Gravity Wave Modes Research Articles

Long-term trends and decadal variability of upper mesosphere/lower thermosphere gravity waves at midlatitudes

Mesosphere/lower thermosphere (MLT) winds over Germany as measured with a low-frequency spaced receiver system at Collm 1984–2007 have been analysed with respect to variations at the time scales of gravity waves. Background winds are also registered to analyse possible gravity wave-mean flow interactions at decadal and interdecadal time scales. In both winter and summer an increasing mesospheric zonal wind jet with time is registered, which is accompanied with increasing gravity wave variances. At greater altitudes in summer, the mean wind jet trend reverses, and negative trends of gravity wave variances are found. This connection between gravity waves and mean wind is also observed on a quasi-decadal scale: during solar maximum stronger mesospheric zonal wind jets as well as larger gravity wave amplitudes are observed. This results in a solar cycle modulation of gravity waves with larger amplitudes during solar maximum. The observed positive correlation between gravity wave amplitudes and the mean zonal wind may follow the theory of saturated waves in the atmosphere, such that stronger mesospheric zonal winds are connected with larger gravity wave amplitudes.

Linear versus Nonlinear Filtering with Scale-Selective Corrections for Balanced Dynamics in a Simple Atmospheric Model

Abstract This paper investigates the role of the linear analysis step of the ensemble Kalman filters (EnKF) in disrupting the balanced dynamics in a simple atmospheric model and compares it to a fully nonlinear particle-based filter (PF). The filters have a very similar forecast step but the analysis step of the PF solves the full Bayesian filtering problem while the EnKF analysis only applies to Gaussian distributions. The EnKF is compared to two flavors of the particle filter with different sampling strategies, the sequential importance resampling filter (SIRF) and the sequential kernel resampling filter (SKRF). The model admits a chaotic vortical mode coupled to a comparatively fast gravity wave mode. It can also be configured either to evolve on a so-called slow manifold, where the fast motion is suppressed, or such that the fast-varying variables are diagnosed from the slow-varying variables as slaved modes. Identical twin experiments show that EnKF and PF capture the variables on the slow manifold well as the dynamics is very stable. PFs, especially the SKRF, capture slaved modes better than the EnKF, implying that a full Bayesian analysis estimates the nonlinear model variables better. The PFs perform significantly better in the fully coupled nonlinear model where fast and slow variables modulate each other. This suggests that the analysis step in the PFs maintains the balance in both variables much better than the EnKF. It is also shown that increasing the ensemble size generally improves the performance of the PFs but has less impact on the EnKF after a sufficient number of members have been used.

Ageostrophic instability in rotating shallow water

AbstractLinear instabilities, both momentum-balanced and unbalanced, in several different $ \overline{u} (y)$ shear profiles are investigated in the rotating shallow water equations. The unbalanced instabilities are strongly ageostrophic and involve inertia–gravity wave motions, occurring only for finite Rossby ($\mathit{Ro}$) and Froude ($\mathit{Fr}$) numbers. They serve as a possible route for the breakdown of balance in a rotating shallow water system, which leads the energy to cascade towards small scales. Unlike previous work, this paper focuses on general shear flows with non-uniform potential vorticity, and without side or equatorial boundaries or vanishing layer depth (frontal outcropping). As well as classical shear instability among balanced shear wave modes (i.e. B–B type), two types of ageostrophic instability (B–G and G–G) are found. The B–G instability has attributes of both a balanced shear wave mode and an inertia–gravity wave mode. The G–G instability occurs as a sharp resonance between two inertia–gravity wave modes. The criterion for the occurrence of the ageostrophic instability is associated with the second stability condition of Ripa (1983), which requires a sufficiently large local Froude number. When $\mathit{Ro}$ and especially $\mathit{Fr}$ increase, the balanced instability is suppressed, while the ageostrophic instabilities are enhanced. The profile of the mean flow also affects the strength of the balanced and ageostrophic instabilities.

Planetary wave characteristics of gravity wave modulation from 30–130 km

Abstract. Fast gravity waves (GW) have an important impact on the momentum transfer between the middle and upper atmosphere. Experiments with a circulation model indicate a penetration of high phase speed GW into the thermosphere as well as an indirect propagation of planetary waves by the modulation GW of momentum fluxes into the thermosphere. Planetary wave characteristics derived from middle atmosphere SABER temperatures, GW potential energy and ionospheric GPS-TEC data at midlatitudes reveal a possible correspondence of PW signatures in the middle atmosphere and ionosphere in winter around solar maximum (2002–2005). In the case of the westward propagating 16-day wave with zonal wavenumber 1 a possible connection could be found in data analysis (November–December 2003) and model simulation. Accordingly, GW with high phase speeds might play an essential role in the transfer of PW and other meteorological disturbances up to the ionospheric F-region.

