Critical Level Interactions Research Articles

Non‐hydrostatic effects on mountain wave breaking in directional shear flows

Mountain waves excited by narrow 3D orography are investigated using idealized numerical simulations of atmospheric flows with directional wind shear. The stability of these waves is compared with the stability of hydrostatic mountain waves. The focus is on understanding how wave breaking is modified via gravity wave–critical level interaction, when non‐hydrostatic (dispersive) effects arise. The influence of non‐hydrostatic effects on wave breaking appears to be a function of the intensity of the background shear, increasing the stability of the flow (inhibiting wave breaking) for weak wind shear, but decreasing it instead (enhancing wave breaking) for stronger wind shear.

Weakly non-linear analysis of small-amplitude internal gravity waves forced by isolated topography

Asymptotic methods and numerical simulations are used to examine the evolution of an internal gravity wave packet comprising a continuous spectrum of horizontal wavenumbers and propagating upwards in a continuously stratified shear flow. In the multiple-scale framework for a horizontally localized wave packet generated by stratified flow over a localized mountain range with multiple peaks, there are in general two horizontal scales: the “fast” scale which is defined by the oscillations within the packet, i.e. the number of peaks, and the “slow scale” which is defined by the horizontal extent of the packet, i.e. the width of the mountain range. The focus here is on the specific case of an isolated mountain where the spectrum of horizontal wavenumbers is centred at zero and the multiple-scaling procedure is thus simplified by the absence of the fast spatial scale. The background flow is vertically sheared and critical-level interactions occur. The time frame within which non-linear critical-level effects become significant is determined by the magnitude of the non-linear terms in the governing equations. With the isolated mountain forcing this time frame is significantly longer than in the case of a multiple-peak mountain range forcing and it depends on the horizontal scale of the forcing, as well as on the amplitude. At leading-order, the non-linear asymptotic solution approaches a steady state in the outer region at late time, but the zero-wavenumber component of the solution continues to evolve with time in the vicinity of the critical level.

Critical level interaction of a gravity wave with background winds driven by a large‐scale wave perturbation

As part of the Maui‐Mesosphere and Lower Thermosphere program, data from the Utah State University Mesospheric Temperature Mapper (MTM) and the University of Illinois Meteor Wind Radar (MWR) have been used to investigate wave‐driven dynamical interactions in the upper mesosphere at low latitudes. On 29 June 2003, short‐period (∼20 min) gravity waves (GWs) were imaged in the MTM in the near‐infrared OH and O2 airglow emissions for most of the night from 0700 to 1500 UT. The GWs were observed to disappear rapidly in the O2 data (peak altitude: ∼94 km) around 1400 UT but remained evident in the lower altitudes OH data (∼87 km) for a further 30 min. Coincident background wind variations measured by the MWR suggest that the GW disappearance at the O2 layer was most probably caused by a critical level (CL) interaction. However, at the OH layer, the GW fading may also have been due to wave saturation and instabilities. During this period (1400−1500 UT), no significant change in OH and O2 rotational temperatures were measured by the MTM; however, the background winds centered on the airglow layers were observed to increase by ∼10 m/s. The background wind acceleration from the disappearing gravity waves estimated from the airglow observations was larger below the CL than at the CL, consistent with the wind variation observed by the MWR.

Statistics and Dynamics of Aircraft Encounters of Turbulence over Greenland

Abstract Historical records of aviation turbulence encounters above Greenland are examined for the period from 2000 to 2006. These data identify an important flow regime that contributes to the occurrence of aircraft turbulence encounters, associated with the passage of surface cyclones that direct easterly or southeasterly flow over Greenland’s imposing terrain. The result of this incident flow is the generation of mountain waves that may become unstable through interactions with the background directional wind shear. It is shown that this regime accounted for approximately 40% of the significant turbulent events identified in the 7-yr database. In addition, two specific cases from the database are examined in more detail using a high-resolution mesoscale model. The model simulations highlight the important role of three-dimensional gravity wave–critical level interactions and demonstrate the utility of high-resolution forecasts in the prediction of such events.

