI responses in &#977;T /&#977;y (panels a-c) are found in the warm T &#8593; phases where the largest local (&#977;U/&#977;z) 2 values occur. The preferential formation of KHI at specific phase locations in the GW domain and similar times within the GW period suggest that the background GW dominantly influences the formation of KHI across di!erent Ri.</p><p>Despite having the same shear layer depth, layers with reduced Ri have deeper subcritical Ri regions that delay the formation of gaps and enable laterally extended KHI.</p><p>In additional to having lower local Ri throughout the layers, the depth of the sub-critical Ri regions within the shear layers (panels d-f) are also much greater in Cases 2 and 3, nearly double the depth of the sub-critical Ri-region in Case 1. When these layers experience the same advection cycle of the GW, attenuation e!ects at T &#8593; phase boundaries take longer to weaken (&#977;U/&#977;z) 2 enough to produce gaps in subcritical Ri. This characteristic, combined with faster KHI formation, yields KH billows in Cases 2 and 3 having longer lateral extents; xy plots of weighted |&#949;| in Figure 12 show initial billows for Case 2 (panel b) extending beyond 0.5 GW &#969; x and billows in Case 3 (panel c) spanning multiple GW &#969; x . These findings suggest that horizontally localized billows observed in the AMTM data arise from layers having larger Ri before passing through the GW field. KHI with longer lateral extents in Cases 2 and 3 also exhibit xy billow curvature in lower-Ri layers. At times when the shear layer altitude has shifted away from z 0 , upward (downward) deflected regions of the layer advect in the positive (negative) y direction as they enter regions of positive (negative) v. The resulting advection path of the shear layer follows sinusoidal xy streamlines corresponding to v traced along the layer in the xz domain. While deflected below z 0 , the shear layer region within the positive T &#8593; phase is o!set in the negative y direction relative to adjacent, upward deflected regions of the layer in the negative T &#8593; phases (e.g., Figure 10a, 10b). KHI forming in this region will thus exhibit xy curvature if their lateral extent is &gt; 0.5 GW &#969; x , as is seen for initial KHI in Case 2 (Figures 11 and 12) and isolated billows in the AMTM as they expand (Figure 6d, Figure 7b and 7e). Continuous billows with extents &gt; 1 GW &#969; x will exhibit curvature determined by orientation of the xy streamlines when each region of the billow intensifies. These findings suggest that extended KHI in the AMTM data with sinusoidal character formed with Ri &lt; 0.1 and developed when the shear layer was most vertically displaced, whereas the milder billow curvature in Case 3 confirms these KHI formed at a less deflected time in the GW advection cycle.</p><p>Crucially, billow curvature from GW modulation of low-Ri shear layers yields environments that promote the formation of T&amp;K in Case 3 (Figure <ref type="figure">12c</ref>). Variable billow orientation along the KHI axis leads to billow regions o!set from the primary shear axis and misaligned billow junctions as KHI form. Near x = 3, a vortex tube spanning y = misaligned billows form a vortex knot at a 2:1 billow junction. Prior studies of KHI T&amp;K dynamics suggests that these sites drive the transition to turbulence and result in elevated mixing wherever they occur (e.g., <ref type="bibr">Mixa et al., 2023</ref><ref type="bibr">Mixa et al., , 2025))</ref>. Misaligned 2:1 billow junctions indicative of vortex knots are seen in the AMTM data in Figure <ref type="figure">6b</ref> and Fig- ure 7b, and parallel angled billow regions in Figure 7b and 7f suggest unresolved vortex tubes forming as the KHI dissipate. 5.3 Trial 2: KHI Formation with Decreasing Layer Depth In Trial 2, decreasing the layer depth from 600 m to 300 m in Cases 3&#8593;5 results in more streamwise-localized billow amplification within the laterally extended billows, promoting faster secondary instability evolution within enhanced KHI regions and reducing the influence of T&amp;K dynamics in the transition to turbulence. Figure 13 shows xz plots of Ri (panels a-c) and xy plots of |&#969; 2 &lt; 0| (panels d-f) for Cases 3-5 at t 0 &#177; 0.5&#1009; GW . Ri plots confirm that at peak deflection times, path integrated e!ects of GW w' advect the layer same vertical distance for all 3 cases, &#8594; &#177;600 m. In Cases 4 and 5, the thinner 450 m and 350 m layers produce subcritical Ri gaps across T &#8593; phase boundaries. Gaps in subcritical Ri yield streamwise-localized KHI forming initially at all &#177;T &#8593; extrema and streamwise amplitude variations as billows ramp up more slowly in regions where gaps occurred ( |&#969; 2 &lt; 0| fields, Figure 13d-f). Reducing the layer depth also limits the formation of T&amp;K by decreasing billow advection in y. Figure <ref type="figure">14</ref>  </p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="6">Summary and Conclusions</head><p>Here we present AMTM observations and modeling results of KHI advecting through a stationary GW field on 18 July 2018 over Tierra del Fuego, Argentina. FFT-Keogram analysis shows a quasi-stationary, 30-50 km &#969; x GW with southwesterly orientation that persists from &#8594; 03:00-06:00 UTC. The orientation and quasi-stationary nature of the GWs suggest they are primary (or higher order) waves resulting from orographic GW forcing that originated near Cordillera Darwin, where Southwesterly ground forcing is typical. From 04:00-05:00 UTC, OH brightness gradient analysis reveals 8-10 km KHI with NW/SE orientation that form and dissipate with 10-15 min lifecycles roughly matching the estimated GW period &#1009; GW &#8599; 14 min. KHI form orthogonal to the GW and exhibit a range of horizontal extents -some localized to a single GW &#969; x with others spanning multiple GW periods. Larger-extent KH billows exhibit axial undulations and dis- continuities known to promote T&amp;K, while localized billows develop angled regions that extend laterally toward adjacent billows. The short 10-15 min duration of the KHI suggests that the underlying GW period influences their formation and dissipation, though AMTM resolution is too coarse to observe any higher order instabilities directly. adjacent parallel billow regions, with larger layer depths increasing the likelihood of T&amp;K formation known to increase mixing in KHI dissipation events. The mixing induced by KHI in a GW field suggests that KHI play a greater role in subgrid-scale turbulence than is currently accounted for in GCM parameterizations. Understanding the relative contributions of GWs and KHI to mixing could benefit GCM turbulence parameterizations applied throughout the atmosphere and will be a topic of future studies.</p></div></body>
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