Gravity Wave Emission Research Articles

Dynamics of localized extreme heatwaves in the mid‐latitude atmosphere: A conceptual examination

AbstractThis study investigates the adjustment of large‐scale localized buoyancy anomalies in mid‐latitude regions and the nonlinear evolution of associated condensation patterns in both adiabatic and moist‐convective environments. This investigation is carried out utilizing the two‐layer idealized moist‐convective thermal rotating shallow water (mcTRSW) model. Our investigation reveals that the presence of a circular positive potential temperature anomaly in the lower layer initiates an anticyclonic high‐pressure rotation, accompanied by a negative buoyancy anomaly in the upper layer, resulting in an anisotropic northeast–southwest tilted circulation of heat flux. The evolution of eddy heat fluxes, such as poleward heat flux, energy, and meridional elongation of the buoyancy field, heavily depends on the perturbation's strength, size, and vertical structure. The heatwave initiates atmospheric instability, leading to precipitation systems such as rain bands and asymmetric latent heat release due to moist convection in a diabatic environment. This creates a comma cloud pattern in the upper troposphere and a comma‐shaped buoyancy anomaly in the lower layer, accompanied by the emission of inertia gravity waves. The southern and eastern sectors of the buoyancy anomaly show an upward flux, generating a stronger cross‐equatorial flow and inertia‐gravity waves in a southward and eastward direction. Furthermore, the simulations reveal a similar asymmetric pattern of total condensed liquid water content distribution, accompanied by the intensification of moist convection as rain bands. This intensification is more pronounced in barotropic structures than in baroclinic configurations with stagnant upper layers. This study highlights the importance of considering moist convection and its effects on atmospheric and oceanic flows in mid‐latitude regions, as well as the role of buoyancy anomalies in generating heatwaves and precipitation patterns.

Gravity Wave Generation in Balanced Sheared Flow Revisited

Abstract The generation of internal gravity waves from an initially geostrophically balanced flow is diagnosed in nonhydrostatic numerical simulations of shear instabilities for varied dynamical regimes. A nonlinear decomposition method up to third order in the Rossby number (Ro) is used as the diagnostic tool for a consistent separation of the balanced and unbalanced motions in the presence of their nonlinear coupling. Wave emission is investigated in an Eady-like and a jet-like flow. For the jet-like case, geostrophic and ageostrophic unstable modes are used to initialize the flow in different simulations. Gravity wave emission is in general very weak over a range of values for Ro. At sufficiently high Ro, however, when the condition for symmetric instability is satisfied with negative values of local potential vorticity, significant wave emission is detected even at the lowest order. This is related to the occurrence of fast ageostrophic instability modes, generating a wide spectrum of waves. Thus, gravity waves are excited from the instability of the balanced mode to lowest order only if the condition of symmetric instability is satisfied and ageostrophic unstable modes obtain finite growth rates. Significance Statement We aim to understand the generation of internal gravity waves in the atmosphere and ocean from a flow field that is initially balanced, i.e., free from any internal gravity waves. To examine this process, we use simulations from idealized numerical models and nonlinear flow decomposition method to identify waves. Our results show that a prominent mechanism by which waves can be generated is related to symmetric or ageostrophic instabilities of the balanced flow possibly occurring during frontogenesis. This process can be a significant mechanism to dissipate the energy of the geostrophic flow in the ocean.

Membrane flutter induced by radiation of surface gravity waves on a uniform flow

Abstract

A new atmospheric-like differentially heated rotating annulus configuration to study gravity wave emission from jets and fronts

Significant inertia-gravity wave activity has been frequently observed in the vicinity of jet and front systems in the atmosphere. Although many studies have established the importance of these non-orographic sources, the mechanisms responsible for spontaneous wave emissions are still not fully understood. The complexity of the three-dimensional flow pattern and distribution of the sources over large areas point towards the need for laboratory experiments and idealised numerical simulations. These will help understand the correct interpretation of the fundamental dynamical processes in a simplified, but yet realistic flow. In this study, we emphasise the importance of using set-ups of the differentially heated rotating annulus experiment with a ratio between the buoyancy frequency N, and the Coriolis parameter f larger than one to investigate atmosphere-like emission of gravity waves from baroclinic jets. Indeed, in the atmosphere $$N/f\sim 100$$, but for table-top size experiments this ratio is smaller than one, resulting in an unfavourable condition for the propagation of gravity waves. For this reason, we offer a newly built laboratory experiment supported by numerical simulations that allow $$N/f>1$$. The conditions for gravity wave emission in this new configuration are examined in detail, and the first evidence of IGWs is reported. Moreover, we compare numerical simulations and experimental data focusing on the variations of the temperature T, and its effects on the buoyancy frequency N. It becomes clear, that despite the fact the global structure and baroclinic instability characteristics are very similar, the model and experiment show deviations in N with implications for gravity wave emission. Due to the complex horizontal structure of N, where the largest values occur along the baroclinic jet axis, the inertia-gravity waves in the experiment are observed to be trapped.

