Internal Wave Spectrum Research Articles

Transient resonant triads: An examination of turbulent patches injected into finite-width internal wave fields

This article presents an experimental investigation into the interaction of a freely evolving turbulent structure with a steadily forced, finite-width internal gravity wave beam. Specifically, a vortex ring is used as the simplified prototype for a propagating turbulent structure and we present an exploration into how it's passage affects the linear stability of the imposed (or forced) wave field. We use the term "vortex ring" to describe an initially axisymmetric, toroidal fluid structure with azimuthal vorticity. We first examine both the vortex ring and the imposed internal gravity wave beam separately and present how they develop in a quiescent, stratified environment. In the absence of any vortex ring, we find—in agreement with many previous studies—there is an amplitude threshold that the wave beam must surpass before it becomes linearly unstable by a process known as triadic resonance instability (TRI). In the absence of an imposed wave field, we present the propagation and collapse of a coherent vortex ring into a turbulent patch, and measure the transient spectrum of internal waves produced. We then combine these two phenomena and investigate how each impacts the other. While we find that the preexisting internal wave beam has no significant influence on the evolution of the incident vortex ring, we do find that the propagation and subsequent collapse of the ring provokes a response from the internal wave beam. This response allows us to demonstrate two key findings relating to the internal wave beams pathway to triadic resonance. First, the passage of a vortex ring propagating through a forced wave field can provide a nonlinear trigger for the transition to a triadic state when the amplitude of the imposed wave field is itself too small for the spontaneous growth of such a triadic state through TRI. Second, we find that in some cases the triadic states induced by this interaction are not self-sustaining and eventually decay, prompting the terminology "transient triads." These surprising findings are further confirmed by the unintentional release of trapped air arising from under our "magic carpet" wavemaker. These air bubbles turbulently propagate vertically through the imposed beam and, in some cases, induce similar triadic state transitions to those of the vortex ring. Our analysis leads to a discussion on the beam's pathway to instability and to question the structure of the underlying dynamical system arising from the distribution of spectral power in a finite-width beam. Published by the American Physical Society 2024

3D hydrodynamic simulations of massive main-sequence stars – II. Convective excitation and spectra of internal gravity waves

ABSTRACT Recent photometric observations of massive stars have identified a low-frequency power excess which appears as stochastic low-frequency variability in light-curve observations. We present the oscillation properties of high-resolution hydrodynamic simulations of a $25\,\,{\rm{M}_\odot }$ star performed with the PPMstar code. The model star has a convective core mass of $\approx 12\,\,{\rm{M}_\odot }$ and approximately half of the envelope simulated. From this simulation, we extract light curves from several directions, average them over each hemisphere, and process them as if they were real photometric observations. We show how core convection excites waves with a similar frequency as the convective time-scale in addition to significant power across a forest of low and high angular degree l modes. We find that the coherence of these modes is relatively low as a result of their stochastic excitation by core convection, with lifetimes of the order of 10s of days. Thanks to the still significant power at higher l and this relatively low coherence, we find that integrating over a hemisphere produces a power spectrum that still contains measurable power up to the Brunt–Väisälä frequency. These power spectra extracted from the stable envelope are qualitatively similar to observations, with the same order of magnitude yet lower characteristic frequency. This work further shows the potential of long-duration, high-resolution hydrodynamic simulations for connecting asteroseismic observations to the structure and dynamics of core convection and the convective boundary.

Energy cascade in the Garrett–Munk spectrum of internal gravity waves

We study the spectral energy transfer due to wave–triad interactions in the Garrett–Munk spectrum of internal gravity waves based on a numerical evaluation of the collision integral in the wave kinetic equation. Our numerical evaluation builds on the reduction of the collision integral on the resonant manifold for a horizontally isotropic spectrum. We evaluate directly the downscale energy flux available for ocean mixing, whose value is in close agreement with the finescale parameterization. We further decompose the energy transfer into contributions from different mechanisms, including local interactions and three types of non-local interactions, namely parametric subharmonic instability, elastic scattering (ES) and induced diffusion (ID). Through analysis on the role of each mechanism, we resolve two long-standing paradoxes regarding the mechanism for forward cascade in frequency and zero ID flux for the GM76 spectrum. In addition, our analysis estimates the contribution of each mechanism to the energy transfer in each spectral direction, and reveals new understanding of the importance of local interactions and ES in the energy transfer.

