Gravity Waves Research Articles

Analysis of edge stress of combined shell under internal waves

Internal wave is essentially a gravity wave induced by the layered structure of water (e.g., density stable layering), with its maximum amplitude occurring within the ocean. Similar to surface waves, internal waves have significant influence on the strength and stability of a submerged body as an external factor. Meanwhile, combined shells are exposed to complicated loads under internal waves, and edge stress is dominant. In this study, the edge stresses of combined shell (typical hemisphere–cylinder combined shell and unfolded sphere–cylinder combined shell) under internal waves were analyzed. Indeed, a semi-empirical, semi-theoretical formula for the edge stress of combined shells (typical hemisphere–cylinder combined shell and unfolded sphere–cylinder combined shell) has been proposed. In this study, the semi-empirical, semi-theoretical formula was corrected by introducing internal wave loads, with the depth of the internal wave taken into consideration. In addition, the corrected formula was verified by finite element analysis, and a simplified equation for the calculation of edge stress of the combined shell under internal waves was developed, with errors in a rational range.

Optical fibre sensing of turbulent-frequency motions in the oceanic environment

Observations of turbulence in the oceanic environment are sparse, with very few cases of coherent measurements with significant spatio-temporal extent due primarily to limitations of current observational tools. Here we propose submarine cables with embedded optical fibres as a potential solution to fill this observational gap, and utilise a recent 12-h observational optical fibre data set from a fast-flowing tidal channel to demonstrate such potential. Firstly, the presence of turbulent-scale signals driven by flow-topography interaction is shown at frequencies of 1 Hz and higher. These signals are consistent with the timing of the tidal flow as recorded by a nearby conventional sensor. Secondly, we show the presence of surface gravity waves with periods of 10 s, which are tight in frequency space further offshore but leak energy into the turbulent frequency range on parts of the cable closer to shore. This is compatible with shoreward-propagating surface waves that break in shallow water. Finally, we fit a theoretical spectral structure to the observations to show that much of the collected data (i) has a spectral slope that is consistent with the turbulent inertial subrange, and (ii) has a range of spectral energy consistent with that expected from turbulence generation by bottom drag acting on the tidal flow. In combination, these results highlight the potential for optical fibre sensing of turbulence, and call for a targeted experiment to characterise the fibre’s turbulence-sensing capabilities.

Establishing patterns of change in the coefficients of reflection, transmission, and dissipation of wave energy depending on parameters of a permeable vertical wall

The object of research is permeable vertical walls (breakwaters) with different degrees of permeability. This paper reports the results of experimental research into the interaction of gravity waves with models of permeable vertical walls (breakwaters), which were formed from cylindrical piles of circular cross-section. With the help of visual and instrumental studies, the features of interaction of surface gravity waves with permeable vertical walls of different permeability have been identified. The degree of wave transformation by these walls was also determined in the form of reflection, transmission, and dissipation coefficients of wave energy. It was established that with a decrease in the permeability of the vertical wall and an increase in the steepness of the initial wave and a decrease in its period, the height of the reflected wave increased. The pattern of the transmitted wave height had the opposite trend. It was determined that the wave reflection coefficient increased with a decrease in the permeability of the vertical wall and the steepness of the initial wave. The wave transmission coefficient had the opposite trend, namely, it increased with increasing wall permeability and with decreasing steepness of the initial wave. The gravity wave energy dissipation coefficient decreased with increasing vertical wall permeability, but for waves with a significant steepness hi/λ>0.038, a decrease in the wave energy dissipation coefficient was observed for walls with low permeability and the appearance of extreme values of this coefficient. Thus, features in the interaction of surface gravity waves with permeable vertical walls (breakwaters) of different permeability have been researched and the degree of wave transformation by these walls has been determined, which could make it possible to effectively design and operate permeable vertical walls as coastal protection structures

