Gravity Wave Modes Research Articles

Odd-parity gravity waves from the Regge–Wheeler gauge perspective in the f(R, T) theory

We mainly intend to discuss the odd-parity (or axial) modes of gravity (or gravitational) waves (GWs) in the Regge–Wheeler formalism. Since, there are plenty of astrophysical data that lead us to a space-time structure entered in a speedy expansion epoch, we perform our analysis in the f(R, T) theory of gravity, where the gravitational Lagrangian is written as an arbitrary function of the Ricci scalar R and the trace of the stress-energy tensor T, from the rainbow formalism of gravity perspective. In our study, we start with perturbing the background metric, background material distribution and the four-velocity components via the Regge–Wheeler gauge. Subsequently, formulating the corresponding field equations for both unperturbed and perturbed forms of the spatially flat conformal Friedmann–Lemaitre–Robertson–Walker metric, we solve them simultaneously to find out exact expressions of the unknown perturbation functions. Also, we focus our attention on Huygens’ principle to discuss additional features of the odd-parity modes of GWs.

Control of Low-Level Wind on the Diurnal Cycle of Tropical Coastal Precipitation

Abstract To understand how coastal precipitation is controlled by the low-level background wind, we performed comprehensive analysis using the 17-yr observations of the TRMM PR over the entire region of the tropics. We classified the data according to the direction (onshore or offshore) and strength of the cross-shore wind. Under weak winds, the contribution of the diurnal cycle to total precipitation is large, indicating that thermally forced precipitation with a symmetrical propagation pattern with opposite sign across the coastline is dominant. As the background wind strengthens, the contribution of the diurnal cycle reduces owing to the predominance of mechanical forcing; however, the effect of the diurnal cycle remains nonnegligible with an asymmetrical propagation pattern across the coastline. Using the linear theory of the sea–land-breeze circulation, we demonstrated that the difference in propagation is attributable to gravity waves excited by the land–ocean surface heating difference. Under weak winds, symmetrical diurnal phase propagation is caused by the two symmetrical modes of landward and seaward gravity waves. Under stronger background winds, in addition to the Doppler-shifted landward and seaward modes, waves propagating toward the upwind side in the flow-relative frame but with slow group velocity are advected to the downwind near the coastline, forming another mode that moves slowly in the downwind direction. The superposition of the three modes leads to asymmetrical propagation of precipitation with varying phase speed depending on the distance from the coastline.

A comparison of methods to balance geophysical flows

We compare a higher-order asymptotic construction for balance in geophysical flows with the method of ‘optimal balance’, a purely numerical approach to separating inertia–gravity waves from vortical modes. Both methods augment the linear geostrophic mode with dependent inertia–gravity wave mode contributions, the so-called slaved modes, such that the resulting approximately balanced states are characterized by very small residual wave emission during subsequent time evolution. In our benchmark setting – the single-layer rotating shallow water equations in the quasi-geostrophic regime – the performance of both methods is comparable across a range of Rossby numbers and for different initial conditions. Cross-balancing, i.e. balancing the model with one method and diagnosing the imbalance with the other, suggests that both methods find approximately the same balanced state. Our results also reinforce results from previous studies suggesting that spontaneous wave emission from balanced flow is very small. We further compare two numerical implementations of each of the methods: one pseudospectral, and the other a finite difference scheme on the standard C-grid. We find that a state that is balanced relative to one numerical scheme is poorly balanced for the other, independent of the method that was used for balancing. This shows that the notion of balance in the discrete case is fundamentally tied to a particular scheme.

A Multicloud Model for Coastal Convection

Coastal convection is often organized into multiple mesoscale systems that propagate in either direction across the coastline (i.e., landward and oceanward). These systems interact non-trivially with synoptic and intraseasonal disturbances such as convectively coupled waves and the Madden–Julian oscillation. Despite numerous theoretical and observational efforts to understand coastal convection, global climate models still fail to represent it adequately, mainly because of limitations in spatial resolution and shortcomings in the underlying cumulus parameterization schemes. Here, we use a simplified climate model of intermediate complexity to simulate coastal convection under the influence of the diurnal cycle of solar heating. Convection is parameterized via a stochastic multicloud model (SMCM), which mimics the subgrid dynamics of organized convection due to interactions (through the environment) between the cloud types that characterize organized tropical convection. Numerical results demonstrate that the model is able to capture the key modes of coastal convection variability, such as the diurnal cycle of convection and the accompanying sea and land breeze reversals, the slowly propagating mesoscale convective systems that move from land to ocean and vice-versa, and numerous moisture-coupled gravity wave modes. The physical features of the simulated modes, such as their propagation speeds, the timing of rainfall peaks, the penetration of the sea and land breezes, and how they are affected by the latitudinal variation in the Coriolis force, are generally consistent with existing theoretical and observational studies.