Gravity Wave Emission by Shear Instability

AbstractGravity wave emission by geostrophically balanced flow is diagnosed in numerical simulations of lateral and vertical shear instabilities. The diagnostic method in use allows for a separation of balanced flow and residual wave signal up to fourth order in the Rossby number (Ro). While evidence is found for a small but finite gravity wave emission from balanced flow in a single-layer model with large lateral shear and large Ro, a vertically resolved model with moderate velocity amplitudes appropriate to the interior ocean hardly shows any wave emission. Only when static instabilities generated by the shear instability of the balanced flow are allowed can a gravity wave signal similar to the ones reported in earlier studies be detected in the vertically resolved case. This result suggests a relatively small role of spontaneous wave emission in the classical sense of Lighthill radiation, and emphasizes the role of convective or symmetric instabilities during frontogenesis for the generation of internal gravity waves in the ocean and atmosphere.

Scattering of surface shallow water waves on a draining bathtub vortex

In the linear approximation we study long wave scattering on an axially symmetric flow in a shallow water basin with a drain in the center. This classical problem can be considered as a model of wave scattering on a rotating black hole. For the low frequencies analytic solutions are derived to describe both pure potential perturbations (surface gravity waves), and perturbations with nonzero potential vorticity. For moderate frequencies such solutions are obtained numerically and illustrated graphically. It is shown that there are two processes governing the dynamics of perturbations, namely, the scattering of incident gravity waves by central vortex, and the emission of gravity waves stimulated by the potential vorticity. Some aspects of their joint action are discussed.

Internal Gravity Wave Emission in Different Dynamical Regimes

AbstractWe aim to diagnose internal gravity waves emitted from balanced flow and investigate their role in the downscale transfer of energy. We use an idealized numerical model to simulate a range of baroclinically unstable flows to mimic dynamical regimes ranging from ageostrophic to quasigeostrophic flows. Wavelike signals present in the simulated flows, seen for instance in the vertical velocity, can be related to gravity wave activity identified by frequency and frequency–wavenumber spectra. To explicitly assign the energy contributions to the balanced and unbalanced (gravity) modes, we perform linear and nonlinear modal decomposition to decompose the full state variable into its balanced and unbalanced counterparts. The linear decomposition shows a reasonable separation of the slow and fast modes but is no longer valid when applied to a nonlinear system. To account for the nonlinearity in our system, we apply the normal mode initialization technique proposed by Machenhauer in 1977. Further, we assess the strength of the gravity wave activity and dissipation related to the decomposed modes for different dynamical regimes. We find that gravity wave emission becomes increasingly stronger going from quasigeostrophic to ageostrophic regime. The kinetic energy tied to the unbalanced mode scales close to Ro2 (or Ri−1), with Ro and Ri being the Rossby and Richardson numbers, respectively. Furthermore, internal gravity waves dissipate predominantly through small-scale dissipation, which emphasizes their role in the downscale energy transfer.

