Inertial Waves Research Articles

Stewartson layer instability and triadic resonances in rotating sphere with oscillating inner core

This work is devoted to an experimental study of the stability of a steady flow in a rotating spherical cavity with an oscillating core. The case of circular core oscillations in a plane perpendicular to the rotation axis is considered. The steady flow structure strongly depends on the dimensionless oscillation frequency. In the frequency range where there are no inertial waves, the flow resembles a classical Taylor column with an almost uniform distribution of the angular velocity. With an increase in the oscillation amplitude above a certain threshold level, a two-dimensional azimuthal wave is excited at the column boundary. The wave velocity is determined by the intensity of the liquid differential rotation and does not depend on the Ekman number. In the case of oscillation with a frequency less than twice the rotation rate, the inertial waves propagate in fluid bulk and introduce a significant correction to the steady velocity profile. At high amplitudes, the triadic subharmonic resonance of inertial waves is excited. The triadic interactions simultaneously manifest themselves in two regions of the spherical shell, generating secondary waves with the same frequencies, but different wavenumbers: subharmonic waves with shorter (respectively, longer) wavelengths are observed in outer (respectively, inner) regions of the shell. In some cases, the third (intermediate) region with subharmonic waves of intermediate wavelength can be observed. The development of the triadic resonance leads to a strongly nonlinear response in the form of a system of steady vortices with well-defined azimuthal periodicity.

Waves in the Earth's core. II. Magneto–Coriolis modes

We investigate the normal modes of a rapidly rotating, electrically conducting, inviscid fluid sphere in the presence of a background magnetic field. Neglecting the fast modes that are essentially slightly modified inertial waves, we focus on the slower branch of modes traditionally called magneto–Coriolis (MC) modes. We focus on the magnetostrophic limit, an approximation that neglects the fluid inertia for these modes by setting the magnetic Rossby number E η equal to zero, converting the momentum equation from a prognostic to a diagnostic equation. In contrast to a local analysis and contrary to previous assertions, this inertialess-inviscid double limit is perfectly well behaved and shows that E η → 0 and E η = 0 are essentially identical. With applied axisymmetric background fields, we find the modes are critically damped, with decay rates greater than or equal to the eigenfrequency, in contrast to the local theory. We find evidence for both eastward and westward propagating columnar modes, in contradiction of commonly perceived wisdom. The results bode well for numerical time integrations based on the magnetostrophic approximation, which is highly suited to the core of the Earth and holds the potential for more realistic solutions of the dynamo equations.

Atmospheric drivers of a winter-to-spring Lagrangian sea-ice drift in the Eastern Antarctic marginal ice zone

AbstractSea-ice drift in the Antarctic marginal ice zone (MIZ) is discussed using data from a 4-month-long drift of a buoy deployed on a pancake ice floe during the winter sea-ice expansion. We demonstrate increased meandering and drift speeds, and changes in the dynamical regimes of the absolute dispersion during cyclone activity, together with high correlations between drift velocities and wind from atmospheric reanalyses. This indicates a dominant physical control of wind forcing on ice drift and the persistence of free-drift conditions. These conditions occurred despite the buoy remaining largely in >80% ice concentrations and at distances >200 km from the estimated ice edge. The drift is additionally characterised by a strong inertial signature at 13.47 h, which appears initiated by passing cyclones. A wavelet analysis of the buoy's velocity confirms that the momentum transfer from winds at the multi-day frequencies is due to atmospheric forcing, while the initiation of inertial oscillations of sea ice has been identified as the secondary effect. Propagating storm-generated waves may initiate inertial oscillations by increasing the mobility of floes and enhance the drag of the inertial current. This analysis indicates that the Antarctic MIZ in the Indian Ocean sector remains much wider and mobile, during austral winter-to-spring, than defined by sea-ice concentration.