Dependence of dense filament frontogenesis in a hydrostatic model

In this study, a hydrostatic model - the Navy Coastal Ocean Model (NCOM) is used to analyze the temporal evolution of a cold filament under moderate wind (along / cross filament) and surface cooling forcing conditions. The experimental framework adhered to the setup used in large eddy simulations by Sulllivan and McWilliams (2018). For each forcing scenario, the impact of horizontal resolutions is systematically explored through varies model resolutions of 100 m, 50 m, and 20 m; and the influence of horizontal mixing is investigated by adjusting the Smagorinsky constant within the Smagorinsky horizontal mixing scheme. The role of surface gravity waves is also assessed by conducting experiments both with and without surface wave forcing.The outcomes of our study revealed that while the hydrostatic model is able to predict the correct characteristics/physical appearance of filament frontogenesis, it fails to capture the precise dynamics of the phenomenon. Horizontal mixing parameterization in the model was found to have marginal effect on frontogenesis, and the frontal arrest is controlled by the model's subgrid-scale artificial regularization procedure instead of horizontal shear instability. Consequently, higher resolution is corresponding to stronger frontogenesis in the model. Thus, whether the hydrostatic model can produce realistic magnitude of frontogenesis is purely dependent on the characteristic of the front/filament simulated and model resolution. Moreover, examination of the parameterized effect of surface gravity wave forcing through vertical mixing unveiled a limited impact on frontogenesis, suggesting that the parameterization falls short in representing the real physics of wave-front interaction.

Oscillations of a fluid in a circular cylinder with bottom elevation

The problem of standing waves in a circular cylindrical vessel with an elevation on the bottom is formulated and numerically solved in the long wave approximation using an accelerated convergence algorithm. As a result of the calculations, the natural frequency of the fundamental wave mode is determined with a high accuracy. To compare the theoretical results, new experimental data on the excitation of standing surface gravity waves in a circular cylindrical vessel with parabolic and conical elevations at the bottom are presented. It is shown that the calculated and measured natural frequencies of the fundamental wave mode in vessels with the profiled bottom coincide between themselves.

Modulational instability and collapse of internal gravity waves in the atmosphere.

Nonlinear two-dimensional (IGWs) in the atmospheres of the Earth and the Sun are studied. The resulting two-dimensional nonlinear equationhas the form of a generalized nonlinear Schrödinger equationwith nonlocal nonlinearity, that is, when the nonlinear response depends on the wave intensity at some spatial domain. The modulation instability of IGWs is predicted, and specific cases for the Earth's atmosphere are considered. In a number of particular cases, the instability thresholds and instability growth rates are analytically found. Despite the nonlocal nonlinearity, we demonstrate the possibility of critical collapse of IGWs due to the scale homogeneity of the nonlinear term in spatial variables.

The Observation of Traveling Ionospheric Disturbances Using the Sanya Incoherent Scatter Radar

In this study, we used the Sanya Incoherent Scatter Radar (SYISR) to observe the altitude profiles of traveling ionospheric disturbances (TIDs) during a moderate magnetic storm from 13 to 15 March 2022. Three TIDs were recorded, including two large-scale TIDs (LSTIDs) and one medium-scale TID (MSTID). These LSTIDs occurred during the storm recovery phase, characterized by periods of ~110–155 min, downward phase velocities of 22–60 m/s, and a relative amplitude of 17–25%. A nearly vertical front was noted at ~350–550 km, differing from AGW theory predictions. This structure is more attributed to the combined effects of sunrise-induced electron density changes and pre-sunrise uplift. Moreover, GNSS observations linked this LSTID to high-latitude origins, indicating a connection to polar magnetic storm excitation. However, the second LSTID was observed at lower altitudes (150–360 km) with a higher elevation angle (~17°). This LSTID, observed by the SYISR, was absent in the GNSS data from mainland China and Japan, suggesting a potential local source. The MSTID exhibited a larger relative amplitude of 29–36% at lower altitudes (130–210 km) with severe upward attenuation. The MSTID may be related to atmospheric gravity waves from the lower atmosphere. AGWs are considered to be the perturbation source for this MSTID event.

Dynamics and Structure of Periodic Flows: Ligaments, Gravity and Acoustic Waves

Dynamics and Structure of Periodic Flows: Ligaments, Gravity and Acoustic Waves

The de Broglie-Einstein-Rosen gravitational wave

de Broglie gravitational waves are solutions of the linearized Einstein's field equations in vacuum, with intriguing properties. They are axially symmetric and have an effective mass, which is responsible for longitudinal effects that are absent in standard gravity waves. Moreover, they represent a classical realization of a form of dynamics proposed for quantum particles by de Broglie one hundred years ago. In this paper we will show that this perturbation field can be obtained, apart from a proportionality constant, in the weak field limit of a particular Einstein-Rosen field, which we call the de Broglie-Einstein-Rosen wave. Some properties of this exact solution are also discussed.