Some Influences of Background Flow Conditions on the Generation of Turbulence due to Gravity Wave Breaking above Deep Convection

Abstract Deep moist convection generates turbulence in the clear air above and around developing clouds, penetrating convective updrafts and mature thunderstorms. This turbulence can be due to shearing instabilities caused by strong flow deformations near the cloud top, and also to breaking gravity waves generated by cloud–environment interactions. Turbulence above and around deep convection is an important safety issue for aviation, and improved understanding of the conditions that lead to out-of-cloud turbulence formation may result in better turbulence avoidance guidelines or forecasting capabilities. In this study, a series of high-resolution two- and three-dimensional model simulations of a severe thunderstorm are conducted to examine the sensitivity of above-cloud turbulence to a variety of background flow conditions—in particular, the above-cloud wind shear and static stability. Shortly after the initial convective overshoot, the above-cloud turbulence and mixing are caused by local instabilities in the vicinity of the cloud interfacial boundary. At later times, when the convection is more mature, gravity wave breaking farther aloft dominates the turbulence generation. This wave breaking is caused by critical-level interactions, where the height of the critical level is controlled by the above-cloud wind shear. The strength of the above-cloud wind shear has a strong influence on the occurrence and intensity of above-cloud turbulence, with intermediate shears generating more extensive regions of turbulence, and strong shear conditions producing the most intense turbulence. Also, more stable above-cloud environments are less prone to turbulence than less stable situations. Among other things, these results highlight deficiencies in current turbulence avoidance guidelines in use by the aviation industry.

Mesospheric gravity waves observed near equatorial and low–middle latitude stations: wave characteristics and reverse ray tracing results

Abstract. Gravity wave signatures were extracted from OH airglow observations using all-sky CCD imagers at four different stations: Cachoeira Paulista (CP) (22.7° S, 45° W) and São João do Cariri (7.4° S, 36.5° W), Brazil; Tanjungsari (TJS) (6.9° S, 107.9° E), Indonesia and Shigaraki (34.9° N, 136° E), Japan. The gravity wave parameters are used as an input in a reverse ray tracing model to study the gravity wave vertical propagation trajectory and to estimate the wave source region. Gravity waves observed near the equator showed a shorter period and a larger phase velocity than those waves observed at low-middle latitudes. The waves ray traced down into the troposphere showed the largest horizontal wavelength and phase speed. The ray tracing results also showed that at CP, Cariri and Shigaraki the majority of the ray paths stopped in the mesosphere due to the condition of m2<0, while at TJS most of the waves are traced back into the troposphere. In summer time, most of the back traced waves have their final position stopped in the mesosphere due to m2<0 or critical level interactions (|m|→∞), which suggests the presence of ducting waves and/or waves generated in-situ. In the troposphere, the possible gravity wave sources are related to meteorological front activities and cloud convections at CP, while at Cariri and TJS tropical cloud convections near the equator are the most probable gravity wave sources. The tropospheric jet stream and the orography are thought to be the major responsible sources for the waves observed at Shigaraki.

Reverse ray tracing of the mesospheric gravity waves observed at 23°S (Brazil) and 7°S (Indonesia) in airglow imagers

Gravity wave observations using all-sky CCD imager to measure the airglow OH, O 2, and OI emissions were made at Cachoeira Paulista (22.7°S, 45°W) (CP), at the low-middle latitude in Brazil, from October 1998 to September 1999. Near the equator, at Tanjungsari observatory (6.9°S, 107.9°E) (TJS), Indonesia, another wide angle CCD imager measuring the OH airglow emission layer has been operated from September 2000 to September 2001. With these data sets, a reverse ray tracing method was used to study propagation of gravity waves through the middle atmosphere and to estimate the source region. The CIRA-86 reference zonal wind and temperature models and the GSWM-02 tidal wind model were used in the present analysis. Both observation sites showed apparently similar wave characteristics, except for the horizontal phase speed, which was much faster in the equatorial region. From the inverse ray tracing calculations, it was found that at CP, only about 15% of the wave events originated in the troposphere. Most of the events were located over the continent within an area of less than 400 km from the observation site. The identified source region in the troposphere showed a seasonal anisotropy, being mainly to the northwest of CP during summer and to the southeast and northwest in winter. This corresponds to the region of high tropospheric convection activity in the South American continent during summer and high meteorological front activity on the southwestern side during winter. At CP more than 70% of the waves showed that the ray tracing paths stopped in the mesosphere. At TJS the ray tracing indicates that 60% of the gravity wave sources might be located in the troposphere with an area of less than 200 km from the observation site, much closer than the case of CP. This corresponds to convective cloud activities on the north and northwest side of TJS. However, during southern hemisphere summer at both observation sites, most of the ray tracing paths stopped at the mesosphere owing to a condition of m 2 < 0 or critical level interactions.

