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At least 307 records · Page 17

Dynamics of McMillan mappings II. axially symmetric map

Here, in this article, we investigate the transverse dynamics of a single particle in a model integrable accelerator lattice, based on a McMillan axially-symmetric electron lens. Although the McMillan e-lens has been considered as a device potentially capable of mitigating collective space charge forces, some of its fundamental properties have not been described yet. The main goal of our work is to close this gap and understand the limitations and potentials of this device. It is worth mentioning that the McMillan axially symmetric map provides the first-order approximations of dynamics for a general linear lattice plus an arbitrary thin lens with motion separable in polar coordinates. Therefore, advancements in its understanding should give us a better picture of more generic and not necessarily integrable round beams. In the first part of the article, we classify all possible regimes with stable trajectories and find the canonical action-angle variables. This provides an evaluation of the dynamical aperture, Poincaré rotation numbers as functions of amplitudes, and thus determines the spread in nonlinear tunes. Also, we provide a parameterization of invariant curves, allowing for the immediate determination of the map image forward and backward in time. The second part investigates the particle dynamics as a function of system parameters. We show that there are three fundamentally different configurations of the accelerator optics causing different regimes of nonlinear oscillations. Each regime is considered in great detail, including the limiting cases of large and small amplitudes. In addition, we analyze the dynamics in Cartesian coordinates and provide a description of observable variables and corresponding spectra.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

MJO in Different Orbital Regimes: Role of the Mean State in the MJO’s Amplitude during Boreal Winter

Abstract The Madden–Julian oscillation (MJO) exhibits pronounced seasonality, with one of the key unanswered questions being the following: what controls the maximum in MJO precipitation variance in the Southern Hemisphere during boreal winter? In this study, we examine a set of global climate model simulations in which the eccentricity and precession of Earth’s orbit are altered to change the boreal winter mean state in an attempt to reveal the processes that are responsible for the MJO’s amplitude in the boreal winter. In response to the forced insolation changes, the north–south asymmetry in sea surface temperature is amplified in boreal fall, which intensifies the Hadley circulation in boreal winter. The stronger Hadley circulation yields higher mean precipitation and stronger mean lower-tropospheric westerlies in the southern part of the Indo-Pacific warm pool. The MJO precipitation variability increases significantly where the mean precipitation and lower-tropospheric westerlies strengthen. In the column-integrated moisture budget of the simulated MJO, only surface latent heat flux feedback shows a trend that is consistent with the MJO’s amplitude, suggesting an important role for the surface latent heat flux feedback in the MJO’s amplitude during the boreal winter. An analysis of the moisture–precipitation relationship in the simulations shows that the increase in the mean precipitation lowers the convective moisture adjustment time scale, leading to the increase in precipitation variance. Our results suggest that the mean-state precipitation plays a critical role in the maintenance mechanism of the MJO.

Meteorology & Atmospheric Sciences↗

Indirect climate impacts of the Hunga eruption

Injection of sulfur and water vapour by the Hunga volcanic eruption significantly altered chemical composition and radiative budget of the stratosphere. Yet, whether the eruption could also affect surface climate, especially via indirect pathways, remains poorly understood. Here we investigate these effects using large ensembles of simulations with the CESM2(WACCM6) Earth system model, incorporating interactive chemistry and aerosols in both coupled ocean and atmosphere-only configurations. We find some statistically significant extratropical regional climate responses to the eruption driven by circulation changes; these are partially linked to the modulation of El Niño–Southern Oscillation, and its associated teleconnections, and to perturbations of the stratospheric polar vortex in both hemispheres. The stratospheric anomalies affect surface climate through modulating the North Atlantic Oscillation in the Northern Hemisphere (up to three boreal winters following the eruption) and the Southern Annular Mode in the Southern Hemisphere in late 2023. The latter is partly related to a concurrent reduction in Antarctic ozone, as increased stratospheric aerosols and water vapor reach the polar vortex. Our study suggests that the eruption could have had a non-negligible influence on regional surface climate, and discusses the mechanisms via which such an influence could occur. However, the results also highlight that this forcing is relatively weak compared to interannual variability, and is subject to model uncertainties in the representation of key processes. More research is thus needed before definitive statements on the role of the eruption in contributing to surface climate and weather events in the following years are made.