Stability of internal gravity wave modes: from triad resonance to broadband instability

A theoretical study is made of the stability of propagating internal gravity wave modes along a horizontal stratified fluid layer bounded by rigid walls. The analysis is based on the Floquet eigenvalue problem for infinitesimal perturbations to a wave mode of small amplitude. The appropriate instability mechanism hinges on how the perturbation spatial scale relative to the basic-state wavelength, controlled by a parameter $\mu$ , compares to the basic-state amplitude parameter, $\epsilon \ll 1$ . For $\mu ={O}(1)$ , the onset of instability arises due to perturbations that form resonant triads with the underlying wave mode. For short-scale perturbations such that $\mu \ll 1$ but $\alpha =\mu /\epsilon \gg 1$ , this triad resonance instability reduces to the familiar parametric subharmonic instability (PSI), where triads comprise fine-scale perturbations with half the basic-wave frequency. However, as $\mu$ is further decreased holding $\epsilon$ fixed, higher-frequency perturbations than these two subharmonics come into play, and when $\alpha ={O}(1)$ Floquet modes feature broadband spectrum. This broadening phenomenon is a manifestation of the advection of small-scale perturbations by the basic-wave velocity field. By working with a set of ‘streamline coordinates’ in the frame of the basic wave, this advection can be ‘factored out’. Importantly, when $\alpha ={O}(1)$ PSI is replaced by a novel, multi-mode resonance mechanism which has a stabilising effect that provides an inviscid short-scale cut-off to PSI. The theoretical predictions are supported by numerical results from solving the Floquet eigenvalue problem for a mode-1 basic state.

Multiwave Structure of Traveling Ionospheric Disturbances Excited by the Tonga Volcanic Eruptions Observed by a Dense GNSS Network in China

AbstractWe used dense global navigation satellite system data from China to track the propagation of traveling ionospheric disturbances (TIDs) triggered by the 2022 January 15 Tonga volcanic eruption. We identified two TIDs originating from the eruption. One, which has been reported widely by a number of recent investigations, had a velocity of ∼361 m/s. However, another long‐distance propagating TID with a velocity of ∼264 m/s has not been widely discussed. The velocities of these TIDs coincide with previous simulation results of gravity‐wave L0 and L1 modes. We propose that these TIDs were caused by the L0 and L1 ducted modes of gravity waves excited by the volcanic eruption. However, the L1 mode is usually negligible due to its weak amplitude in comparison with that of the L0 mode. The enormous energy release resulted in a stronger amplitude of the L1 mode, which induced a detectable TID in the ionosphere.

The Tropical Diurnal Cycle under Varying States of the Monsoonal Background Wind

Abstract The impact of the environmental background wind on the diurnal cycle near tropical islands is examined in observations and an idealized model. Luzon Island in the northern Philippines is used as an observational test case. Composite diurnal cycles of CMORPH precipitation are constructed based on an index derived from the first empirical orthogonal function (EOF) of ERA5 zonal wind profiles. A strong precipitation diurnal cycle and pronounced offshore propagation in the leeward direction tends to occur on days with a weak, offshore prevailing wind. Strong background winds, particularly in the onshore direction, are associated with a suppressed diurnal cycle. Idealized high-resolution 2D Cloud Model 1 (CM1) simulations test the dependence of the diurnal cycle on environmental wind speed and direction by nudging the model base state toward composite profiles derived from the reanalysis zonal wind index. These simulations can qualitatively replicate the observed development, strength, and offshore propagation of diurnally generated convection under varying wind regimes. Under strong background winds, the land–sea contrast is reduced, which leads to a substantial reduction in the strength of the sea-breeze circulation and precipitation diurnal cycle. Weak offshore prevailing winds favor a strong diurnal cycle and offshore leeward propagation, with the direction of propagation highly sensitive to the background wind in the lower free troposphere. Offshore propagation speed appears consistent with density current theory rather than a direct coupling to a single gravity wave mode, though gravity waves may contribute to a destabilization of the offshore environment.