Explosive instability of dust settling in a protoplanetary disc

ABSTRACT It is shown that gas-dust perturbations in a disc with dust settling to the disc mid-plane exhibit the non-linear three-wave resonant interactions between streaming dust wave (SDW) and two inertial waves (IW). In the particular case considered in this paper, SDW at the wavenumber k• = 2κ/(g$z$ts), where κ, g$z$, and ts are, respectively, epicyclic frequency, vertical gravitational acceleration, and particle’s stopping time, interacts with two IW at the lower wavenumbers k′ and k″ such that k′ < kDSI < k″ < k•, where kDSI = κ/(g$z$ts) is the wavenumber of the linear resonance between SDW and IW associated with the previously discovered linear dust settling instability. The problem is solved analytically in the limit of the small dust fraction. As soon as the dynamical dust back reaction on gas is taken into account, k•, k′, and k″ become slightly non-collinear and the emerging interaction of waves leads to simultaneous explosive growth of their amplitudes. This growth is explained by the conservative exchange with energy between the waves. The amplitudes of all three waves grow because the negative energy SDW transfers its energy to the positive energy IW. The product of the dimension-less amplitude of initially dominant wave and the time of explosion can be less than Keplerian time in a disc. It is shown that, generally, the three-wave resonance of an explosive type exists in a wide range of wavenumbers 0 < k• ≤ 2κ/(g$z$ts). An explosive instability of gas-dust mixture may facilitate the dust clumping and the subsequent formation of planetesimals in young protoplanetary discs.

Comments on: nonlinear wind-drift ocean currents in arctic regions

ABSTRACT We clarify and correct an oversight from a recent paper, thus confirming the possibility of a nonlinear coupling of inertial oscillations and Ekman-type spiralling wind-drift currents to yield an exact solution of the system describing the leading-order dynamics of wind-drift arctic flows.

Multiscale Processes of Heavy Rainfall over East Asia in Summer 2020: Diurnal Cycle in Response to Synoptic Disturbances

Abstract Multiscale processes from synoptic disturbances to diurnal cycles during the record-breaking heavy rainfall in summer 2020 were examined in this study. The heavy rainfall consisted of eight episodes, each lasting about 5 days, and were associated with two types of synoptic disturbances. The Type-1 episodes featured a northwestward extending western Pacific subtropical high (WPSH), while the Type-2 episodes had approaching midlatitude troughs with southward retreat in the WPSH. Each heavy rainfall episode had 2–3 occurrences of nocturnal low-level jets (NLLJs), in close association with intense rainfall in the early morning. The NLLJs formed partly due to the geostrophic wind by increased pressure gradients under both types of synoptic disturbances. The NLLJs were also driven by the ageostrophic wind that veered to maximum southerlies at late night due to the boundary-layer inertial oscillation. The diurnal amplitudes of low-level southerlies increased remarkably after the onset of Type-1 episodes, in which the extending WPSH provided strong daytime heating from solar radiation. By contrast, the wind diurnal amplitudes were less changed after the onset of Type-2 episodes. The NLLJs strengthened the mesoscale mean ascent, net moisture flux convergence, and convective instability in elevated warm moist air, which led to the upscale growth of MCSs at the northern terminus of the LLJ after midnight. The MCSs-induced Meiyu rainband was re-established in Central China during the Type-1 episodes with the increased diurnal variations. The findings highlight that the regional diurnal cycles of low-level winds in response to synoptic disturbances can strongly regulate mesoscale convective activities in a downscaling manner, and thus produce heavy rainfall.

One-Dimensional Modeling for Pulsed Flow Twin-Entry Turbine

Abstract One-dimensional (1D) modeling is critical for turbomachinery unsteady performance prediction and system response assessment of internal combustion engines. This paper uses a novel 1D modeling (TURBODYNA) and proposes two additional features for the application to a twin-entry turbocharger turbine. Compared to single-entry turbines, twin-entry turbines enhance turbocharger transient response and reduce engine exhaust valve overlap periods. However, out-of-phase high-frequency pulsating pressure waves lead to an unsteady mixing process from the two flows and pose great challenges to traditional 1D modeling. The present work resolves the mixing problem by directly solving mass, momentum, and energy conservation equations during the mixing process instead of applying constant pressure assumption at the limb–rotor joint. Comparisons of TURBODYNA and an experimentally validated CFD suggest that TURBODYNA cannot only provide a very good agreement on turbine performance but also accurately capture unsteady features due to flow field inertial and pressure wave propagation. Levels of accuracy achieved by TURBODYNA have proved superior to traditional 1D modeling on turbine performance and the generality of the current 1D modeling has been explored by extending the application to other turbine featuring distinct characteristics.