Geosciences↗

Adapting Optimal Velocity Tracking Control to Account for WEC Constraints and Power-Take-Off Efficiencies: Preprint

Wave energy converters (WECs) come in many different forms, from point absorbers, oscillating water columns, to bulge wave devices. This paper focuses on the control of point absorber WECs, which typically have a narrow-banded frequency response and, therefore, control is well placed to improve the energy capture of such WECs. The acausal nature of the control problem means that theoretically optimal control is almost impossible to achieve inpractice; however optimal velocity tracking (OVT) offers a simple and robust approximation to optimal control that can achieve better power capture than passive linear damping methods, albeit with necessarily higher force demands. OVT is a form of impedance matching and the magnitude of the power-take off (PTO) force demand is often not linearly proportional to the WEC velocity, which can lead to PTO force and speed combinations far from the optimalPTO efficiency. The highly non-linear PTO force and speed to efficiency mapping can, without remedial measures, severely diminish the effectiveness of OVT techniques. In this paper, limits to the movement and force of the PTO are demonstrated, allowing OVT to be more easily applied in practice. The effect of PTO efficiency is explored, and a potential solution to the problem of adapting control to account for efficiency is presented. Both aspects of the work presented highlight the requirement for co-design of the WEC, PTO, and controller.

conversion efficiency↗

Hydrodynamics of two-dimensional compressible fluid with broken parity: Variational principle and free surface dynamics in the absence of dissipation

In this paper, we consider an isotropic compressible nondissipative fluid with broken parity subject to free surface boundary conditions in two spatial dimensions. The hydrodynamic equations describing the bulk dynamics of the fluid and the free surface boundary conditions depend explicitly on the parity-breaking nondissipative odd viscosity term. We construct an effective action which gives both bulk hydrodynamic equations and free surface boundary conditions. The free surface boundary conditions require an additional boundary term in the action which resembles a 1+1D chiral boson field coupled to the background geometry. We solve the linearized hydrodynamic equations for the deep water case and derive the dispersion of chiral surface waves. We show that in the long-wavelength limit the flow profile exhibits an oscillating vortical boundary layer near the free surface. The layer thickness is controlled by the ratio between the odd viscosity (ν o ) and the sound velocity (c s ), δ ~ ν o /c s . In the incompressible limit, c s → ∞, the vortical boundary layer becomes singular with the vorticity within the layer diverging as ω ~ c s . The boundary layer is formed by odd viscosity coupling the divergence of velocity ∇ • v to vorticity ∇ × v. It results in nontrivial chiral free surface dynamics even in the absence of external forces. The structure of the odd-viscosity-induced boundary layer is very different from the conventional free surface boundary layer associated with dissipative shear viscosity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

TEAMER: Biofouling Analysis for Wave Energy Piston Design - Load Cell Data

Biofouling and corrosion are a major concern for all ocean-deployed components, especially when mechanical motion is involved. Triton has developed the concept of a biofouling mitigation seal as part of the piston sealing assembly for the Triton Wave Energy Converter (TSI-WEC). This mitigation seal has the purpose of preventing the formation of a biofilm on the inside of the piston cylinder. It is hypothesized that the prevention of a biofilm will reduce the amount of macro-biofouling that can occur in the piston assembly. The mitigation seal can also reduce the wear on the main dynamic seal, helping to maintain smooth operation and water-tightness. The cylinder is made from a thermoset composite epoxy, which is resistant to corrosion. However, no studies have researched the material's performance with biofouling. Triton placed two prototype Power Take-Off (PTO) assemblies in a PNNL biofouling tank, one with a biofouling mitigation seal and one without, allowing for an evaluation of seal effectiveness at the prevention of biofouling. In actual WEC operation, wave action would react against the piston, which would drive the linear actuator and electric generator, providing electrical power. In the test setup, this was reversed; a linear actuator was powered to drive the piston in a consistent motion within the cylinder. There are two assemblies: one has a biofouling mitigation seal, the other (control) does not. The following data encompasses a 4 month test period, with load cells being used to monitor piston friction force. Results from this testing will be used to improve seal design and material selection, mitigating risk of premature failure during open water testing and evaluation. This project is part of the TEAMER RFTS 3 (request for technical support) program.