Gravity Wave Momentum Fluxes from 1 km Global ECMWF Integrated Forecast System

Progress in understanding the impact of mesoscale variability, including gravity waves (GWs), on atmospheric circulation is often limited by the availability of global fine-resolution observations and simulated data. This study presents momentum fluxes due to atmospheric GWs extracted from four months of an experimental “nature run", integrated at a 1 km resolution (XNR1K) using the Integrated Forecast System (IFS) model. Helmholtz decomposition is used to compute zonal and meridional flux of vertical momentum from ~1.5 petabytes of data; quantities often emulated by climate model parameterization of GWs. The fluxes are validated using ERA5 reanalysis, both during the first week after initialization and over the boreal winter period from November 2018 to February 2019. The agreement between reanalysis and IFS demonstrates its capability to generate reliable flux distributions and capture mesoscale dynamic variability in the atmosphere. The dataset could be valuable in advancing our understanding of GW-planetary wave interactions, GW evolution around atmospheric extremes, and as high-quality training data for machine learning (ML) simulation of GWs.

Very Long-periodic Pulsations Detected Simultaneously in a White-light Flare and Sunspot Penumbra

We investigate the origin of very long-periodic pulsations in the white-light emission of an X6.4 flare on 2024 February 22 (SOL2024-02-22T22:08), which occurred at the edge of a sunspot group. The flare white-light fluxes reveal four successive and repetitive pulsations, which are simultaneously measured by the Helioseismic and Magnetic Imager and the White-light Solar Telescope. A quasi-period of 8.6−1.9+1.5 minutes, determined by the Morlet wavelet transform, is detected in the visible continuum channel. The modulation depth, which is defined as the ratio between the oscillatory amplitude and its long-term trend, is smaller than 0.1%, implying that the quasi-periodic pulsation (QPP) feature is a weak wave process. Imaging observations show that the X6.4 flare occurs near a sunspot group. Moreover, the white-light brightening is located in sunspot penumbra, and a similar quasi-period of about 8.5 −1.8+1.6 minutes is identified in one penumbral location of the nearest sunspot. The map of Fourier power distribution suggests that a similar periodicity is universally existing in most parts of the penumbra that is close to the penumbral–photospheric boundary. Our observations support the scenario that the white-light QPP is probably modulated by the slow-mode magnetoacoustic gravity wave leaking from the sunspot penumbra.

Effect of atmospheric density stratification on the generation of water waves by wind

The critical level instability mechanism for the generation of water waves by wind is re-examined for the situation when the atmosphere is density stratified. The density stratification is confined to the middle and upper atmosphere and then two cases are investigated. In case (A) no internal gravity waves are generated in the upper atmosphere and the effect of the density stratification is very small. In case (B) vertically propagating internal gravity waves form in the upper atmosphere and travel to infinity causing an energy loss, thus inhibiting the critical level instability in the lower atmosphere. Both cases are examined quantitatively for a logarithmic wind shear profile.

On geomagnetic and ionospheric variations after the strong eruption of Shiveluch volcano 2023

Ground-based magnetometers and vertical ionospheric sounding stations were used to record specific variations in the geomagnetic field caused by disturbances in the current systems of the lower ionosphere and the electron density of the upper ionosphere after a strong volcanic eruption in Kamchatka (Russia) on April 10, 2023. Analysis of the measurement results of two series of explosions showed that the impact on the lower ionosphere is carried out through both seismic Rayleigh waves (which are a source of acoustic waves propagating into the ionosphere), and atmospheric internal gravity waves generated by explosions. At distances from the source of up to a thousand kilometers, a repeatability of the pattern of ionospheric disturbances was discovered after each of the six volcanic explosions. At larger distances in the ionosphere, signals from acoustic waves caused by Rayleigh waves are clearly recorded, and isolating signals from atmospheric internal waves is difficult due to the influence of disturbances from other external sources.