Investigation on mesospheric gravity waves over Indian low latitude stations using sodium airglow observations and a few case studies based on thermal and wind structures

Systematic measurements using sodium (Na) airglow photometers were carried out from Mt. Abu (24.6°N, 72.7°E) and Gadanki (13.5°N, 79.2°E) during cloudless and moonless nights of winter and spring equinoctial months during 2006–2009. Na airglow intensity fluctuations with periodicities ranging from 5min to 3h are analyzed to determine the systematic pattern, if any, in the gravity wave modes that affect Na airglow emission. The power spectra derived from Na airglow intensity variation from Mt. Abu and Gadanki reveal common occurrence of 15–30min periodicities although spectral powers maximize at longer periodicities over these stations. Further, a few case studies were performed using mesospheric temperature and horizontal wind obtained from the SABER and TIDI onboard TIMED satellite nearly over both places. This investigation provides an experimental indication on the possible relationship between the gravity wave periodicities and the occurrence of neutral instabilities in mesosphere. Based on the case studies, it is shown that whenever the neutral instabilities occur within the Na airglow emission layer, the periodicities of gravity waves tend to become shorter in comparison with the periodicities that are observed when the neutral instabilities occur beyond Na airglow emission altitude or do not occur.

Coupling between Gravity Waves and Tropical Convection at Mesoscales

Abstract An idealized cloud-system-resolving model simulation is used to examine the coupling between a tropical cloud population and the mesoscale gravity waves that it generates. Spectral analyses of the cloud and gravity wave fields identify a clear signal of coupling between the clouds and a deep tropospheric gravity wave mode with a vertical wavelength that matches the depth of the convection, which is about two-thirds of the tropospheric depth. This vertical wavelength and the period of the waves, defined by a characteristic convective time scale, means that the horizontal wavelength is constrained through the dispersion relation. Indeed, the wave–convection coupling manifests at the appropriate wavelength, with the emergence of quasi-regular cloud-system spacing of order 100 km. It is shown that cloud systems at this spacing achieve a quasi-resonant state, at least for a few convective life cycles. Such regular spacing is a key component of cloud organization and is likely a contributor to the processes controlling the upscale growth of convective systems. Other gravity wave processes are also elucidated, including their apparent role in the maintenance of convective systems by providing a mechanism for renewed convective activity and system longevity.

Possible planetary wave coupling between the stratosphere and ionosphere by gravity wave modulation

A possible planetary wave (PW) coupling between the stratosphere and ionosphere by the modulation of gravity waves (GW) is studied using midlatitude atmospheric datasets from 2002 to 2008. Information of GW is retrieved from space-based SABER temperature profiles by extracting the potential energy for vertical wavelengths shorter than 6km. For calculating stationary and travelling proxies of wave activity the data are arranged to a daily evenly spaced 3-dimensional basis. From temperature and potential energy fields direct and indirect (modulation) indices of PW activity are obtained between 30 and 130km. From the comparison with stratospheric PW, analysed from MetOffice reanalyses, and ionospheric PW type oscillations (PWTO) from GPS-TEC data, a possible coupling process is derived.The results reveal a potential connection between the stratosphere and ionosphere by PW activity around solar maximum (2002–2005) caused by the modulation of GW at midlatitudes.

High-frequency gravity waves observed in the low-latitude mesosphere-lower thermosphere (MLT) region and their possible relationship to lower-atmospheric convection

[1] Observations of Medium Frequency (MF) radar winds made at Pameungpeuk (7.5°S, 107.5°E) and Tirunelveli (8.7°N, 78°E) between February and March 2010 are used to study gravity wave activity in the equatorial mesosphere and lower thermosphere (80–100 km). Gravity wave variances in the 20–120 min period band and their spectra are computed. Daily values of gravity wave variances show modulations on time scales ranging from diurnal to planetary waves. Spectra of wave variances display peaks at tidal periods and show evidence of gravity wave modulation at 24, 12, and 8 h periods. Statistical investigation of waves, made using Stokes parameter technique, indicates that the directionality of the mesospheric wave field is highly anisotropic. The role of lower-atmospheric sources on the MLT gravity wave variability is also examined. Spatial distribution of cloud top temperature and rainfall rates are used. GW activity at mesosphere-lower thermosphere (MLT) heights shows clear anticorrelation with the cloud top temperature and positive correlation with rainfall rates suggesting a possible link between observed gravity wave variability and the variations in the deep tropical convection.