Sensitivity of the Lorenz energy cycle of the global ocean

We re-examine the Lorenz energy cycle (LEC) for the global ocean by assessing its sensitivity to model and forcing differences. We do so by comparing LECs derived from two simulations based on different eddy-rich ocean models, ICON-O and MPI-OM, both driven by NCEP/NCAR reanalysis, and by comparing LECs derived from two simulations generated using ICON-O model but driven by two different reanalyses, NCEP/NCAR and ERA5. Regarding model difference, we find weaker eddy kinetic energy, k_e, in the ICON-O simulation than in the MPI-OM simulation. We attribute this to the higher horizontal resolution of MPI-OM in the Southern Ocean. The weaker k_e in ICON-O is not caused by the lack of eddy available potential energy, p_e, but by the strong dissipation of p_e and the resulting weak conversion from p_e to k_e. Regarding forcing difference, we find that considerably more mechanical energy is generated by the ERA5 forcing, which has a higher spatial-temporal resolution compared to the NCEP/NCAR forcing. In particular, the generation of k_e, which also contains the resolved part of the internal wave spectrum, is enhanced by about 1 TW (40%). However, the dominance of the baroclinic and the barotropic pathways forces the enhanced generation of k_e to be balanced by an enhanced dissipation in the surface layer. The gross features of LEC are insensitive to both model and forcing differences, picturing the ocean as an inefficient “windmill” that converts only a small portion of the inputted mechanical energy into the interior mean and transient circulations.

The Influence of Random Internal Waves on the Characteristics of a Horizontal Antenna in a Shallow Sea

The effect of random internal waves on the gain and pattern of a horizontal antenna array in a shallow sea has been investigated. An algorithm for calculating the correlation matrix of the point source field at the grating aperture is proposed. The antenna gain is analyzed for different spatial processing methods: the beam forming method, the optimal linear processing method, and the optimal quadratic processing method. The effect of internal waves on the directivity pattern is described by the dispersion of the angular response of the grating. Numerical simulation results are presented for a model summer-type waveguide and an exponential Brunt–Väisälä frequency profile. The empirical internal wave spectrum proposed earlier from the SWARM95 experiment is used. The dependences of the antenna array characteristics on the number of its elements, orientation with respect to the source, radiation frequency, and the acoustic characteristics of the bottom are analyzed.

A VARIETY OF TRANSFORMATIONS OF NONLINEAR INTERNAL TIDAL WAVES ON THE NORTH-WEST AUSTRALIAN SHELF

Highly non-linear internal waves at the continental margin on the northwest shelf of Australia are discussed using detailed velocity and temperature time series recorded from moored current meters. The region has a vigorous semidiurnal inland tide that propagates towards the shore along the shelf. In this area, there is an increase in the internal tide and the formation of bore-like formations, often accompanied by internal solitary waves. In this paper, the emphasis is on the analysis of the shape and properties of the internal tide. The frequency spectrum of internal waves is presented, calculated from the records of the current component directed along the normal to the coast. Five different types of waves are distinguished, which consist of burrs on the front or back side of the wave, “square” waveforms with a bores on both the front and back sides of the wave at the same time, as well as linear waves of small and large amplitude. The statistics of transformations of the types of internal tides during their propagation along the section of the route from the slope to the shelf is given. The main types of waves passing without transformation and waves with a short lifetime, which include “square” tidal waves and waves with bores on the back slope of the wave, are revealed. In general, the analysis showed a real picture of the ongoing nonlinear transformations of tidal internal waves occurring on the north-west shelf of Australia.

