Higher Vertical Modes Research Articles

Recovering Quasi-Biennial Oscillations from Chaos

Abstract The Quasi-Biennial Oscillation (QBO) is understood to result from wave-mean-flow interactions, but the reasons for its relative stability remain a subject of ongoing debate. In addition, consensus has yet to be reached regarding the respective roles of different equatorial wave types in shaping the QBO’s characteristics. Here we employ Holton-Lindzen-Plumb’s quasilinear model to shed light on the robustness of periodic behavior in the presence of multiple wave forcings. A comprehensive examination of the various dynamical regimes in this model reveals that increased vertical wave propagation at higher altitudes favors periodicity. In the case of single standing wave forcing, enhanced vertical propagation is controlled by the wave attenuation length scale. The occurrence of non-periodic states at high forcing amplitudes is explained by the excitation of high vertical unstable modes. Increasing the attenuation length scale prevents the emergence of such modes. When multiple wave forcing is considered, the mean flow generated by a dominant primary wave facilitates greater vertical propagation of a perturbation wave. Raising the altitude where most of the wave damping occurs favors periodicity by preventing the development of secondary jets responsible for the aperiodic behavior. This mechanism underscores the potential role of internal gravity waves in supporting the periodicity of a QBO primarily driven by planetary waves.

Influences of Mesoscale Ocean Eddies on Flow Vertical Structure in a Resolution‐Based Model Hierarchy

AbstractThe understanding and representation of energetic transfers associated with ocean mesoscale eddies is fundamental to the development of parameterizations for climate models. We investigate the influence of eddies on flow vertical structure as a function of underlying dynamical regime and grid resolution. We employ the GFDL‐MOM6 in an idealized configuration and systematically consider four horizontal resolutions: 1/4°, 1/8°, 1/16°, and 1/32°. We analyze the distributions of potential and kinetic energy, decomposed into barotropic and baroclinic, and eddy and mean parts. As resolution increases and baroclinically unstable modes are better captured, kinetic energy increases and potential energy decreases. The dominant trend in vertical structure is an increasing fraction of kinetic energy going into the barotropic mode, particularly its eddy component, as eddies are increasingly resolved. We attribute the increased baroclinicity at low resolutions to inaccurate representation of vertical energy fluxes, leading to suppressed barotropization and energy trapping in high vertical modes. We also explore how the underlying dynamical regime influences energetic pathways. In cases where large‐scale flow is dominantly barotropic, resolving the deformation radius is less crucial to accurately capturing the flow's vertical structure. We find the barotropic kinetic energy fraction to be a useful metric in assessing vertical structure. In the highest‐resolution case, the barotropic kinetic energy fraction correlates with the scale separation between the deformation scale and the energy‐containing scale, that is, the extent of the eddy‐driven inverse cascade. This work suggests that mesoscale eddy parameterizations should incorporate the energetic effects of eddies on vertical structure in a scale‐aware, physically informed manner.

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.

A Barium Titanate-on-Oxide Insulator Optoelectronics Platform.

Electro-optic modulators are among the most important building blocks in optical communication networks. Lithium niobate, for example, has traditionally been widely used to fabricate high-speed optical modulators due to its large Pockels effect. Another material, barium titanate, nominally has a 50times stronger r-parameter and would ordinarily be a more attractive material choice for such modulators or other applications. In practice, barium titanate thin films for optical waveguide devices are usually grown on magnesium oxide due to its low refractive index, allowing vertical mode confinement. However, the crystal quality is normally degraded. Here, a group of scandate-based substrates with small lattice mismatch and low refractive index compared to that of barium titanate is identified, thus concurrently satisfying high crystal quality and vertical optical mode confinement. This work provides a platform for nonlinear on-chip optoelectronics and can be promising for waveguide-based optical devices such as Mach-Zehnder modulators, wavelength division multiplexing, and quantum optics-on-chip.