Scattering of gravity waves by potential vorticity in a shallow-water fluid

The influence of a geostrophically balanced or potential vorticity (PV) containing background flow on the propagation of a coherent gravity wave is examined in a rotating shallow-water model. Over inertial time scales, we find that the gravity wave energy is scattered into other modes of similar wavelength, but with different directions of propagation. We attribute this response to nonlinear resonant interactions between the PV and gravity wave modes, despite the absence of any exchange of energy between the two, and show that the response is consistent with resonant triad theory. We first consider the scattering of a gravity wave mode due to a single PV mode, and compare the theoretical response to numerical solutions. This is followed by consideration of the propagation of a coherent gravity mode through a turbulent PV background. These results are expected to have relevance to the propagation of coherent internal tides in the open ocean.

Study on the layered dusty plasma structures in the summer polar mesopause

Abstract. Traditional hydrodynamic equations are adopted to build a one-dimensional theoretical model to study the effect of gravity wave on layered dusty plasma structures formation and evolution near the polar summer mesospause region associated with polar mesosphere summer echoes (PMSE). The proposed mechanism gives consideration to the charged ice particle motion by the gravity wave modulation, making a significant contribution to the vertical transport of heavy ice particles and convergence into thin layers. And numerical results show that the pattern of the multi-layer structure depends on the ration of the initial ice particles density distribution to the vertical wavelength of the gravity waves, the ice particle size and the wind velocity caused by gravity wave. Also, the variation of ion density distribution under the influence of gravity wave has also been examined. Finally, the electron density depletions (bite-outs) layers has been simulated according to the charge conservation laws, and the results are compared to the ECT02 rocket sounding data, which agree well with the measuring.

Normalized radar cross section of the sea for backscatter: 2. Modulation by internal waves

We report measurements of microwave surface signatures of internal waves with dual‐polarized, coherent, X band radars mounted on three ships and an airplane. In shipboard measurements in the South China Sea, internal waves generally increased the backscattering cross section near the peaks of the internal waves with little detectable decrease afterward. The peak of the cross‐section signature shifted its location relative to the internal wave crest depending on the maximum strain rate of the internal wave. We show that a similar shift is produced in the modulation of short‐gravity waves by internal waves. We suggest that this modulation of “intermediate‐scale” waves causes small‐scale radar scatterers to maximize at this location. In shipboard measurements off the New Jersey coast, the range resolution of the radar was sufficiently small to allow us to detect significant modulation of gravity waves on the order of 15–30 m long by the internal waves. At the high incidence angles of the shipboard measurements, the cross section for horizontally polarized transmit and receive signals, σo(HH), regularly exceeded that for vertically polarized transmit and receive signals, σo(VV), near the internal wave crest by 5–10 dB. At the more moderate incidence angles observed from the aircraft, maximum values of σo(HH) and σo(VV) are more nearly equal, with σo(HH) often being comparable to σo(VV) and only occasionally exceeding it. These observations suggest that roughness due to breaking short‐gravity waves plays a significant role in producing microwave signatures of internal waves, even at moderate incidence angles where it competes with the modulation of wind‐generated waves. The intensity of modulation of the cross section caused by internal waves observed from the plane depended little on the direction of observation. Internal wave surface signatures from the aircraft became less visible with increasing wind speed, being very difficult to observe at 9 m/s.

Modulation of Internal Gravity Waves in a Multiscale Model for Deep Convection on Mesoscales

Abstract Starting from the conservation laws for mass, momentum, and energy together with a three-species bulk microphysics model, a model for the interaction of internal gravity waves and deep convective hot towers is derived using multiscale asymptotic techniques. From the leading-order equations, a closed model for the large-scale flow is obtained analytically by applying horizontal averages conditioned on the small-scale hot towers. No closure approximations are required besides adopting the asymptotic limit regime on which the analysis is based. The resulting model is an extension of the anelastic equations linearized about a constant background flow. Moist processes enter through the area fraction of saturated regions and through two additional dynamic equations describing the coupled evolution of the conditionally averaged small-scale vertical velocity and buoyancy. A two-way coupling between the large-scale dynamics and these small-scale quantities is obtained: moisture reduces the effective stability for the large-scale flow, and microscale up- and downdrafts define a large-scale averaged potential temperature source term. In turn, large-scale vertical velocities induce small-scale potential temperature fluctuations due to the discrepancy in effective stability between saturated and nonsaturated regions. The dispersion relation and group velocity of the system are analyzed and moisture is found to have several effects: (i) it reduces vertical energy transport by waves, (ii) it increases vertical wavenumbers but decreases the slope at which wave packets travel, (iii) it introduces a new lower horizontal cutoff wavenumber in addition to the well-known high wavenumber cutoff, and (iv) moisture can cause critical layers. Numerical examples reveal the effects of moisture on steady-state and time-dependent mountain waves in the present hot-tower regime.