16 TIDAL AND WAVE POWER↗

Development of Integrated Education, Training and Research Program with Interdisciplinary Applications

Plasma models have been formulated including realistic spatial profiles of both flow and radio frequency induced ponderomotive force. With these inclusions the picture of stability of various plasma and fluid instabilities, as expected, changed drastically with ground-breaking consequences. The inhomogeneous parallel flow and the radio frequency waves can actually shown to stabilize turbulence. This is different from the prevalent notion that both parallel flow shear and radio frequency waves are responsible for the excitation (destabilization) of plasma turbulence. This has several ground-breaking consequences:- (1) the stabilization by parallel flow clearly goes against the conventional notion of the origin of ionospheric oscillation which invokes parallel flow destabilization as the origin, (2) the stabilization by parallel flow opens us a new avenue for improved mode formation in fusion devices - which mostly rely on the perpendicular flow shear stabilization for improved mode formation but the perpendicular flow is damped in a tokamak - so the improved mode formed by the parallel flow can sustain longer and has more prospect for ignition, (3) the complete stabilization of the ITG mode (and consequent suppression of transport) not only explain many unknown phenomena in the space physics but it also raises a prospect for transport barrier formation by the RF waves but not by the RF induced flow (as most works suggest) which is never observed in a tokamak of that magnitude to create a barrier. These are indeed ground-breaking consequences.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Development of Integrated Education, Training and Research Program with Interdisciplinary Applications II

Plasma models have been formulated including realistic spatial profiles of both flow and radio frequency induced ponderomotive force. With these inclusions the picture of stability of various plasma and fluid instabilities, as expected, changed drastically with ground-breaking consequences. The inhomogeneous parallel flow and the radio frequency waves can actually shown to stabilize turbulence. This is different from the prevalent notion that both parallel flow shear and radio frequency waves are responsible for the excitation (destabilization) of plasma turbulence. This has several ground-breaking consequences:- (1) the stabilization by parallel flow clearly goes against the conventional notion of the origin of ionospheric oscillation which invokes parallel flow destabilization as the origin, (2) the stabilization by parallel flow opens us a new avenue for improved mode formation in fusion devices - which mostly rely on the perpendicular flow shear stabilization for improved mode formation but the perpendicular flow is damped in a tokamak - so the improved mode formed by the parallel flow can sustain longer and has more prospect for ignition, (3) the complete stabilization of the ITG mode (and consequent suppression of transport) not only explain many unknown phenomena in the space physics but it also raises a prospect for transport barrier formation by the RF waves but not by the RF induced flow (as most works suggest) which is never observed in a tokamak of that magnitude to create a barrier. These are indeed ground-breaking consequences.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Coastal Sea Level Observations Record the Twentieth-Century Enhancement of Decadal Climate Variability

Changes in the amplitude of decadal climate variability over the twentieth century have been noted, with most evidence derived from tropical Pacific sea surface temperature records. However, the length, spatial coverage, and stability of most instrumental records are insufficient to robustly identify such nonstationarity, or resolve its global spatial structure. Here, it is found that the long-term, stable, observing platform provided by tide gauges reveals a dramatic increase in the amplitude and spatial coherence of decadal (11–14-yr period) coastal sea level (ζ) variability between 1960 and 2000. During this epoch, western North American ζ was approximately out of phase with ζ in Sydney, Australia, and led northeastern U.S. ζ by approximately 1–2 years. The amplitude and timing of changes in decadal ζ variability in these regions are consistent with changes in atmospheric variability. Specifically, central equatorial Pacific wind stress and Labrador Sea heat flux are highly coherent and exhibit contemporaneous, order-of-magnitude increases in decadal power. These statistical relationships have a mechanistic underpinning: Along the western North American coastline, equatorial winds are known to drive rapidly propagating ζ signals along equatorial and coastal waveguides, while a 1–2-yr lag between Labrador Sea heat fluxes and northeastern United States ζ is consistent with a remotely forced, buoyancy-driven, mechanism. Tide gauges thus provide strong independent support for an increase in interbasin coherence on decadal time scales over the second half of the twentieth century, with implications for both the interpretation and prediction of climate and sea level variability.