Internal Tide Cycle and Topographic Scattering Over the North Mid‐Atlantic Ridge

AbstractInternal tides are a predominant source of high‐frequency variability and diapycnal mixing in the ocean. Understanding their dynamics and lifecycle is necessary to better understand their role in the ocean circulation. In this study, we describe and quantify internal tide generation, propagation, and dissipation in a sector of the North Mid‐Atlantic Ridge, using high‐resolution numerical simulations with realistic bathymetry and stratification. We show that the generation and dissipation of internal tides, as well as the distribution of internal tides among vertical modes, exhibit high spatial variability. We find that topographic scattering leads to a significant transfer of energy toward high vertical modes and thereby enhances internal tide dissipation. On average, and especially on the ridge, this mechanism is dominant over the conversion from the barotropic tide for transferring energy to high (7) vertical modes. The magnitude of the scattering of the first baroclinic internal mode is found to be in good agreement with theoretical predictions.

An empirical parametrization of internal seiche amplitude including secondary effects

An internal wave is a propagating disturbance within a stable density-stratified fluid. The internal seiche amplitude is often estimated through theories that describe the amplitude growth based on the Bulk Richardson number (Ri). However, most theoretical formulations neglect secondary effects that may influence the evolution of internal seiches. Since these waves have been pointed out as the most important process of vertical mixing, influencing the biogeochemical fluxes in stratified basins, the wrong estimation may have several impacts on the prediction of the system dynamics. This research paid particular attention to the importance of secondary effects that may play a major role on the basin-scale internal wave amplitude, especially related to the interaction between internal waves and lake boundaries, internal wave depth, and mixing processes due to turbulence. Based on a set of methods, which include auto- and cross-correlations, spectral analysis, and mathematical models, we analyzed the effect of total water depth, wind-resonance, and higher vertical modes on the amplitude growth. We based our analysis on underwater temperature measurements and meteorological data obtained from two small thermally-stratified basins, complemented with numerical simulations. We introduce here a new parametrization which takes into account the total water depth (H), lake length (L), epilimnion thickness ( $$h_e$$ ), as well as the resonance effect. We observed that the rate of amplitude growth decreases compared to linear theory when $$Ri~h_e/L\le 1$$ . In these cases, we suggests that previous theories overestimate the internal seiche amplitude, neglecting the instabilities generated near the wave crest due to weak stability and wave interactions. However, under shallow thermocline conditions, due to extra pressure in the upper layer, the vertical displacement may be higher than that predicted by the linear theory.

Long lived second mode internal solitary waves in the Andaman Sea

Internal waves are density oscillations propagating along the ocean’s inner stratification, which are now acknowledged as a key constituent of the ocean’s dynamics. They usually result from barotropic tides, which flow over bottom topography, causing density oscillations to propagate along the pycnocline with a tidal frequency (i.e. internal tides). These large-scale waves propagate away from their forcing bathymetry and frequently disintegrate into nonlinear short-scale (higher-frequency) internal wave packets. Typically, short-scale internal wave observations in the ocean are associated with vertical structures (in the water column) of the lowest fundamental mode. Higher vertical modes have recently been documented as well, but these are commonly short-lived (up to a few hours). However, unprecedented satellite images showing long-lived short-scale mode-2 internal waves have now been documented in the Andaman Sea, and we report here the companion results of a non-hydrostatic and fully nonlinear numerical model. The simulations reproduce the waves’ main characteristics as observed in satellite imagery, and the results suggest a resonant coupling with a larger-scale mode-4 internal tide as an explanation for their long-lived character.