Improving ionospheric predictability requires accurate simulation of the mesospheric polar vortex

The mesospheric polar vortex (MPV) plays a critical role in coupling the atmosphere-ionosphere system, so its accurate simulation is imperative for robust predictions of the thermosphere and ionosphere. While the stratospheric polar vortex is widely understood and characterized, the mesospheric polar vortex is much less well-known and observed, a short-coming that must be addressed to improve predictability of the ionosphere. The winter MPV facilitates top-down coupling via the communication of high energy particle precipitation effects from the thermosphere down to the stratosphere, though the details of this mechanism are poorly understood. Coupling from the bottom-up involves gravity waves (GWs), planetary waves (PWs), and tidal interactions that are distinctly different and important during weak vs. strong vortex states, and yet remain poorly understood as well. Moreover, generation and modulation of GWs by the large wind shears at the vortex edge contribute to the generation of traveling atmospheric disturbances and traveling ionospheric disturbances. Unfortunately, representation of the MPV is generally not accurate in state-of-the-art general circulation models, even when compared to the limited observational data available. Models substantially underestimate eastward momentum at the top of the MPV, which limits the ability to predict upward effects in the thermosphere. The zonal wind bias responsible for this missing momentum in models has been attributed to deficiencies in the treatment of GWs and to an inaccurate representation of the high-latitude dynamics. In the coming decade, simulations of the MPV must be improved.

GPU-Accelerated Computation of EM Scattering of a Time-Evolving Oceanic Surface Model II: EM Scattering of Actual Oceanic Surface

Based on marine environmental factors of different sea areas, a high-performance sea clutter time series modeling algorithm for the real sea surface is developed to study the amplitude mean and Doppler spectrum characteristics of sea clutter. The European Centre for Medium-Range Weather Forecasts (ECMWF) data set (ERA-Interim) and ESA’s soil moisture and ocean salinity (SMOS) data set are utilized to establish databases of different marine environmental factors. Combined with the mixed spectrum model, the geometric fine structure of wind-driven sea surface with swell superposition is established by using the double-superposition method (DSM) and comprehensively considering small-scale capillary ripples, large-scale gravity waves and swell. A triangle facet-based sea clutter series modeling algorithm is developed, in which the quasi-specular scattering based on a triangle and the scattering based on gravity wave modulation capillary spectrum are calculated, respectively, and compared with the measured results. For high-resolution radar, dynamic sea surface modeling and sea clutter calculation are very time consuming. In this paper, the Tesla K80 GPU manufactured by NVIDIA in Santa Clara, Computed Unified Device architecture (CUDA) high-performance parallel technology and some optimization strategies are adopted to improve the efficiency of sea clutter modeling. The results can be used to analyze the distribution characteristics of marine factors, the average amplitude and Doppler characteristics of sea clutter in different sea areas.

Gravity Waves in Titan's Atmosphere: A Comparison Between Linearized Wave Model Calculations and HASI Observations

AbstractThe Huygens Atmospheric Structure Instrument (HASI) detected wavelike temperature fluctuations from 500 to 1,000 km on Titan. However, these fluctuation structures have not been satisfactorily reproduced by any theoretical model to date. In this study, we construct a full‐wave model to simulate the observed gravity wave structure. The model includes dissipation processes due to molecular viscosity, which increases exponentially with altitude, and eddy viscosity, which dominates the lower atmosphere. Using our model, we reproduced the observed temperature perturbations with the superposition of two gravity wave modes, one with λz = 600 km and λx = 1,600 km while the other with λz = 140 km and λx = 8,000 km. We estimate the thermal effects introduced by gravity waves and find that gravity waves below 900 km may significantly modify temperature structure of the upper atmosphere by tens of Kelvins. The wave‐induced thermal effect is sensitive to the eddy viscosity, which controls the dissipation and thermal conductivity below 900 km. When the eddy viscosity is increased by a factor of five, the thermal effect of gravity waves changes from −89 K cooling to nearly zero. This heating mechanism may contribute to the large temperature variability of 60 K in Titan's upper atmosphere.