Impacts of inertial internal wave breaking mixing parameterization on a global ocean model

A parameterization of vertical mixing induced by fine-scale near-inertial internal waves (F-scheme) is implemented in the Parallel Ocean Program, version 2 (POP2). The F-scheme is based on the spectrum model via solving the non-traditional approximation internal wave equations and the observed internal wave spectra. The structure of the resulting dissipation and diffusivity fields and its impacts on the ocean model simulations are investigated. The diffusivity coefficient derived from F-scheme varies spatiotemporally, and is generally in consistent magnitude with observed results in the middle to high latitude ocean, and show the similar latitude dependent characteristics with the current observations, depending on the product of the horizontal and vertical components of the Coriolis parameter (f·f∼) as well as the local stratification condition. The interior mixing induced by F-scheme has some noticeable impacts on the temperature and salinity structure near the main thermocline, the meridional overturning circulation and northward heat transport as has been demonstrated in the other two OGCMs (LICOM and MOM4). The temperature and salinity structure simulated using F-scheme are statistically closer to observations, especially it improves the simulation of the Pacific Ocean, Indian Ocean and Antarctic Circumpolar Circulation. But the involved background mixing coefficients or F-scheme enlarges the temperature and salinity biases in the Atlantic Ocean, the cause is related to the pre-existing weak Antarctic Intermediate Water intrusion toward north and the inexact Atlantic Meridional Overturn Circulation simulation in the present model. F-scheme provides weak mixing in some regions, where an appropriate parameterization of turbulent mixing induced by wave-wave interaction also should be considered in the future.

A Detailed Analysis on Hydrodynamic Response of a Highly Stratified Lake to Spatio-Temporally Varying Wind Field

Wind is generally considered an important factor driving the transport and mixing processes in stratified enclosed systems such as lakes and reservoirs. Lake Abashiri is one of the instances of such a system. For these systems, typically, the temporally unsteady but spatially uniform nature of wind has been assumed for simplicity. However, the spatial non-uniformity of wind could significantly alter compound hydrodynamic responses. In this study, such responses were investigated under the continuous imposition of different inhomogeneous wind conditions by applying numerical models and integrated analysis. The resultant tracer transport in both uniform and non-uniform wind cases was insignificant for the total study period of 9 days. However, under the short interval of Ti, where Ti is the internal fundamental period, different behaviors of both surface particle transport and the internal wave field were identified. Particularly, surface mass transport responses to higher spatial wind variance were obviously different from those in the uniform case. In addition, internal wave spectra under strong wind magnitude, which has low spatial variances, became identical to that of uniform wind; however, there were some discrepancies in the non-uniform case in the wave spectra under the influence of weak-to-moderate wind of high spatial variances. The results could provide an in-depth understanding of the lake’s hydrodynamic response to inhomogeneous wind which could improve water management in lakes and reservoirs.

A Simple Model for an Internal Wave Spectrum Dominated by Non-Linear Interactions

Ocean motions at frequencies of the internal wave band are generally associated with freely propagating waves that are supported by stable vertical stratification in density. Previous analyses of yearlong current observations from the Bay of Biscay showed that a finestructure of semidiurnal tidal and near-inertial higher harmonics fills the spectrum. Here, a simple model is presented of forced nondispersive motions with forward energy cascade. The model fits the spectral shape of higher harmonics well within statistical significance and shows that such interactions imply maximum wave steepness in a balance between forcing and turbulent mixing. The single fitting parameter takes a value of approximately one, at which the barotropic tidal flow speed equals the internal wave phase speed. We infer that the barotropic tide sets a non-linear limit to baroclinic current scales without generating non-linear higher harmonics directly.

Eddy Vertical Structure and Variability: Deepglider Observations in the North Atlantic