Spontaneous inertia–gravity wave emission in the differentially heated rotating annulus experiment

The source mechanism of inertia–gravity waves (IGWs) observed in numerical simulations of the differentially heated rotating annulus experiment is investigated. The focus is on the wave generation from the balanced part of the flow, a process presumably contributing significantly to the atmospheric IGW field. Direct numerical simulations are performed for an atmosphere-like configuration of the annulus and possible regions of IGW activity are characterised by a Hilbert-transform algorithm. In addition, the flow is separated into a balanced and unbalanced part, assuming the limit of a small Rossby number, and the forcing of IGWs by the balanced part of the flow is derived rigorously. Tangent-linear simulations are then used to identify the part of the IGW signal that is rather due to radiation by the internal balanced flow than to boundary-layer instabilities at the side walls. An idealised fluid set-up without rigid horizontal boundaries is considered as well, to investigate the effect of the identified balanced forcing unmasked by boundary-layer effects. The direct simulations of the realistic and idealised fluid set-ups show a clear baroclinic-wave structure exhibiting a jet–front system similar to its atmospheric counterparts, superimposed by four distinct IGW packets. The subsequent tangent-linear analysis indicates that three wave packets are radiated from the internal flow and a fourth one is probably caused by boundary-layer instabilities. The forcing by the balanced part of the flow is found to play a significant role in the generation of IGWs, so it supplements boundary-layer instabilities as a key factor in the IGW emission in the differentially heated rotating annulus.

Construction of Hamiltonian and Nambu Forms for the Shallow Water Equations

A systematic method to derive the Hamiltonian and Nambu form for the shallow water equations using the conservation for energy and potential enstrophy is presented. Different mechanisms, such as vortical flows and emission of gravity waves, emerge from different conservation laws for total energy and potential enstrophy. The equations are constructed using exterior differential forms and self-adjoint operators, and result in the sum of two Nambu brackets—one for the vortical flow and one for the wave-mean flow interaction—and a Poisson bracket representing the interaction between divergence and geostrophic imbalance. The advantage of this approach is that the Hamiltonian and Nambu forms can here be written in a coordinate-independent form.

Generation of Gravity Waves by Singular Potential Vorticity Disturbances in Shear Flows

Abstract The linear mechanism of generation of gravity waves by potential vorticity (PV) disturbances in flows with constant horizontal and vertical shears is studied. The case of the initial singular distribution of PV, in which the PV is localized in one coordinate and is periodic with respect to other coordinates, is considered. In a stratified rotating medium, such a distribution induces a vortex wave (continuous mode), the propagation of which is accompanied by the emission of gravity waves. To find the emission characteristics, a linearized system of dynamical equations is reduced to wave equations with sources that are proportional to the initial distributions of PV. The asymptotic solutions of the equations are constructed for small Rossby numbers (horizontal shear) and large Richardson numbers (vertical shear). When passing through the inertial levels symmetrically located with respect to a vortex source, the behavior of the solutions for wave amplitudes radically changes. Directly in the vicinity of the source, the solutions are of monotonic character, corresponding to a quasigeostrophic vortex wave. At long distances from the source, the solutions oscillate. The horizontal momentum flux and the Eliassen–Palm flux are estimated using asymptotic solutions. It is found that, within the indicated range of both Rossby and Richardson numbers, these fluxes are exponentially small: that is, the emission of waves is weak.

Understanding Instabilities of Tropical Cyclones and Their Evolution with a Moist Convective Rotating Shallow-Water Model

Abstract Instabilities of hurricane-like vortices are studied with the help of a rotating shallow-water model, including the effects of moist convection. Linear stability analysis demonstrates that dominant unstable modes are mixed Rossby–inertia–gravity waves. It is shown that, depending on fine details of the vorticity profile, a wavenumber selection of the instability may operate or not, leading in some cases to an unstable mode with a distinctively maximal growth rate and in other cases to an ensemble of unstable modes with close growth rates. Numerical simulations are performed in order to investigate nonlinear saturation of the instability and to understand the dynamical role of moisture. In agreement with previous studies, the authors confirm axisymmetrization of vorticity in the course of the development of the instability, which induces changes of intensity of the hurricane. In “dry” simulations, winds are intensified only inside the radius of maximum wind, while the maximum value of the wind decreases. “Moist precipitating” simulations (with and without evaporation) exhibit a net increase of winds, also at the radius of maximum wind, as compared to the dry simulations. Dynamical effects of moisture on the reorganization of the vortex and on the efficiency of inertia–gravity wave emission are quantified and shown to be considerable. Periodic bursts in the emission of waves related to the development of the unstable modes inside the vortex are evidenced, as well as the appearance of convectively coupled waves in the moist precipitating simulations with evaporation.