On Internal Waves Propagating across a Geostrophic Front

AbstractReflection and transmission of normally incident internal waves propagating across a geostrophic front, like the Kuroshio or Gulf Stream, are investigated using a modified linear internal wave equation. A transformation from depth to buoyancy coordinates converts the equation to a canonical partial differential equation, sharing properties with conventional internal wave theory in the absence of a front. The equation type is determined by a parameter Δ, which is a function of horizontal and vertical gradients of buoyancy, the intrinsic frequency of the wave, and the effective inertial frequency, which incorporates the horizontal shear of background geostrophic flow. In the Northern Hemisphere, positive vorticity of the front may produce Δ ≤ 0, that is, a “forbidden zone,” in which wave solutions are not permitted. Thus, Δ = 0 is a virtual boundary that causes wave reflection and refraction, although waves may tunnel through forbidden zones that are weak or narrow. The slope of the surface and bottom boundaries in buoyancy coordinates (or the slope of the virtual boundary if a forbidden zone is present) determine wave reflection and transmission. The reflection coefficient for normally incident internal waves depends on rotation, isopycnal slope, topographic slope, and incident mode number. The scattering rate to high vertical modes allows a bulk estimate of the mixing rate, although the impact of internal wave-driven mixing on the geostrophic front is neglected.

Choice of function spaces for thermodynamic variables in mixed finite‐element methods

We study the dispersion properties of three choices for the buoyancy space in a mixed finite‐element discretization of geophysical fluid flow equations. The problem is analogous to that of the staggering of the buoyancy variable in finite‐difference discretizations. Discrete dispersion relations of the two‐dimensional linear gravity wave equations are computed. By comparison with the analytical result, the best choice for the buoyancy space basis functions is found to be the horizontally discontinuous, vertically continuous option. This is also the space used for the vertical component of the velocity. At lowest polynomial order, this arrangement mirrors the Charney–Phillips vertical staggering known to have good dispersion properties in finite‐difference models. A fully discontinuous space for the buoyancy corresponding to the Lorenz finite‐difference staggering at lowest order gives zero phase velocity for high vertical wavenumber modes. A fully continuous space, the natural choice for scalar variables in a mixed finite‐element framework, with degrees of freedom of buoyancy and vertical velocity horizontally staggered at lowest order, is found to entail zero phase velocity modes at the large horizontal wavenumber end of the spectrum. Corroborating the theoretical insights, numerical results obtained on gravity wave propagation with fully continuous buoyancy highlight the presence of a computational mode in the poorly resolved part of the spectrum that fails to propagate horizontally. The spurious signal is not removed in test runs with higher‐order polynomial basis functions. Runs at higher order also highlight additional oscillations, an issue that is shown to be mitigated by partial mass‐lumping. In light of the findings and with a view to coupling the dynamical core to physical parametrizations that often force near the horizontal grid scale, the use of the fully continuous space should be avoided in favour of the horizontally discontinuous, vertically continuous space.

Indirect evidence for substantial damping of low‐mode internal tides in the open ocean

AbstractA global high‐resolution ocean circulation model forced by atmospheric fields and the M2 tidal constituent is used to explore plausible scenarios for the damping of low‐mode internal tides. The plausibility of different damping scenarios is tested by comparing the modeled barotropic tides with TPXO8, a highly accurate satellite‐altimetry‐constrained tide model, and by comparing the modeled coherent baroclinic tide amplitudes against along‐track altimetry. Five scenarios are tested: (1) a topographic internal wave drag, argued here to represent the breaking of unresolved high vertical modes, applied to the bottom flow (default configuration), (2) a wave drag applied to the barotropic flow, (3) absence of wave drag, (4) a substantial increase in quadratic bottom friction along the continental shelves (with wave drag turned off), and (5) application of wave drag to the barotropic flow at the same time that quadratic bottom friction is substantially increased along the shelves. Of the scenarios tested here, the default configuration (1) yields the most accurate tides. In all other scenarios (2–5), the lack of damping on open ocean baroclinic motions yields baroclinic tides that are too energetic and travel too far from their sources, despite the presence of a vigorous mesoscale eddy field which can scatter and decohere internal tides in the model. The barotropic tides are also less accurate in the absence of an open ocean damping on barotropic motions, that is, in scenarios (3) and (4). The results presented here suggest that low‐mode internal tides experience substantial damping in the open ocean.