A single-mode approximation for gravity waves in the thermosphere

In previous work (Knight et al., 2019) a multilayer Fourier method was introduced for obtaining solutions for a partial differential equation (PDE) associated with a dispersion relation for linear gravity waves in a vertically varying, anelastic, nonhydrostatic, viscous, and thermally diffusive atmosphere over some altitude range, given boundary conditions that allow waves to enter at the lower boundary and exit at the top. The previous work described an exact solution method for the dispersion-relation PDE using all wave modes. The current work describes a type of approximate solution, based on a single upgoing gravity-wave mode for each Fourier component, which is computationally cheaper and simpler to implement. Two different approaches to defining the single-mode solution are presented, one based on the Wentzel–Kramers–Brillouin (WKB) method and the other based on a simplified version of the multilayer approximation. The two approaches are shown to be mathematically equivalent. The accuracy of the single-mode approximation is investigated through comparison with the all-mode solution for a realistic example in which gravity waves generated by a convective storm in the troposphere propagate into the upper thermosphere and for which the single-mode approximation gives reasonably accurate results. It is necessary to include imaginary frequency shifts in some Fourier components in order for the different types of modes (e.g., upgoing vs. downgoing and gravity-wave vs. dissipative) to be well-defined in the presence of molecular viscosity. A systematic approach to determining the smallest possible imaginary frequency shift for any given Fourier component is introduced. The new method efficiently suppresses a specific type of numerical artifact associated with large imaginary frequency shifts.

Modulation of surface gravity waves by internal waves

AbstractInternal waves are a regular feature of the open ocean and coastal waters. As a train of internal waves propagate, their surface induced currents modulate the surface waves, generating a characteristic rough and smooth banded structure. While the surface expression of these internal waves is well known and has been observed from a variety of remote sensing instruments, direct quantitative observations of the directional properties of the surface gravity wave field modulated by an internal wave remain sparse. In this work, we report on a comprehensive field campaign conducted off the coast of Point Sal, CA in September 2017. Using a unique combination of airborne remote sensing observations, along with in-situ surface and subsurface measurements, we investigate and quantify the interaction between surface gravity and internal wave processes. We find that surface waves are significantly modulated by the currents induced by the internal waves. Through novel observations of ocean topography, we characterize the rapid modification of the directional and spectral properties of surface waves over very short spatial scales (O(100)m or less). Over a range of wavelengths (3-9m waves), geometrical optics and wave action conservation predictions show good agreement with the observed wavenumber spectra in smooth and rough regions of the modulated surface waves. If a parameterization of wave action source terms is used, good agreement is found over a larger range of wavenumbers, down to 4rad/m. These results elucidate properties of surface waves interacting with a submesoscale ocean current, and should provide insight into more general interactions between surface waves and the fine scale structure of the upper ocean.

The role of viscoelastic foundation on flexural gravity wave blocking in shallow water

A hydroelastic model is developed to study the interaction of linear long gravity waves with a very large floating flexible plate resting on a viscoelastic foundation, which is based on the Kelvin–Voigt model. Flexural gravity wave blocking occurs for specific values of the compressive force in the absence of viscous damping. During wave blocking, the group velocity vanishes, and mode swapping occurs. Within wave blocking and plate buckling limit in the presence of compressive force, three distinct propagating modes occur in the absence of viscous damping. Moreover, the study reveals that irrespective of the values of viscous damping constant, the blocking/buckling points shift to a higher wavenumber with an increase in the value of elastic foundation constant. On the other hand, the flexural gravity wave modes become complex in the presence of a viscoelastic foundation. The complex wave modes are classified as predominant progressive wave modes and rapidly decaying modes. In the presence of viscous damping, wave blocking does not happen before the buckling limit of the compressive force. However, the phase velocity vanishes, and the group velocity becomes continuous irrespective of the value of non-zero viscous damping at the buckling limit for the compressive force. The detailed behavior of the roots of the dispersion equation and the mode shapes are illustrated through contour plots and by analyzing the roots’ loci. Furthermore, plate deflections are exhibited for different wave and structural parameters.

Spatiotemporal structure of Baltic free sea level oscillations in barotropic and baroclinic conditions from hydrodynamic modelling

Abstract. Free sea level oscillations in barotropic and baroclinic conditions were examined using numerical experiments based on a 3-D hydrodynamic model of the Baltic Sea. In a barotropic environment, the highest amplitudes of free sea level oscillations are observed in the northern Gulf of Bothnia, eastern Gulf of Finland, and south-western Baltic Sea. In these areas, the maximum variance appears within the frequency range corresponding to periods of 13–44 h. In a stratified environment, after the cessation of meteorological forcing, water masses relax to the equilibrium state in the form of mesoscale oscillations at the same frequencies as well as in the form of rapidly decaying low-frequency (seasonal) oscillations. The total amplitudes of free baroclinic perturbations are significantly larger than those of barotropic perturbations, reaching 15–17 cm. Contrary to barotropic, oscillations in baroclinic conditions are strongly pronounced in the deep-water areas of the Baltic Sea proper. Specific spatial patterns of amplitudes and phases of free barotropic and baroclinic sea level oscillations identified them as progressive–standing waves representing barotropic or baroclinic modes of gravity waves and topographic Rossby waves.