54 ENVIRONMENTAL SCIENCES↗

Tropical Indian Ocean Mediates ENSO Influence Over Central Southwest Asia During the Wet Season

El Niño–Southern Oscillation (ENSO) modulates wet season (November–April) precipitation over Central Southwest Asia (CSWA), however, intraseasonal characteristics of its influence are largely unknown, which can be important for its subseasonal to seasonal hydroclimate predictability. Here we show that the ENSO-CSWA teleconnection varies intraseasonally and is a combination of direct and indirect positive influences. The direct influence is through a Rossby wave-like pattern in the tail months. The indirect influence is through an atmospheric dipole of diabatic heating anomalies in the tropical Indian Ocean (TIO) as a result of ENSO-forced response, which also generates a Rossby wave-like forcing and persists throughout the wet season. ENSO exerts its strongest influence when both direct and indirect modes are in phase, while the relationship breaks down when the two modes are out of phase. The atmospheric teleconnection through the atmospheric diabatic heating anomalies in the TIO is reproducible in numerical simulations.

54 ENVIRONMENTAL SCIENCES↗

Maglev for dark matter: Dark-photon and axion dark matter sensing with levitated superconductors

Ultraprecise mechanical sensors offer an exciting avenue for testing new physics. While many of these sensors are tailored to detect inertial forces, magnetically levitated (Maglev) systems are particularly interesting, in that they are also sensitive to electromagnetic forces. In this work, we propose the use of magnetically levitated superconductors to detect dark-photon and axion dark matter through their couplings to electromagnetism. Several existing laboratory experiments search for these dark-matter candidates at high frequencies, but few are sensitive to frequencies below 1 kHz (corresponding to dark-matter masses m DM ≲ 10 − 12 eV ). As a mechanical resonator, magnetically levitated superconductors are sensitive to lower frequencies, and so can probe parameter space currently unexplored by laboratory experiments. Dark-photon and axion dark matter can source an oscillating magnetic field that drives the motion of a magnetically levitated superconductor. This motion is resonantly enhanced when the dark matter Compton frequency matches the levitated superconductor’s trapping frequency. We outline the necessary modifications to make magnetically levitated superconductors sensitive to dark matter, including specifications for both broadband and resonant schemes. We show that in the Hz ≲ f DM ≲ kHz frequency range our technique can achieve the leading sensitivity among laboratory probes of both dark-photon and axion dark matter. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Molecular-Level Insights into the NMR Relaxivity of Gadobutrol Using Quantum and Classical Molecular Simulations

MRI is an indispensable diagnostic tool in modern medicine; however, understanding the molecular-level processes governing NMR relaxation of water in the presence of MRI contrast agents remains a challenge, hindering the molecular-guided development of more effective contrast agents. By using quantum-based polarizable force fields, the first-of-its-kind molecular dynamics (MD) simulations of Gadobutrol are reported where the 1 H NMR longitudinal relaxivity r 1 of the aqueous phase is determined without any adjustable parameters. The MD simulations of r 1 dispersion (i.e., frequency dependence) show good agreement with measurements at frequencies of interest in clinical MRI. Importantly, the simulations reveal key insights into the molecular level processes leading to r 1 dispersion by decomposing the NMR dipole–dipole autocorrelation function G(t) into a discrete set of molecular modes, analogous to the eigenmodes of a quantum harmonic oscillator. The molecular modes reveal important aspects of the underlying mechanisms governing r 1 , such as its multiexponential nature and the importance of the second eigenmodal decay. By simply analyzing the MD trajectories on a parameter-free approach, the Gadobutrol simulations show that the outer-shell water contributes ∼50% of the total relaxivity r 1 compared to the inner-shell water, in contrast to simulations of (nonchelated) gadolinium-aqua where the outer shell contributes only ∼15% of r 1 . The deviation between simulations and measurements of r 1 below clinical MRI frequencies is used to determine the low-frequency electron-spin relaxation time for Gadobutrol, in good agreement with independent studies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Shivalik Plasma Device-I, a glow discharge device to study the collective dynamics of dusty plasma