Shoaling of the internal solitary waves over the continental shelf of the northern South China Sea

The activities of internal solitary waves (ISWs) over the continental shelf of the northern South China Sea (SCS) are of high complexity. In this study, we investigated the spatial-temporal characteristics of the shoaling ISWs over the northern SCS continental shelf using the satellite images and the results of numerical simulation. The examination of the ISW signals in the satellite optical images revealed the existence of three types of ISWs in the region north to the Dongsha Island, namely, mode-1 depression ISW, mode-1 elevation ISW, and mode-2 convex ISW. The geographical distributions of these ISWs were derived from the satellite images. Numerical results exhibited the process of polarity conversion of ISWs, by which mode-1 elevation waves were transformed from the shoaling mode-1 depression waves. The mode-2 convex ISWs generally followed the mode-1 depression ISWs. The numerical results suggested that the interaction of the mode-1 depression ISWs with the up-slope topography locally generated mode-2 ISWs, and such waves of high vertical mode dissipated rapidly during the inshore propagation.

Persistent presence of small vertical scale velocity features during three-dimensional equilibration of equatorial inertial instability

Small vertical scale velocity features (SVSs) are ubiquitous in the upper equatorial ocean but their lifecycle and role in the large scale dynamics are only beginning to be understood. In this article, we study the development of SVSs generated through inertial instability of a prototypical equatorial zonal flow with a uniform meridional shear, U(y) = Λy. While previous studies employ a zonally symmetric setting, in which the flow is constrained to remain invariant in the streamwise direction throughout its evolution, here we use a fully three-dimensional framework. We choose a setting, in which the fastest growing linear modes are zonally symmetric and the initial perturbation is almost zonally symmetric, so that the flow remains nearly two-dimensional until the symmetric instability is fully neutralized. The secondary instabilities of the modified zonal mean flow favor zonally nonsymmetric modes, which leads to three-dimensionalization of the flow. It has been previously conjectured in the literature that the dominant secondary instability is an inflection point-type barotropic instability that favors disturbances with a large vertical scale and the necessary condition for which is the reversal of the meridional gradient of the background potential vorticity. We show that although the conditions necessary for barotropic instability indeed arise after the neutralization of the symmetric instability, the dominant secondary instabilities form a sequence of high vertical mode disturbances excited through zonally nonsymmetric inertial instability of the evolving zonal mean flow. The barotropic eddies, therefore, remain underdeveloped and do not play an important role in the dynamics. We cannot rule out the possible influence of the applied lateral hyperdiffusion (used to control near-grid point noise in the integrations) on the relative roles of barotropic and inertial instability. The competition between these two possible secondary instabilities needs further investigation with higher resolution experiments. We note, however, that when zonally asymmetric inertial instability is not possible (achieved here by shortening the zonal extent of the integration region while keeping the hyperdiffusion coefficient the same), barotropic instability fully develops and the flow is dominated by the barotropic mode.

Collocated Z-Axis Control of a High-Speed Nanopositioner for Video-Rate Atomic Force Microscopy

A key hurdle to achieve video-rate atomic force microscopy (AFM) in constant-force contact mode is the inadequate bandwidth of the vertical feedback control loop. This paper describes techniques used to increase the vertical tracking bandwidth of a nanopositioner to a level that is sufficient for video-rate AFM. These techniques involve the combination of: a high-speed XYZ nanopositioner; a passive damping technique that cancels the inertial forces of the Z actuator which in turns eliminates the low 20-kHz vertical resonant mode of the nanopositioner; an active control technique that is used to augment damping to high vertical resonant modes at 60 kHz and above. The implementation of these techniques allows a tenfold increase in the vertical tracking bandwidth, from 2.3 (without damping) to 28.1 kHz. This allows high-quality, video-rate AFM images to be captured at 10 frames/s without noticeable artifacts associated with vibrations and insufficient vertical tracking bandwidth.