Propagation of gravity wave packet near critical level

A couple of two-dimensional linear and fully nonlinear numerical models for compressible atmosphere are used to numerically study the propagation of the gravity wave packet into a mean wind shear. For a linear propagation wave packet, the critical level interactions are in good agreement with the linear critical level theory. The dynamically and convectively unstable regions are formed due to the critical level interaction of a finite-amplitude wave packet, but they would not break. The free exchange of potential energy with kinetic energy in the background atmosphere at rest ceases after entering the mean wind shear. However, it still goes on in the nonlinear propagation. It is shown that the nonlinear effects modify the mean flow markedly, reduce the momentum and energy propagation velocity and drop the elevation of the critical level. The gravity wave packet becomes unstable and breaks down into smaller scales in some regions. It expends much more kinetic energy than potential energy in the early phase of the breakdown. This means that the wave breakdown sets up due to the action of the shear instability rather than a convective one.

Mixing Layer Formation near the Tropopause Due to Gravity Wave–Critical Level Interactions in a Cloud-Resolving Model

Abstract A plausible mechanism for the formation of mixing layers in the lower stratosphere above regions of tropical convection is demonstrated numerically using high-resolution, two-dimensional (2D), anelastic, nonlinear, cloud-resolving simulations. One noteworthy point is that the mixing layer simulated in this study is free of anvil clouds and well above the cloud anvil top located in the upper troposphere. Hence, the present mechanism is complementary to the well-known process by which overshooting cloud turrets causes mixing within stratospheric anvil clouds. The paper is organized as a case study verifying the proposed mechanism using atmospheric soundings obtained during the Central Equatorial Pacific Experiment (CEPEX), when several such mixing layers, devoid of anvil clouds, had been observed. The basic dynamical ingredient of the present mechanism is (quasi stationary) gravity wave–critical level interactions, occurring in association with a reversal of stratospheric westerlies to easterlies below the tropopause region. The robustness of the results is shown through simulations at different resolutions. The insensitivity of the qualitative results to the details of the subgrid scheme is also evinced through further simulations with and without subgrid mixing terms. From Lagrangian reconstruction of (passive) ozone fields, it is shown that the mixing layer is formed kinematically through advection by the resolved-scale (nonlinear) velocity field.

Evidence for viscosity, thermal conduction and diffusion waves in the Earth’s atmosphere (invited)

Over the last 40 years, radar studies of atmospheric backscatter have shown tantalizing evidence for flat, mirror-like partial reflectors embedded in the air. These have been observed at all heights, but especially in the stratosphere (above ∼10 km) and mesosphere (especially in the region 60–90 km altitude), and at a variety of frequencies, from 2 to at least 50 MHz. These structures appear to have vertical depths of only a few meters or less. They often seem independent of atmospheric turbulence scatter. Various explanations have been advanced to account for these unusual structures, but a strong candidate is the possibility that they are due to diffusion waves generated by reflection and/or critical level interactions of gravity waves or infrasound. In this review, we will examine the evidence for these structures, and expand on the possibility that they are indeed organized structures which develop due to the diffusive characteristics of the medium.

A simulation study of space‐based observations of gravity waves in the airglow using observed ALOHA‐93 wave parameters

We use gravity wave parameters derived from the ALOHA‐93 campaign to model four gravity waves in airglow emissions as observed from the ground to numerically predict whether these waves could have been observed from space. In spite of encountering critical levels, some waves may still be observed in the airglow provided the critical level lies within the airglow emission region. One of the four waves experiences a critical level in the lower region of an airglow layer such that the disturbance to the volume emission rate would be effectively limited to a short distance along a satellite line of sight. The effect of this is to mitigate the effects of destructive interference in the airglow making the wave more observable from space. For this particular wave the amplitude is derived by normalizing the model‐derived airglow fluctuation amplitude to that observed from the ground during the ALOHA‐93 campaign. The model then provides momentum and energy fluxes as a function of height as well as the flux divergences, from which the mean state forcing is evaluated. The results suggest that the observed wave could provide significant mean state forcing. Therefore, we conclude that some waves experiencing critical level interactions in the airglow regions are not only likely to be important to the momentum balance of the upper mesosphere/lower thermosphere region but also are more likely to be observed from space.

Nonlinear dissipative critical level interaction in a stratified shear flow: Instabilities and gravity waves

Abstract A two-dimensional numerical model is used to investigate the nonlinear dissipative interaction between a disturbance and an unbounded stratified shear flow. The disturbances considered are Kelvin-Helmholtz instabilities and forced gravity waves. The nonlinear stabilization (destabilization) of Kelvin-Helmholtz instabilities at Prandtl number, Pr 1), found by Brown et al. (1981) is recovered. The model confirms that it is mostly due to a stabilization (destabilization) of the mean flow by the wave. The nonlinear evolution of instabilities existing when thermal dissipation is large and when the Richardson number is everywhere larger than 0.25 is also investigated. It is shown that such a mode stops growing when the nonlinear distortion of the mean flow becomes significant. For forced gravity waves, and when the initial minimum Richardson number, J = 0.25, it is found that mean flow stabilization (destabilization) also occurs at the critical level for Pr 1). More generally, the v...