Gravity wave emission in an atmosphere-like configuration of the differentially heated rotating annulus experiment

AbstractA finite-volume model of the classic differentially heated rotating annulus experiment is used to study the spontaneous emission of gravity waves (GWs) from jet stream imbalances, which may be an important source of these waves in the atmosphere and for which no satisfactory parameterisation exists. Experiments were performed using a classic laboratory configuration as well as using a much wider and shallower annulus with a much larger temperature difference between the inner and outer cylinder walls. The latter configuration is more atmosphere-like, in particular since the Brunt–Väisälä frequency is larger than the inertial frequency, resulting in more realistic GW dispersion properties. In both experiments, the model is initialised with a baroclinically unstable axisymmetric state established using a two-dimensional version of the code, and a low-azimuthal-mode baroclinic wave featuring a meandering jet is allowed to develop. Possible regions of GW activity are identified by the horizontal velocity divergence and a modal decomposition of the small-scale structures of the flow. Results indicate GW activity in both annulus configurations close to the inner cylinder wall and within the baroclinic wave. The former is attributable to boundary layer instabilities, while the latter possibly originates in part from spontaneous GW emission from the baroclinic wave.

An Improved Weak Pressure Gradient Scheme for Single-Column Modeling

Abstract A new formulation of the weak pressure gradient approximation (WPG) is introduced for parameterizing large-scale dynamics in limited-domain atmospheric models. This new WPG is developed in the context of the one-dimensional, linearized, damped, shallow-water equations and then extended to Boussinesq and compressible fluids. Unlike previous supradomain-scale parameterizations, this formulation of WPG correctly reproduces both steady-state solutions and first baroclinic gravity waves. In so doing, this scheme eliminates the undesirable gravity wave resonance in previous versions of WPG. In addition, this scheme can be extended to accurately model the emission of gravity waves with arbitrary vertical wavenumber.

Dipolar modes in luminous red giants

Lots of information on solar-like oscillations in red giants has been obtained thanks to observations with CoRoT and Kepler space telescopes. Data on dipolar modes appear most interesting. We study properties of dipolar oscillations in luminous red giants to explain mechanism of mode trapping in the convective envelope and to assess what may be learned from the new data. Equations for adiabatic oscillations are solved by numerical integration down to the bottom of convective envelope, where the boundary condition is applied. The condition is based on asymptotic decomposition of the fourth order system into components describing a running wave and a uniform shift of radiative core. If the luminosity of a red giant is sufficiently high, for instance at M = 2 Msun greater than about 100 Lsun, the dipolar modes become effectively trapped in the acoustic cavity, which covers the outer part of convective envelope. Energy loss caused by gravity wave emission at the envelope base is a secondary or negligible source of damping. Frequencies are insensitive to structure of the deep interior.

Gravity Waves in a Horizontal Shear Flow. Part II: Interaction between Gravity Waves and Potential Vorticity Perturbations

Abstract Interaction among potential vorticity perturbations and propagating internal gravity waves in a horizontally sheared zonal flow is investigated. In the strong stratification limit, an initial vorticity perturbation weakly excites two propagating gravity waves while the density component of the potential vorticity perturbation is significantly amplified, potentially leading to convective collapse. If stratification is sufficiently weak, a strong coupling between vorticity perturbations and gravity waves is found and spontaneous gravity wave generation occurs. This coupling can be traced to the nonnormal interaction between the potential vorticity and gravity wave manifolds in the weak stratification limit. Vorticity perturbations amplify in energy due to downgradient Reynolds stress when their phase lines tilt against the shear and the large growth attained is transferred to propagating gravity waves. When the flow geometry is such that the excited gravity waves are confined in the vicinity of the vorticity perturbation by their trapping levels, an overall convective collapse of this region can be anticipated. On the other hand, when the flow geometry permits wave propagation, significant gravity wave emission occurs.

Decoupling of Balanced and Unbalanced Motions and Inertia–Gravity Wave Emission: Small versus Large Rossby Numbers

Abstract This paper provides a brief review of recent results on decoupling of fast [inertia–gravity wave (IGW)] and slow (vortex) motions at small Rossby numbers obtained in the framework of the geostrophic adjustment of localized perturbations. Special attention is paid to the IGW emission and its interpretation in the context of “spontaneous imbalance.” Several mechanisms that lead to spontaneous IGW emission and, thus, to violations of fast–slow splitting at large Rossby numbers are reviewed: Lighthill radiation, symmetric/inertial instability, and ageostrophic shear (Rossby–Kelvin) instability. New results on the saturation of symmetric instability and on the existence of Rossby–Kelvin instability in continuously stratified fluid are presented.