Using a uniquely configured glow discharge-based Shivalik Plasma Device-I, we demonstrate a variety of collective phenomena in dusty plasma away from the glow discharge region. The cylindrical glass device produces plasma using parallel disc-shaped electrodes with a smaller anode size than the cathode. The dust microparticles are initially sprinkled over the grounded cathode. These particles acquire a significant negative charge upon plasma formation, resulting in their levitation due to the balance between the Coulomb force and gravity. The new device supports the levitation of a big-sized (10 × 8 × 5 cm 3 ) three-dimensional dust cloud over the glass surface. It contrasts the dusty plasma formations in-between electrodes reported earlier. As the discharge voltage varies from high to low, the dust cloud travels from over the glass surface to between the electrodes. A complex interplay of dust void over the cathode, a sharp density gradient, and gravity lead to self-excitation of collective dust phenomena. It includes dust density waves (phase velocity, v ph ~4 cm/s), dust cloud oscillation (frequency, f = 5 Hz), sheared flow (flow velocity, v f ~ 1 cm/s), and multiple-sized dust vortices. These dust vortices provided an excellent platform for studying turbulent mixing phenomena. The power spectrum analysis agreed with two-dimensional Kolmogorov power-law scaling. This is an ideal dusty plasma apparatus where we can create or move the dust cloud to a location of choice from the glass surface to in-between the electrodes and excite one among many collective dust dynamics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Record-Breaking Precipitation in Indonesia's Capital of Jakarta in Early January 2020 Linked to the Northerly Surge, Equatorial Waves, and MJO

A rare record-breaking extreme rainfall event, the highest amount recorded since 1866, hit Indonesia’s capital, Jakarta, in early January 2020. The torrential rainfall was mainly caused by an active cross-equatorial northerly surge (CENS) that occurred concurrently with equatorial waves and Madden-Julian oscillation (MJO). A strong and persistent low-level northerly wind and moisture transport induced by CENS created favorable atmospheric conditions for the formation of deep convection and heavy rainfall over Jakarta. The concurrent occurrences of convectively active phases of equatorial waves (mainly Kelvin, TD-type, and eastward propagating inertia-gravity waves) and MJO during the event further supported the development of heavy rainfall by increasing low-level moisture flux convergence, whereas equatorial Rossby waves contributed indirectly to the increased moisture transport by amplifying cross-equatorial meridional flows toward Jakarta. Together, these large-scale dynamical forcing factors provided a conducive convective environment for the development of mesoscale convective systems and, hence, extreme rainfall over the region.

54 ENVIRONMENTAL SCIENCES↗

Incorporating the Effect of Large‐Scale Vertical Motion on Convection Through Convective Mass Flux Adjustment in E3SMv2

Abstract Recent observational studies suggest that the large‐scale dynamical forcing (vertical motion) plays important roles in deep convection development. In this study we propose a convective mass flux adjustment (MAdj) approach to represent the dynamical effects of large‐scale vertical motion on convection in the Department of Energy's Energy Exascale Earth System Model version 2 (E3SMv2). With MAdj, convection is enhanced (suppressed) when there is large‐scale ascending (descending) motion at the planetary boundary layer top. The coupling of convection with large‐scale circulation significantly improves the simulation of climate variability in E3SMv2 across multiple scales from the diurnal cycle, convectively coupled equatorial waves, to the Madden‐Julian Oscillation (MJO). The standard E3SMv2 tends to simulate overly weak diurnal amplitude of precipitation and overly weak variance of convectively coupled equatorial Kelvin and westward inertio‐gravity (WIG) waves. It also fails to simulate the essential characteristics of the MJO: continuous eastward propagation. With MAdj, the amplitude of diurnal cycle of precipitation is systematically increased and its probability density distribution is much closer to observations. The MAdj can also simulate more realistic eastward propagation of the MJO and much stronger convectively coupled Kelvin and WIG waves. Moreover, the MAdj approach slightly improves the climatology simulations in precipitation, cloud, radiation, circulation, temperature, and moisture fields, with overall root‐mean‐square error (RMSE) of major climatological fields reduced by about 2%. The MAdj approach suppresses excessive grid‐scale precipitation, reducing precipitation wet biases over South China Sea, Philippine Sea, Himalayas, and South Pacific Convergence Zone in western Pacific in summer.