The effect of vertical temperature gradient on the equivalent depth in thin atmospheric layers

AbstractThe equivalent depth of an atmospheric layer is of importance in determining the phase speed of gravity waves and characterizing wave phenomena. The value of the equivalent depth can be obtained from the eigenvalues of the vertical structure equation (the vertical part of the primitive equations) where the mean temperature profile is a coefficient. Both numerical solutions of the vertical structure equation and analytical considerations are employed to calculate the equivalent depth, , as a function of the atmospheric layer's thickness, . Our solutions for layers of thickness 100 2000 m show that for baroclinic modes, can be over two orders of magnitudes smaller than . Analytic expressions are derived for in layers of uniform temperature and numerical solutions are derived for layers in which the temperature changes linearly with height. A comparison between the two cases shows that a slight temperature gradient (of say 0.65 K across a 100 m layer) decreases by a factor of 3 (but can reach a factor of 10 for larger gradients) compared with its value in a layer of uniform temperature, while a change of 10 K in the layer's uniform temperature hardly changes . The baroclinic mode exists in all combinations of boundary conditions top and bottom while the barotropic mode only exists when the vertical velocity vanishes at both boundaries of the layer.

Characteristics of monochromatic gravity waves in the mesosphere observed by Rayleigh lidar above Logan, Utah

Atmospheric gravity wave (AGW) characteristics were examined using Rayleigh lidar data collected over a period spanning 11 years above Logan, UT (41.7°N, 111.8°W), over an altitude range of 45–90 km. Variations of the relative density perturbations obtained with 3-km vertical resolution and 10-min temporal resolution are used to identify the presence of monochromatic gravity wave features throughout the mesosphere. The measured vertical wavelengths λz ranged over 6–19 km with 12–14 km the most prevalent and the measured wave period τ ranged over 2–8 h with 5–6 h the most prevalent. The values of λz, τ and mean wind velocity u were used to infer vertical phase velocities cz, horizontal wavelengths λx, horizontal phase velocities cx and horizontal distances to the source region x. There appears to be a clear seasonal dependence in cz, τ, cx, λx, and x but not in λz. The cz values maximize in summer, τ and x maximize in winter whereas cx and λx, maximize in winter and summer but minimize in spring and autumn. The values of x ranged over 1300–5000 km for waves at 60 km and ∼2000–7500 km for waves at 90 km. The source of these AGWs is, thus, far away. Furthermore, for one of these monochromatic waves to exist all night or appear to extend over 45–90 km, it has to originate from a very extended region and persist for a long time.

Non-local gravity wave turbulence in presence of condensate

The $k^{-23/6}$ wave action spectrum with an inverse cascade is one of the fundamental Kolmogorov–Zakharov solutions for gravity wave turbulence, which is part of the citation for the Dirac Medal in 2003. Instead of confirming this solution, however, several existing simulations and experiments suggest a spectrum of $k^{-3}$ in set-ups corresponding to the inverse cascade. We provide a theoretical explanation for the latter, considering the condensate that naturally forms in finite domains of experiments/simulations. Our new theory hinges on: (1) derivation of a spectral diffusion equation when non-local interactions with the condensate become dominant, for the first time systematically formulated for quartet-interaction systems; and (2) careful analysis of the asymptotics of interaction coefficient with a remarkable cancellation of all leading-order terms.

A Puzzling Quasi‐Periodic Variability in the Tropical Middle Atmosphere

AbstractThe Quasi‐Biennial Oscillation and the Semiannual Oscillation have been identified to be the leading modes of variability in the tropical middle atmosphere. With reanalysis data and independent rocket soundings from a low latitude site, we report the existence of yet another variability in the tropical lower mesosphere which is primarily evident as easterly bursts in zonal winds during the months of May‐July. It occurs with a variable interval of 2–5 yrs in the late 20th century and 7–9 yrs in the early 21st century. These Quasi‐Periodic Easterly Bursts are found to have remote influences on the Antarctic polar vortex as well as residual circulation in the lower mesosphere. We identify a potential causative mechanism for the easterly bursts that involve enhanced cross equatorial advection of momentum as well as gravity wave drag. A close association with Quasi Biennial Oscillation winds is observed, however, cause of the observed periodicity remains elusive.