Viscosity waves and thermal‐conduction waves as a cause of “specular” reflectors in radar studies of the atmosphere

We present a new theory to explain the cause of the atmospheric structures which are responsible for specular reflection of radar signals from the atmosphere. Evidence recorded with the middle and upper atmosphere (MU) VHF radar at Shigaraki in Japan, as well as previous reports of specular reflections from other radars and at other frequencies, is used to support our assertions. The theory postulates that the reflectors are produced by a form of highly damped wave which arises in a fluid as a result of the effects of viscosity and thermal conduction. They occur at altitudes where gravity waves are partially reflected and in the vicinity of gravity wave critical levels but are particularly prevalent when such reflections and critical level interactions occurs in a laminar region of the atmosphere. The typical scales of the waves, their reflection efficiency, and their likely location are all considered and found to be consistent with what is currently known about specular reflectors in the atmosphere. Some predictions which will allow further tests of the model are also presented.

山岳波とクリティカルレベルの相互作用の数値シミュレーションによる研究の補稿

山岳波とクリティカルレベルの相互作用の数値シミュレーションによる研究の補稿

A Case Study of Gravity Waves–Convective Storms Interaction: 9 May 1979

An analysis is presented of a series of severe storms which occurred in the north central United States on 9 May 1979 and whose spatial distribution and movement correlate well with observed gravity waves. Two gravity wave trains of 2.1-3 mb amplitude, 2.5-3.3 h period and 240-265 km horizontal wavelength were isolated through power spectra analysis and cross-correlation techniques applied to National Weather Service barograph traces. The wave trains propagated in the 200 deg direction, which coincided with the jet axis, with a phase velocity of 20-30 m/s and within a 300 km wide band. The storms were identified on enhanced infrared GOES satellite pictures with the help of radar summaries. These convective systems initially developed in Nebraska and propagated north-northeast at 25 m/s, revealing wave-like characteristics with a separation of 300-400 km. The convective systems were closely linked to the observed wave trains with cell intensity, height and associated rainfall maximized at the wave ridge. One of the two wave trains developed in regions of weak or no convection and appeared to initiate more intense convective clusters downstream from the point of origin. It is shown that the characteristics of the wave trains are consistent with those of gravity waves generated in a region of strong vertical shear associated with the jet. It is suggested that the wave trains continue to extract energy from the basic state all along their track through critical level interaction.

The Nonlinear Gravity Wave-Critical Level Interaction

A nonlinear numerical model of the gravity wave-critical level interaction is developed in this paper. This model is used to examine and compare the effects of viscosity, time-dependence and nonlinear interactions on the development of the critical level interaction. It is found, in agreement with earlier studies, that viscosity and heat conduction strongly stabilize the interaction very near the critical level. Time-dependence and nonlinear interactions are found to be strongly stabilizing only for very transient or low viscosity flows, respectively. These two effects are very important, however, in the development of Kelvin-Helmholtz instabilities within unstable velocity shears. Once excited, these instabilities grow on the excess energy available in the unstable shears. When large unstable velocity shears are produced, the Kelvin-Helmholtz instabilities grow until they dominate the critical level interaction. It is argued that the break-down of these Kelvin-Helmholtz billows produced by the critical level interaction can explain some of the thin turbulent layers observed in the atmosphere and the oceans.

Viscous Stabilization of Gravity Wave Critical Level Flows

Abstract A criterion for the viscous stabilization of gravity wave critical level flow is derived to be Z¼≤ 2.5 Zr where Z¼is the vertical thickness of the unstable region in the vicinity of a gravity wave critical level calculated with an inviscid linear theory and Zy is the viscous length scale for gravity wave critical level interaction. The stability implications of this criterion are examined for gravity wave critical level flows in the laboratory, the atmospheric planetary boundary layer, the upper atmosphere and the ocean thermocline region. Laboratory flows, where no turbulence in the vicinity of a gravity wave critical level was observed, are found to meet our criterion for stability. Applying this criterion to atmospheric boundary layer flows implies that no such regions of instability should be observed in the fully developed turbulent convective region, but such turbulent regions should exist in stably stratified cases. Using observed gravity wave parameters for the upper atmosphere the stabil...