Abstract Hundreds of full-depth temperature and salinity profiles collected by Deepglider autonomous underwater vehicles (AUVs) in the North Atlantic reveal robust signals in eddy isopycnal vertical displacement and horizontal current throughout the entire water column. In separate glider missions southeast of Bermuda, subsurface-intensified cold, fresh coherent vortices were observed with velocities exceeding 20 cm s−1 at depths greater than 1000 m. With vertical resolution on the order of 20 m or less, these full-depth glider slant profiles newly permit estimation of scaled vertical wavenumber spectra from the barotropic through the 40th baroclinic mode. Geostrophic turbulence theory predictions of spectral slopes associated with the forward enstrophy cascade and proportional to inverse wavenumber cubed generally agree with glider-derived quasi-universal spectra of potential and kinetic energy found at a variety of locations distinguished by a wide range of mean surface eddy kinetic energy. Water-column average spectral estimates merge at high vertical mode number to established descriptions of internal wave spectra. Among glider mission sites, geographic and seasonal variability implicate bottom drag as a mechanism for dissipation, but also the need for more persistent sampling of the deep ocean. Significance Statement Relative to upper-ocean measurements of temperature, salinity, and velocity, deep ocean measurements (below 2000 m) are fewer in number and more difficult to collect. Deep measurements are needed, however, to explore the nature of deep ocean circulation contributing to the global redistribution of heat and to determine how upper-ocean behavior impacts or drives deep motions. Understanding of geographic and temporal variability in vertical structures of currents and eddies enables improved description of energy pathways in the ocean driven by turbulent interactions. In this study, we use newly developed autonomous underwater vehicles, capable of diving to the seafloor and back on a near daily basis, to collect high-resolution full ocean depth measurements at various locations in the North Atlantic. These measurements reveal connections between surface and deep motions, and importantly show their time evolution. Results of analyzing these vertical structures reveal the deep ocean to regularly “feel” events in the upper ocean and permit new comparisons to deep motions in climate models.

Turbulent Heat Fluxes in a Mediterranean Eddy Quantified Using Seismic and Hydrographic Observations

Mediterranean eddies (meddies) play an essential role in transferring heat, salinity and momentum into the Atlantic Ocean. The rate of heat (and salt) flux from the meddy and its ultimate lifetime are key proxies to understanding how meddies impact the redistribution of heat and salt in the ocean system. A Mediterranean eddy was observed in the Gulf of Caidz in 2007 using seismic and hydrographic data. The spatial distribution of turbulent dissipation rates around the meddy is estimated from the seismically derived internal wave spectra subrange using fine-scale parameterization. Turbulent dissipated rates are lowest (10−11 W/kg) within the core of the meddy but rise by nearly two orders of magnitude at the upper and lower boundaries, where signs of double diffusive convection are observed. Along the left flank of the meddy, thermohaline intrusions and interleaving of water masses are found in inverted temperature and salinity profiles, transporting heat laterally from the warm core to the Atlantic water with a flux of around 470 Wm−2. The meddy presented in this study is shown to decay in 2 years, primarily due to the heat loss associated with thermohaline intrusions. For the first time, heat fluxes around the meddy and its lifetime are quantified using seismic oceanography data, and the methods proposed here can be applied to more seismic datasets in the global oceans.

Contamination of Finescale Strain Estimates of Turbulent Kinetic Energy Dissipation by Frontal Physics

Abstract Finescale strain parameterization (FSP) of turbulent kinetic energy dissipation rate has become a widely used method for observing ocean mixing, solving a coverage problem where direct turbulence measurements are absent but CTD profiles are available. This method can offer significant value, but there are limitations in its broad application to the global ocean. FSP often fails to produce reliable results in frontal zones where temperature–salinity (T/S) intrusive features contaminate the CTD strain spectrum, as well as where the aspect ratio of the internal wave spectrum is known to vary greatly with depth, as frequently occurs in the Southern Ocean. In this study we use direct turbulence measurements from Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean (DIMES) and glider microstructure measurements from Autonomous Sampling of Southern Ocean Mixing (AUSSOM) to show that FSP can have large biases (compared to direct turbulence measurement) below the mixed layer when physics associated with T/S fronts are meaningfully present. We propose that the FSP methodology be modified to 1) include a density ratio (Rρ)-based data exclusion rule to avoid contamination by double diffusive instabilities in frontal zones such as the Antarctic Circumpolar Current, the Gulf Stream, and the Kuroshio, and 2) conduct (or leverage available) microstructure measurements of the depth-varying shear-to-strain ratio Rω(z) prior to performing FSP in each dynamically unique region of the global ocean. Significance Statement Internal waves travel through the ocean and collide, turbulently mixing the interior ocean and homogenizing its waters. In the absence of actual turbulence measurements, oceanographers count the ripples associated with these internal waves and use them estimate the amount of turbulence that will transpire from their collisions. In this paper we show that the ripples in temperature and salinity that naturally occur at sharp fronts masquerade as internal waves and trick oceanographers into thinking there is up to 100 000 000 times more turbulence than there actually is in these frontal regions.