Intrusion-generated waves in a linearly stratified fluid

AbstractWe present an experimental and numerical study of the upstream internal wavefield in a channel generated by constant density intrusions propagating into a linearly stratified ambient fluid during the initial phase of translation. Using synthetic schlieren imaging and two-dimensional direct numerical simulations, we quantify this wave motion within the ambient stratified fluid ahead of the advancing front. We show that the height of the neutral buoyancy surface in the ambient fluid determines the vertical modal response with the predominant waves being mode 2 for intrusions near the mid-depth of the channel and mode 1 waves being produced by intrusions nearer the top or bottom of the domain. All higher vertical modes travel slower than the intrusion and so do not appear upstream ahead of the intrusion front. We find the energy flux into this upstream wavefield to be approximately constant, and to be between 10 and 30 % of the rate of available potential energy transfer into the flow.

Acoustic modes in a curved internal wave duct

Observations and numerical simulations have shown that nonlinear internal waves in continental shelf and shelfbreak regions can form 3-D acoustic ducts. The strength of ducting depends on the size of internal waves, the width of the gap between waves and the curvature of the wave front, and also on the acoustic frequency and the vertical mode number. It has been seen in numerical simulations and simplified ray theory that for a given internal wave structure and a given frequency, higher vertical modes are easier being trapped in a curved internal wave duct. Also, the number of the lowest mode trapped between curved waves increases as the frequency goes up. In this talk, a 3-D normal mode theory is employed to analyze these observed characteristics. The analysis is carried out in a cylindrical coordinates, and two types of horizontal modes are found: whispering-gallery modes and full bouncing modes. Both types of modes can be described by Bessel functions, and the asymptotic formulas can be used in some li...

Model‐predicted distribution of wind‐induced internal wave energy in the world's oceans

The distribution of wind‐induced internal wave energy in the world's oceans is investigated using a full three‐dimensional primitive equation model. Special attention is directed to the global energy input to the surface near‐inertial motions and the subsequent downward energy propagation into the deep ocean. We find that the model results for near‐inertial energy in the oceanic mixed layer, depth‐integrated horizontal energy fluxes, and vertical structures of WKB‐scaled kinetic energy are all consistent with the available observations in the regions of significant wind energy input and that the annual mean of the global wind energy input becomes ∼0.4 TW. It is also found that most of the wind‐induced energy resides in high vertical modes, 75–85% of which is dissipated in the surface 150 m. The present study therefore predicts that the total wind‐induced near‐inertial energy available for deep‐ocean mixing is limited to, at most, 0.1 TW, which is an order of magnitude smaller than previously estimated. Adding the energy flux from tide‐topography interactions of ∼0.9 TW, we can conclude that the total energy available for deep‐ocean mixing is ∼1.0 TW, obviously falling short of the required power to sustain the global overturning circulation. This might suggest the existence of other important energy sources, such as the one through geostrophic adjustment processes, and/or additional mechanisms sustaining the global overturning circulation, such as effects of Ekman upwelling in the Southern Ocean. Another possibility is that previous estimates of the volume transport of the global overturning circulation might be too large.

The seasonal evolution of high vertical‐mode internal waves in a deep reservoir

The causal mechanism and seasonal evolution of the internal wave field in a deep, warm, monomictic reservoir are examined through the analysis of field observations and numerical techniques. The study period extends from the onset of thermal stratification in the spring until midsummer in 2005. During this time, wind forcing was periodic, with a period of 24 h (typical of land‐sea breezes), and the thermal structure in the lake was characterized by the presence of a shallow surface layer overlying a thick metalimnion, typical of small to medium sized reservoirs with deep outtakes. Basin‐scale internal seiches of high vertical mode (ranging from mode V3 to V5) were observed in the metalimnion. The structure of the dominant modes of oscillation changed as stratification evolved on seasonal timescales, but in all cases, their periods were close to that of the local wind forcing (i.e., 24 h), suggesting a resonant response. Nonresonant oscillatory modes of type V1 and V2 became dominant after large frontal events, which disrupted the diurnal periodicity of the wind forcing.