Tidal Dissipation Due to Inertial Waves Can Explain the Circularization Periods of Solar-type Binaries

Abstract Tidal dissipation is responsible for circularizing the orbits and synchronizing the spins of solar-type close binary stars, but the mechanisms responsible are not fully understood. Previous work has indicated that significant enhancements to the theoretically predicted tidal dissipation rates are required to explain the observed circularization periods (P circ) in various stellar populations and their evolution with age. This was based partly on the common belief that the dominant mechanism of tidal dissipation in solar-type stars is turbulent viscosity acting on equilibrium tides in convective envelopes. In this paper, we study tidal dissipation in both convection and radiation zones of rotating solar-type stars following their evolution. We study equilibrium tide dissipation, incorporating a frequency-dependent effective viscosity motivated by the latest hydrodynamical simulations, and inertial wave (dynamical tide) dissipation, adopting a frequency-averaged formalism that accounts for the realistic structure of the star. We demonstrate that the observed binary circularization periods can be explained by inertial wave (dynamical tide) dissipation in convective envelopes. This mechanism is particularly efficient during pre-main-sequence phases, but it also operates on the main sequence if the spin is close to synchronism. The predicted P circ due to this mechanism increases with the main-sequence age in accordance with observations. We also demonstrate that both equilibrium tide and internal gravity-wave dissipation are unlikely to explain the observed P circ, even during the pre-main sequence, based on our best current understanding of these mechanisms. Finally, we advocate more realistic dynamical studies of stellar populations that employ tidal dissipation due to inertial waves.

Tidal Erasure of Stellar Obliquities Constrains the Timing of Hot Jupiter Formation

Abstract Stars with hot Jupiters sometimes have high obliquities, which are possible relics of hot Jupiter formation. Based on the characteristics of systems with and without high obliquities, it is suspected that obliquities are tidally damped when the star has a thick convective envelope, as is the case for main-sequence stars cooler than ∼6100 K, and the orbit is within ∼8 stellar radii. A promising theory for tidal obliquity damping is the dissipation of inertial waves within the star’s convective envelope. Here, we consider the implications of this theory for the timing of hot Jupiter formation. Specifically, hot stars that currently lack a convective envelope possess one during their pre-main sequence. We find that hot Jupiters orbiting within a critical distance of ∼0.02 au from a misaligned main-sequence star lacking a thick convective envelope must have acquired their tight orbits after a few tens of millions of years in order to have retained their obliquities throughout the pre-main sequence. There are four known systems for which this argument applies–XO-3b, Corot-3b, WASP-14b, and WASP-121b–subject to uncertainties surrounding inertial wave dissipation. Moreover, we conclude that a recently identified overabundance of near-polar hot Jupiters is unlikely sculpted by tides, instead reflecting their primordial configuration. Finally, hot Jupiters arriving around cool stars after a few hundreds of millions of years likely find the host star rotating too slowly for efficient obliquity damping. We predict that the critical effective temperature separating aligned and misaligned stars should vary with metallicity, from 6300 to 6000 K as [Fe/H] varies from −0.3 to +0.3.

Path-dependent dynamics induced by rewiring networks of inertial oscillators.

In networks of coupled oscillators, it is of interest to understand how interaction topology affects synchronization. Many studies have gained key insights into this question by studying the classic Kuramoto oscillator model on static networks. However, new questions arise when the network structure is time varying or when the oscillator system is multistable, the latter of which can occur when an inertial term is added to the Kuramoto model. While the consequences of evolving topology and multistability on collective behavior have been examined separately, real-world systems such as gene regulatory networks and the brain may exhibit these properties simultaneously. It is thus relevant to ask how time-varying network connectivity impacts synchronization in systems that can exhibit multistability. To address this question, we study how the dynamics of coupled Kuramoto oscillators with inertia are affected when the topology of the underlying network changes in time. We show that hysteretic synchronization behavior in networks of coupled inertial oscillators can be driven by changes in connection topology alone. Moreover, we find that certain fixed-density rewiring schemes induce significant changes to the level of global synchrony that remain even after the network returns to its initial configuration, and we show that these changes are robust to a wide range of network perturbations. Our findings highlight that the specific progression of network topology over time, in addition to its initial or final static structure, can play a considerable role in modulating the collective behavior of systems evolving on complex networks.