54 ENVIRONMENTAL SCIENCES↗

Quantifying the influence of natural climate variability on in situ measurements of seasonal total and extreme daily precipitation

Abstract While various studies explore the relationship between individual sources of climate variability and extreme precipitation, there is a need for improved understanding of how these physical phenomena simultaneously influence precipitation in the observational record across the contiguous United States. In this work, we introduce a single framework for characterizing the historical signal (anthropogenic forcing) and noise (natural variability) in seasonal mean and extreme precipitation. An important aspect of our analysis is that we simultaneously isolate the individual effects of seven modes of variability while explicitly controlling for joint inter-mode relationships. Our method utilizes a spatial statistical component that uses in situ measurements to resolve relationships to their native scales; furthermore, we use a data-driven procedure to robustly determine statistical significance. In Part I of this work we focus on natural climate variability: detection is mostly limited to DJF and SON for the modes of variability considered, with the El Niño/Southern Oscillation, the Pacific–North American pattern, and the North Atlantic Oscillation exhibiting the largest influence. Across all climate indices considered, the signals are larger and can be detected more clearly for seasonal total versus extreme precipitation. We are able to detect at least some significant relationships in all seasons in spite of extremely large (> 95%) background variability in both mean and extreme precipitation. Furthermore, we specifically quantify how the spatial aspect of our analysis reduces uncertainty and increases detection of statistical significance while also discovering results that quantify the complex interconnected relationships between climate drivers and seasonal precipitation.

54 ENVIRONMENTAL SCIENCES↗

Programmable soft valves for digital and analog control

In soft devices, complex actuation sequences and precise force control typically require hard electronic valves and microcontrollers. Existing designs for entirely soft pneumatic control systems are capable of either digital or analog operation, but not both, and are limited by speed of actuation, range of pressure, time required for fabrication, or loss of power through pull-down resistors. Using the nonlinear mechanics intrinsic to structures composed of soft materials—in this case, by leveraging membrane inversion and tube kinking—two modular soft components are developed: a piston actuator and a bistable pneumatic switch. These two components combine to create valves capable of analog pressure regulation, simplified digital logic, controlled oscillation, nonvolatile memory storage, linear actuation, and interfacing with human users in both digital and analog formats. Three demonstrations showcase the capabilities of systems constructed from these valves: 1) a wearable glove capable of analog control of a soft artificial robotic hand based on input from a human user’s fingers, 2) a human-controlled cushion matrix designed for use in medical care, and 3) an untethered robot which travels a distance dynamically programmed at the time of operation to retrieve an object. This work illustrates pathways for complementary digital and analog control of soft robots using a unified valve design.

42 ENGINEERING↗

On the Regionality of Moist Kelvin Waves and the MJO: The Critical Role of the Background Zonal Flow

Abstract A global model with superparameterized physics is used to shed light on the observed regionality of convectively coupled Kelvin waves and the Madden‐Julian Oscillation (MJO). A series of aquaplanet simulations over zonally uniform sea‐surface temperatures is performed, in which the axisymmetric structure of the background zonal flow is altered through nudging, while maintaining a quasi‐fixed rainfall climatology. Results show that nudging at the equator to match profiles typical of the Indo‐Pacific or eastern Pacific sectors yields eastward‐moving tropical rain spectra typical of those sectors. Two different mechanistic pathways are identified as being responsible for this mean‐flow dependence, in addition to Doppler shifting effects. The first is through shifts of the Rossby wave critical line in the subtropical upper troposphere that affect the lateral forcing of Kelvin‐mode circulations at the equator by eastward and equatorward‐propagating eddies impinging on the tropics from higher latitudes. The second is through changes in the strength of the mean cyclonic shear in the lower tropical troposphere that affect the degree to which intraseasonal fluctuations in Kelvin‐mode zonal winds modulate the activity of higher‐frequency equatorial Rossby‐type eddies. In cases where the mean low‐level cyclonic shear is enhanced, the strength of this modulation, referred to as “shear‐induced eddy modulation” or SIEM, is also seen to be enhanced, such that MJO‐like modes of variability are rendered either unstable or near neutral, depending on the strength of the shear.

Tulich, S. N.↗