Continuous wave operation of a superlattice quantum cascade laser emitting at 2 THz

We report the operation of a 2 THz quantum cascade laser based on a GaAs/Al(0.1)Ga(0.9)As heterostructure. The laser transition is between an isolated subband and the upper state of a 14 meV wide miniband. Lasing action takes place on a high order vertical mode of a 200 microm thick double-metallic waveguide. In pulsed mode operation, with a 3.16mm long device, we report a threshold current density of 115 A/cm(2) at T = 4K, with a maximum measured peak power of 50 mW. The device shows lasing action in continuous wave up to 47K, with a maximum power in excess of 15 mW at T = 4K.

Temporal Variability of High Vertical Wavenumber Shear over the Izu-Ogasawara Ridge

Recent numerical studies (Hibiya et al., 1996, 1998, 2002) showed that the energy cascade across the internal wave spectrum down to small dissipation scales was un- der strong control of parametric subharmonic instabilities (PSI) which transfer en- ergy from low vertical mode double-inertial frequency internal waves to high vertical mode near-inertial internal waves. To see whether or not the numerically-predicted energy cascade process is actually dominant in the real deep ocean, we examine the temporal variability of vertical profiles of horizontal velocity observed by deploying a number of expendable current profilers (XCPs) at one location near the Izu- Ogasawara Ridge. By calculating EOFs, we find the observed velocity profiles are dominated by low mode semidiurnal (~double-inertial frequency) internal tides and high mode near-inertial internal waves. Furthermore, we find that the WKB-stretched vertical scales of the near-inertial current shear are about 250 sm and 100 sm. The observed features are reasonably explained if the energy cascade down to small dissi- pation scales is dominated by PSI.

Equatorial inertial-parametric instability of zonally symmetric oscillating shear flows

This study revisits the problem of the zonally symmetric instability on the equatorial β-plane. Rather than treating the classical problem of a steady basic flow, it treats a sequence of problems of increasing complexity in which the basic flow is oscillatory in time with a frequency ω 0 . First, for the case of a homogeneous fluid, a time-oscillating barotropic shear forcing may excite a subharmonic parametric resonance of inertial oscillations. Because of the continuous distribution of inertial oscillation frequencies, this resonance occurs at critical inertial latitudes y c such that βy c = ±ω 0 /2. Next the effects of stratification, characterized by Brunt-Vaisala frequency N, are taken into account. It is shown analytically (in the asymptotic limit of a weak shear) that the forced temporal oscillation leads to an inertial-parametric instability, when a resonance condition between the basic flow frequency and the sum of two inertio-gravity free-mode frequencies is met. This inertial-parametric instability has a well-defined inviscid vertical scale selection favouring the high-vertical mode m c ∼ 7.45m 0 , where m 0 =βN/ω 2 0 is the equatorial vertical mode characteristic of frequency ω 0 . The viscous critical shear of inertial-parametric instability is lower than the steady inertial instability one. Finally, this type of setting naturally arises when the basic flow is considered to be an equatorial wave, so the problem is recast with the nonlinear adjustment of the vertically sinusoidal basic state of a zonally symmetric mixed Rossby-gravity (MRG) wave. Initial-value numerical simulations show that the same inertial-parametric instability exists leading to a resonant subharmonic excitation of free modes with vertical scales 7 and 8 times smaller than the basic-state wave. A simplified dynamical model of the instability is introduced, demonstrating that the oscillatory nature of the shear with height for the MRG wave necessarily implies a resonance between distinct vertical modes, the most unstable ones being modes 7 and 8 for a large enough Froude number of the MRG wave. The nonlinear action of the instability is described in terms of angular momentum and potential vorticity changes: a significant mixing due to the breaking of the excited high vertical modes creates a vertically averaged westward flow at the equator and extra-equatorial eastward flows. The ideas exposed may play a part in explaining layering phenomena and the latitudinal structure of the zonal flow in the equatorial oceans below the thermocline.