A Brief Overview of Gravity Wave Retrieval Techniques From Observations

Atmospheric gravity waves (GWs) are important in driving the middle and upper atmosphere dynamics on Earth. Here, we provide a brief review of the most common techniques of retrieving gravity wave activity from observations. Retrieval of gravity wave activity from observations is a multi-step process. First, the background fields have to be removed as the retrieval of the wave activity highly depends on this. Second, since a broad spectrum of internal waves contributes to atmospheric fluctuations, the contribution of GWs has to be extracted carefully. We briefly discuss the strengths, limitations/barriers, and applications of each technique. We also outline some future research questions to improve the treatment of these wave extraction methods.

Triads and Rogue Events for Internal Waves in Stratified Fluids with a Constant Buoyancy Frequency

Internal waves in a stratified fluid with a constant buoyancy frequency were studied, with special attention given to rogue modes, extreme waves, dynamical evolution, and Fermi–Pasta–Ulam–Tsingou type recurrence phenomena. Rogue waves for triads in a general physical setting have recently been derived analytically, but the implications in a fluid mechanics context have not yet been fully assessed. Numerical simulations were conducted for cases of coupled triads where the common member is a daughter wave mode. In sharp contrast with previous studies, rogue modes instead of plane waves were used as the initial condition. Furthermore, spatial dependence was incorporated. Rogue or extreme waves in one set of triads provided a possible mechanism for significant energy transfer among modes of the internal wave spectrum, in addition to the other known theories, e.g., weak turbulence. Remarkably, Fermi–Pasta–Ulam–Tsingou recurrence types of growth and decay cycles arose, similar to those observed for surface gravity wave groups governed by the cubic nonlinear Schrödinger equation. These mechanisms will enhance our understanding of transport processes in oceans.

Application of the Bispectral Wavelet Analysis for Searching Three-Wave Interactions in the Spectrum of Internal Waves

Purpose. The aim of the work is to test the bispectral wavelet analysis being applied as a tool for studying resonance interactions between the frequency components in the spectrum of internal waves (based on the example both of the model signals, the shape of which is similar to that of the solitons and boras, and the field observations data on temperature fluctuations resulted from the internal waves in the Gorlo Strait of the White Sea). Methods and Results. The paper represents a technique for detecting three-wave interactions in the internal waves’ spectrum. The method is based on the bispectral wavelet analysis. It permits to identify the interharmonic correlation and the magnitude of the quadratic phase relationship arising as a result of nonlinear interactions between the signal frequency components. In the first part of the paper, efficiency of the applied method was evaluated using the example of various artificial signals with quadratic nonlinearity in order to demonstrate the method features and advantages. In its second part, the method was used to analyze the temperature profiles obtained by scanning thermohaline sounding, in which the oscillations related to passing of the internal wave groups were recorded. It is shown that the waves with the 40 min period are generated due to quadratic nonlinearity. The auto-bicoherence function values confirm the fact that the higher harmonics are formed in the 60–120 min range as a result of the three-wave interactions. They change synchronously in time, and their amplitudes are proportional, that is typical of the initial stage of the waves’ nonlinear transformation. Absence of a periodic change in the biphase sign in the considered range indicates insignificant influence of the dispersion effects upon the short-period internal waves’ structure. Conclusions. The example of observations in the Gorlo Strait of the White Sea shows that the recorded asymmetric structure of the isotherm oscillations was formed being influenced by the three-wave interaction. Possibility of further application of the method for studying the processes of the internal waves’ nonlinear transformation and breaking is discussed.