Fractality of metal pad instability threshold in rectangular cells

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A generalized wave-vortex decomposition for rotating Boussinesq flows with arbitrary stratification

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Newly Identified Instabilities Enhance Atmospheric Turbulence

New high-resolution imaging and modeling reveal the first evidence of enhanced turbulence due to gravity wave modulation of Kelvin-Helmholtz instabilities.

Flutter and resonances of a flag near a free surface

We investigate the effects of a nearby free surface on the stability of a flexible plate in axial flow. Confinement by rigid boundaries is known to affect flag flutter thresholds and fluttering dynamics significantly, and this work considers the effects of a more general confinement involving a deformable free surface. To this end, a local linear stability is proposed for a flag in axial uniform flow and parallel to a free surface, using one-dimensional beam and potential flow models to revisit this classical fluid–structure interaction problem. The physical behaviour of the confining free surface is characterized by the Froude number, corresponding to the ratio of the incoming flow velocity to that of the gravity waves. After presenting the simplified limit of infinite span (i.e. two-dimensional problem), the results are generalized to include finite-span and lateral confinement effects. In both cases, three unstable regimes are identified for varying Froude number. Rigidly-confined flutter is observed for low Froude number, i.e. when the free surface behaves as a rigid wall, and is equivalent to the classical problem of the confined flag. When the flow and wave velocities are comparable, a new instability is observed before the onset of flutter (i.e. at lower reduced flow speed) and results from the resonance of a structural bending wave and one of the fundamental modes of surface gravity waves. Finally, for large Froude number (low effect of gravity), flutter is observed with significant but passive deformation of the free surface in response of the flag’s displacement.

Streaming controlled by meniscus shape

Surface waves called meniscus waves often appear in systems that are close to the capillary length scale. Since the meniscus shape determines the form of the meniscus waves, the resulting streaming circulation has features distinct from those caused by other capillary–gravity waves recently reported in the literature. In the present study, we produce symmetric and antisymmetric meniscus shapes by controlling boundary wettability and excite meniscus waves by oscillating the meniscus vertically. The symmetric and antisymmetric configurations produce different surface capillary–gravity wave modes and streaming flow structures. The root-mean-square speed of the streaming circulation increases with the second power of the forcing amplitude in both configurations. The flow symmetry of streaming circulation is retained under the symmetric meniscus, while it is lost under the antisymmetric meniscus. The streaming circulation pattern beneath the meniscus observed in our experiments is qualitatively explained using the method introduced by Nicolas & Vega (Fluid Dyn. Res., vol. 32 (4), 2003, pp. 119–139) and Gordillo & Mujica (J. Fluid Mech., vol. 754, 2014, pp. 590–604).

Optimal balance for rotating shallow water in primitive variables

ABSTRACT Optimal balance is a near-optimal computational algorithm for nonlinear mode decomposition of geophysical flows into balanced and unbalanced components. It was first proposed as “optimal potential vorticity balance” by Viúdez and Dritschel [J. Fluid Mech., 2004, 521, 343] in the specific setting of semi-Lagrangian potential vorticity-based numerical codes. Later, it was recognised as an instance of the more general principle of adiabatic invariance of fast degrees of motion under slow perturbations. From this point of view, the system is slowly deformed from a linearised configuration to the full nonlinear dynamics. In the former, linear analysis yields an exact separation of balanced and unbalanced flow. In the latter, a given base-point coordinate, e.g. the height or potential vorticity field, can be matched. This formulation leads to a boundary value problem in time. In this paper, we show that this more general viewpoint leads to practical implementations of optimal balance on top of a primitive variables (here, velocity-height variables) numerical code. We identify preferred choices for several design parameters. The most critical choices concern the linear projector onto the slow modes at the linear-end boundary and the choice of base-point coordinate at the nonlinear end. We find that, even though the evolutionary model is formulated in primitive variables, potential vorticity based end-point conditions are advantageous. In particular, the only universally robust linear projector is the oblique projector onto the Rossby modes along the gravity-wave modes, which can be interpreted as the distinct non-orthogonal projector onto the Rossby modes that preserves the linear potential vorticity. Hence, the projector can be formulated as an elliptic partial differential equation which holds promise for using the method to produce an accurate nonlinear mode decomposition for more general models without the need to resort to asymptotic analysis.