The Climatology of Gravity Waves over the Low-Latitude Region Estimated by Multiple Meteor Radars

Atmospheric gravity waves (GWs) can strongly modulate middle atmospheric circulation and can be a significant factor for the coupling between the lower atmosphere and the middle atmosphere. GWs are difficult to resolve in global atmospheric models due to their small scale; thus, GW observations play an important role in middle atmospheric studies. The climatology of GW variance and momentum in the low-latitude mesosphere and lower thermosphere (MLT) region are revealed using multiple meteor radars, which are located at Kunming (25.6°N, 103.8°E), Sanya (18.4°N, 109.6°E), and Fuke (19.5°N, 109.1°E). The climatology and longitudinal variations in GW momentum fluxes and variance over the low-latitude region are reported. The GWs show strong seasonal variations and can greatly control the mesospheric horizontal winds via modulation of the quasi-geostrophic balance and momentum deposition. The different GW activities between Kunming and Sanya/Fuke are possibly consistent with the unique prevailing surface winds over Kunming and the convective system over the Tibetan Plateau according to the European Centre for Medium-Range Weather Forecasts (ECMWF), Reanalysis v5 (ERA5) data, and outgoing longwave radiation (OLR) data. These findings provide insight for better understanding the coupling between the troposphere and mesosphere.

Augmented Four‐Dimensional Mesosphere and Lower Thermosphere Wind Field Reconstruction via the Physics‐Informed Machine Learning Approach HYPER

AbstractThe mesosphere and lower thermosphere (MLT) is a fluid framework whose multiscale dynamics is determined by a superposition of non‐linear processes and by the interplay of gravity waves and turbulent motions. A thorough comprehension of this atmospheric region requires substantial observational infrastructure, needed to resolve and disentangle its complex dynamics. State‐of‐the‐art observational methods struggle to accurately capture mesoscale dynamics due to the inherent difficulty to perform observations at MLT altitudes. A majority of the observational methods rely on assumptions such as homogeneity, smoothness of the prognostic fields, or zero vertical wind velocities, which may not hold in the upper atmosphere at the mesoscales. In this study, we introduce a novel machine learning‐based approach HYPER (HYdrodynamic Point‐wise Environment Reconstructor), designed to characterize MLT dynamics. HYPER utilizes a physics‐informed neural network to project sparse Doppler meteor detections into four‐dimensional time‐series arrays containing the Cartesian components of the velocity field. This method combines meteor radar observations with the physics prescribed by the Navier‐Stokes equations. The validation of HYPER was conducted through a series of benchmarks on numerical data and the application of our algorithm on actual meteor radar observations, all of which yielded realistic approximations of the reconstructed physical fields. This innovative approach represents a significant step toward an accurate characterization of the MLT dynamics, overcoming the limitations of existing methods, and providing valuable insights into the behavior of this poorly accessible region of the atmosphere.

Directional swimming patterns in jellyfish aggregations

Having a profound influence on marine and coastal environments worldwide, jellyfish hold significant scientific, economic, and public interest.1,2,3,4,5 The predictability of outbreaks and dispersion of jellyfish is limited by a fundamental gap in our understanding of their movement. Although there is evidence that jellyfish may actively affect their position,6,7,8,9,10 the role of active swimming in controlling jellyfish movement, and the characteristics of jellyfish swimming behavior, are not well understood. Consequently, jellyfish are often regarded as passively drifting or randomly moving organisms, both conceptually2,11 and in process studies.12,13,14 Here we show that the movement of jellyfish is modulated by distinctly directional swimming patterns that are oriented away from the coast and against the direction of surface gravity waves. Taking a Lagrangian viewpoint from drone videos that allows the tracking of multiple adjacent jellyfish, and focusing on the scyphozoan jellyfish Rhopilema nomadica as a model organism, we show that the behavior of individual jellyfish translates into a synchronized directional swimming of the aggregation as a whole. Numerical simulations show that this counter-wave swimming behavior results in biased correlated random-walk movement patterns that reduce the risk of stranding, thus providing jellyfish with an adaptive advantage critical to their survival. Our results emphasize the importance of active swimming in regulating jellyfish movement and open the way for a more accurate representation in model studies, thus improving the predictability of jellyfish outbreaks and their dispersion and contributing to our ability to mitigate their possible impact on coastal infrastructure and populations.