Nonlinear inertia-gravity wave-mode interactions in three dimensional rotating stratified flows

To investigate the dynamics of gravity waves in stratified Boussinesq flows, a model is derived that consists of all three-gravity-wave-mode interactions (the GGG model), excluding interactions involving the vortical mode. The GGG model is a natural extension of weak turbulence theory that accounts for exact three-gravity-wave resonances. The model is examined numerically by means of random, large-scale, high-frequency forcing. An immediate observation is a robust growth of the so-called vertically sheared horizontal flow (VSHF). In addition, there is a forward transfer of energy and equilibration of the nonzero-frequency (sometimes called “fast”) gravity-wave modes. These results show that gravity-wave-mode interactions by themselves are capable of systematic interscale energy transfer in a stratified fluid. Comparing numerical simulations of the GGG model and the full Boussinesq system, for the range of Froude numbers (Fr) considered (0.05 ≤ Fr ≤ 1), in both systems the VSHF is hardest to resolve. When adequately resolved, VSHF growth is more vigorous in the GGG model. Furthermore, a VSHF is observed to form in milder stratification scenarios in the GGG model than the full Boussinesq system. Finally, fully three-dimensional nonzero-frequency gravity-wave modes equilibrate in both systems and their scaling with vertical wavenumber follows similar power-laws. The slopes of the power-laws obtained depend on Fr and approach −2 (from above) at Fr = 0.05, which is the strongest stratification that can be properly resolved with our computational resources

Wave Mode Analyses of Gravity Waves Propagating in the Mesospheric Thermal Duct

AbstractA new model of gravity waves propagating in the mesospheric thermal duct is presented in this paper, partially ducted modes of gravity waves in the thermal duct are also discussed in detail. Analytic eigenfunctions and dispersion equations of the symmetric and asymmetric modes are separately derived; numerical solutions of these two dispersion equations are also presented. Furthermore, a two‐dimensional full‐implicit‐continuous‐Eulerian (FICE) scheme is used to simulate propagation of ducted gravity waves. The numerical results show that symmetric and asymmetric waves can be excited simultaneously after the penetration of initial disturbances into duct area. Wave structures of different wave modes would be separated due to their different travelling velocities in the duct layer. Calculated horizontal group velocities of ducted gravity waves agree well with those derived from the model analyses, and frequencies of these two ducted gravity waves are almost the same, though these waves are excited by disturbance with different initial frequencies. Both model analyses and numerical simulations indicate that characteristic of the gravity wave in a certain thermal duct is primarily determined by the initial horizontal wavenumber.

Power spectrum features of the near-Earth atmospheric electric field in Kamchatka

Power spectrum of the diurnal variations of the quasi-electrostatic field Ez in the near-Earth atmosphere have been presented for the first time. The Ez power spectrum variations in the period of fine weather have been shown to exhibit two bands of the periods of natural atmospheric oscillations with T = 1-5 and 6-24 h. These oscillations are the modes of the internal gravity and tidal waves in the lower atmosphere. On the days under atmospheric precipitation, the spectral power of Ez increases by an order of magnitude. During the pre-earthquake period, when the diurnal Ez variation had an anomaly, the intensity of harmonics with T = 1.8, 2.2, and 3.8 h increased by an order of magnitude or more in comparison with the Ez spectra in fine weather. Two additional spectral bands with T = 0.6 and 1 h have appeared simultaneously.

Occurrence of standing surface gravity waves modulation in shallow water

Arising of modulations of surface gravity waves in a shallow water resonator under harmonic forcing is investigated in laboratory experiments. Different types of modulations are found, when the wave amplitude exceeds a certain threshold. Bifurcation diagram on the plane “amplitude of excitation – frequency of excitation” is determined. Numerical simulations of the Euler equations within the frameworks of the High-Order Spectral Method are performed with the purpose of reproducing the modulational regimes observed in the laboratory experiments. The simulations allowed us to determine physical mechanisms responsible for the occurrence of modulated waves.