Primeneniye bispektral'nogo veyvlet-analiza dlya poiska trekhvolnovykh vzaimodeystviy v spektre vnutrennikh voln

Purpose. The aim of the work is to test the bispectral wavelet analysis being applied as a tool for studying resonance interactions between the frequency components in the spectrum of internal waves (based on the example both of the model signals, the shape of which is similar to that of the solitons and boras, and the field observations data on temperature fluctuations resulted from the internal waves in the Gorlo Strait of the White Sea). Methods and Results. The paper represents a technique for detecting three-wave interactions in the internal waves’ spectrum. The method is based on the bispectral wavelet analysis. It permits to identify the interharmonic correlation and the magnitude of the quadratic phase relationship arising as a result of nonlinear interactions between the signal frequency components. In the first part of the paper, efficiency of the applied method was evaluated using the example of various artificial signals with quadratic nonlinearity in order to demonstrate the method features and advantages. In the second part, the method was used to analyze the temperature profiles obtained by scanning thermohaline sounding, in which the oscillations related to passing of the internal wave groups were recorded. It is shown that the waves with the 40 min period are generated due to quadratic nonlinearity. The auto-bicoherence function values confirm the fact that the higher harmonics are formed in the 60–120 min range as a result of the three-wave interactions. They change synchronously in time, and their amplitudes are proportional, that is typical of the initial stage of the waves’ nonlinear transformation. Absence of a periodic change in the biphase sign in the considered range indicates insignificant influence of the dispersion effects upon the short-period internal waves’ structure. Conclusions. The example of observations in the Gorlo Strait of the White Sea shows that the recorded asymmetric structure of the isotherm oscillations was formed being influenced by the three-wave interaction. Possibility of further application of the method for studying the processes of the internal waves’ nonlinear transformation and breaking is discussed.

A mode based broadband scattering model for deep water sound propagation

Internal-wave induced sound-speed perturbations cause phase and intensity fluctuations of time-fronts. This paper focuses on predictions for broadband Transmission Losses (TL), time wander, and Scintillation Index (SI), along various sections of a typical deep water time-front. These statistics are usually predicted using Monte-Carlo Parabolic Equation (PE) simulations, or the high frequency based path-integral method. A physics based model that fully connects the wave-field statistics, and the internal wave spectrum, to the broadband statistics is not yet available. This paper uses the mode-based transport theory approach to predict the pressure field scattering at different frequencies, and from that the broadband statistics. This requires calculations for cross-modal correlations over mode number and frequency, which becomes computationally intensive for large bandwidths. This paper considers the adiabatic phase coherence to simplify the computations, and tests the final predictions against PE simulations and observations from the Philippine Sea 2010 experiment.

Downscale energy fluxes in scale-invariant oceanic internal wave turbulence

Abstract

Forward flux and enhanced dissipation of geostrophic balanced energy

Abstract

Numerical Investigation of Mechanisms Underlying Oceanic Internal Gravity Wave Power-Law Spectra

AbstractWe consider the power-law spectra of internal gravity waves in a rotating and stratified ocean. Field measurements have shown considerable variability of spectral slopes compared to the high-wavenumber, high-frequency portion of the Garrett–Munk (GM) spectrum. Theoretical explanations have been developed through wave turbulence theory (WTT), where different power-law solutions of the kinetic equation can be found depending on the mechanisms underlying the nonlinear interactions. Mathematically, these are reflected by the convergence properties of the so-called collision integral (CL) at low- and high-frequency limits. In this work, we study the mechanisms in the formation of the power-law spectra of internal gravity waves, utilizing numerical data from the high-resolution modeling of internal waves (HRMIW) in a region northwest of Hawaii. The model captures the power-law spectra in broad ranges of space and time scales, with scalings ω−2.05±0.2 in frequency and m−2.58±0.4 in vertical wavenumber. The latter clearly deviates from the GM76 spectrum but is closer to a family of induced-diffusion-dominated solutions predicted by WTT. Our analysis of nonlinear interactions is performed directly on these model outputs, which is fundamentally different from previous work assuming a GM76 spectrum. By applying a bicoherence analysis and evaluations of modal energy transfer, we show that the CL is dominated by nonlocal interactions between modes in the power-law range and low-frequency inertial motions. We further identify induced diffusion and the near-resonances at its spectral vicinity as dominating the formation of power-law spectrum.