Instability of a stratified boundary layer and its coupling with internal gravity waves. Part 2. Coupling with internal gravity waves via topography

The aim of this paper is to show that the viscous shear instability identified in Part 1 is intrinsically coupled with internal gravity waves when a localized surface topography is present within a boundary layer. The coupling involves two aspects: receptivity and radiation. The former refers to excitation of shear instability modes by gravity waves, and the latter to emission of gravity waves by instability modes. Both physical processes are studied using triple-deck theory. In particular, the radiated gravity waves are found to produce a leading-order back action on the source, and this feedback effect, completely ignored in the acoustic analogy type of approach, is naturally taken into account by the triple-deck formalism. A by-product is that for certain incident angles, gravity waves are over-reflected by the boundary layer, i.e. the reflected waves are stronger than the incident waves.

Theory and numerics of gravitational waves from preheating after inflation

Preheating after inflation involves large, time-dependent field inhomogeneities, which act as a classical source of gravitational radiation. The resulting spectrum might be probed by direct detection experiments if inflation occurs at a low enough energy scale. In this paper, we develop a theory and algorithm to calculate, analytically and numerically, the spectrum of energy density in gravitational waves produced from an inhomogeneous background of stochastic scalar fields in an expanding universe. We derive some generic analytical results for the emission of gravity waves by stochastic media of random fields, which can test the validity/accuracy of numerical calculations. We contrast our method with other numerical methods in the literature, and then we apply it to preheating after chaotic inflation. In this case, we are able to check analytically our numerical results, which differ significantly from previous works. We discuss how the gravity-wave spectrum builds up with time and find that the amplitude and the frequency of its peak depend in a relatively simple way on the characteristic spatial scale amplified during preheating. We then estimate the peak frequency and amplitude of the spectrum produced in two models of preheating after hybrid inflation, which for some parameters may be relevant for gravity-wave interferometric experiments.

Momentum and Energy Transport by Gravity Waves in Stochastically Driven Stratified Flows. Part I: Radiation of Gravity Waves from a Shear Layer

Abstract In this paper, the emission of internal gravity waves from a local westerly shear layer is studied. Thermal and/or vorticity forcing of the shear layer with a wide range of frequencies and scales can lead to strong emission of gravity waves in the region exterior to the shear layer. The shear flow not only passively filters and refracts the emitted wave spectrum, but also actively participates in the gravity wave emission in conjunction with the distributed forcing. This interaction leads to enhanced radiated momentum fluxes but more importantly to enhanced gravity wave energy fluxes. This enhanced emission power can be traced to the nonnormal growth of the perturbations in the shear region, that is, to the transfer of the kinetic energy of the mean shear flow to the emitted gravity waves. The emitted wave energy flux increases with shear and can become as large as 30 times greater than the corresponding flux emitted in the absence of a localized shear region. Waves that have horizontal wavelengths larger than the depth of the shear layer radiate easterly momentum away, whereas the shorter waves are trapped in the shear region and deposit their momentum at their critical levels. The observed spectrum, as well as the physical mechanisms influencing the spectrum such as wave interference and Doppler shifting effects, is discussed. While for large Richardson numbers there is equipartition of momentum among a wide range of frequencies, most of the energy is found to be carried by waves having vertical wavelengths in a narrow band around the value of twice the depth of the region. It is shown that the waves that are emitted from the shear region have vertical wavelengths of the size of the shear region.

On the Forcing of Inertia–Gravity Waves by Synoptic-Scale Flows

Abstract Studies on the spontaneous emission of gravity waves from jets, both observational and numerical, have emphasized that excitation of gravity waves occurred preferentially near regions of imbalance. Yet a quantitative relation between the several large-scale diagnostics of imbalance and the excited waves is still lacking. The purpose of the present note is to investigate one possible way to relate quantitatively the gravity waves to diagnostics of the large-scale flow that is exciting them. Scaling arguments are used to determine how the large-scale flow may provide a forcing on the right-hand side of a wave equation describing the linear dynamics of the excited waves. The residual of the nonlinear balance equation plays an important role in this forcing.