Wind-forced modulations of finite-depth gravity waves

It has been shown recently that the modulations of deep-water gravity waves grow superexponentially under the effect of wind [S. Leblanc, “Amplification of nonlinear surface waves by wind,” Phys. Fluids 19, 101705 (2007)]. Finite depth is considered here. Based on Davey–Stewartson equations with forcing, stability analysis shows that longitudinal modulations are amplified when kh>1.363, where k is the wave number of the carrier wave and h is the water depth, but that oblique modulations dominate when 0<kh<2.199. In each case, amplification is characterized in the linear stage by superexponential growth. This latter is, however, so small when kh<0.380 that no modulation is expected in shallow water, although the carrier wave still grows, thanks to wind forcing.

An efficient mode-splitting method for a curvilinear nearshore circulation model

A mode-splitting method is applied to the quasi-3D nearshore circulation equations in generalized curvilinear coordinates. The gravity wave mode and the vorticity wave mode of the equations are derived using the two-step projection method. Using an implicit algorithm for the gravity mode and an explicit algorithm for the vorticity mode, we combine the two modes to derive a mixed difference–differential equation with respect to surface elevation. McKee et al.'s [McKee, S., Wall, D.P., and Wilson, S.K., 1996. An alternating direction implicit scheme for parabolic equations with mixed derivative and convective terms. J. Comput. Phys., 126, 64–76.] ADI scheme is then used to solve the parabolic-type equation in dealing with the mixed derivative and convective terms from the curvilinear coordinate transformation. Good convergence rates are found in two typical cases which represent respectively the motions dominated by the gravity mode and the vorticity mode. Time step limitations imposed by the vorticity convective Courant number in vorticity-mode-dominant cases are discussed. Model efficiency and accuracy are verified in model application to tidal current simulations in San Francisco Bight.

Oscillation of shallow flow past a cavity: Resonant coupling with a gravity wave

Self-excited oscillations of flow past a cavity are generated in a shallow free-surface system. The shear layer past the cavity opening has two basic forms: a separated free-shear flow; and a shear flow along a slotted plate. Instabilities of these classes of shear flows can couple with the fundamental gravity-wave mode of the adjacent cavity. The dimensionless frequencies of both types of oscillations scale on the length of the cavity opening, rather than the gap distance between the slats, i.e., a large-scale instability is always prevalent. A technique of high-image-density particle image velocimetry allows acquisition and interpretation of global, instantaneous images of the flow pattern, including patterns of vorticity and Reynolds stress correlation. Use of a cinema approach provides representations of the timewise evolution of the global, instantaneous flow structure, and thereby definition of the amplitude peaks and phase angles of the coupled fluctuations via auto- and cross-spectral techniques. These methods, along with global, averaged representations of the fluctuating flow field, provide insight into the onset of fully coupled (phase-locked) oscillations of the shear flow past the resonator cavity. The common, as well as the distinctive, features of the resonant-coupled instability of the shear flow past the slotted plate are characterized, relative to the corresponding coupled instability of the free-shear layer. Varying degrees of resonant coupling between the unstable shear layer and the adjacent resonator are attained by variations of the inflow velocity, which yield changes of the predominant oscillation frequency, relative to the resonant frequency of the adjacent cavity. Well-defined, coherent oscillations are indeed attainable for the case of the shear flow along the slotted plate, though their amplitude is significantly mitigated relative to the case of a free-shear layer. The degree of organization of the self-excited, resonant-coupled oscillation and the manner in which it varies with open area ratio and geometry of the plate are interpreted in terms of the flow structure on either side of, and within, the slotted plate; these features are compared with the corresponding structure of the free-shear layer oscillations.

Planetary wave and gravity wave influence on the occurrence of polar stratospheric clouds over Davis Station, Antarctica, seen in lidar and radiosonde observations

We present Rayleigh lidar observations of polar stratospheric clouds (PSC) from Davis Station (68.6°S, 78.0°E), Antarctica, from the 2001, 2002, 2003, and 2004 austral winter seasons. The PSC are detected as enhanced backscatter returns at lower stratospheric heights. We use operational radiosonde balloon data to compare the PSC detections with stratospheric temperature and wave properties. As documented by others, we find that the occurrence of PSC is closely tied to average stratospheric temperatures (which, in turn, are closely related to the location of Davis with respect to the Antarctic vortex), with PSC being seen when the temperature falls to near or below the calculated formation temperature of nitric acid trihydrate. There is clear evidence in the sonde data for gravity wave and planetary wave modulation of the stratospheric temperature. We see small‐scale wavelike structure in the PSC profiles, which likely arises from gravity waves, but find little direct correlation between a given (vertical) lidar PSC profile and near‐contemporaneous sonde profile, probably because the sonde flight is not an instantaneous sounding at the exact spatial location of the lidar. The planetary‐wave‐induced temperature variations are of the order of 10 times the size of the gravity wave variations and have a greater and more direct influence in PSC occurrence over Davis.