Can We Improve the Realism of Gravity Wave Parameterizations by Imposing Sources at All Altitudes in the Atmosphere?

AbstractA multiwave non‐orographic gravity wave (GW) scheme is adapted to represent waves of small intrinsic phase speed, inertial waves, and wave emission from all altitudes. This last change removes the launching altitude parameter, an arbitrary parameter systematically used in GW schemes. In offline calculations using reanalysis fields, these changes impose larger amplitude, saturated waves everywhere in the middle atmosphere, which produces more realistic GW vertical spectra than in previous configurations. The same scheme, tested online in the Laboratoire de Météorologie Dynamique Zoom (LMDz) general circulation model, performs at least as well as the operational non‐orographic GW scheme. Some modest benefits are seen, for instance, in the equatorial tilt with altitude of the winter jets in the middle atmosphere. Although the scheme includes the effects of inertial waves, which are detected in the mesosphere by different observational platforms, the configuration that gives a reasonable climatology in LMDz hinders their vertical propagation and limits their presence at mesospheric altitudes.

The saturation of the VSI in protoplanetary discs via parametric instability

ABSTRACT The vertical shear instability (VSI) is a robust and potentially important phenomenon in irradiated protoplanetary discs (PPDs), yet the mechanism by which it saturates remains poorly understood. Global simulations suggest that the non-linear evolution of the VSI is dominated by radially propagating inertial wavetrains (called ‘body modes’), but these are known to be susceptible to a parametric instability. In this paper, we propose that the global VSI saturates via this secondary instability, which initiates a redistribution of energy from the large scales to smaller scale inertial waves, and finally into a turbulent cascade. We present an analytic theory of the instability in a simple idealized model that captures the main physical and mathematical details of the problem. In addition, we conduct numerical simulations with the snoopy code to consolidate the theory. We argue that it is challenging to capture parametric instability in global simulations unless the radial resolution is very fine, possibly ∼300 grid cells per scale height in radius; thus the VSI is likely far more disordered and incoherent than current global simulations suggest.

Dynamic analysis and performance assessment of the Inertial Sea Wave Energy Converter (ISWEC) device via harmonic balance

Given the particular energy-maximising performance objective, wave energy converter (WEC) systems are prone to exhibit highly nonlinear behaviour. We present, in this paper, a detailed dynamic analysis and control synthesis for the Inertial Sea Wave Energy Converter (ISWEC) system, deriving and considering a comprehensive associated nonlinear model. In particular, we adopt a harmonic balance (HB) method to achieve this objective, producing the so-called amplitude-frequency curves (AFC) for the corresponding ISWEC nonlinear model, derived via a Lagrangian approach. We demonstrate that the system can present a variety of different behaviours which are completely neglected by its linear model counterpart. Leveraging both the efficiency, and convenient representation of the HB method, we synthesise so-called ‘passive’ (i.e. proportional) energy-maximising controllers using a variety of input conditions. We provide a comparison of the obtained control parameters with those arising from standard linear modelling, showing a consistent improvement in performance by effectively considering the relevant nonlinear ISWEC dynamics.

Inertial Waves in a Rotating Spherical Shell with Homogeneous Boundary Conditions

We find the analytical form of inertial waves in an incompressible, rotating fluid constrained by concentric inner and outer spherical surfaces with homogeneous boundary conditions on the normal components of velocity and vorticity. These fields are represented by Galerkin expansions whose basis consists of toroidal and poloidal vector functions, i.e., products and curls of products of spherical Bessel functions and vector spherical harmonics. These vector basis functions also satisfy the Helmholtz equation and this has the benefit of providing each basis function with a well-defined wavenumber. Eigenmodes and associated eigenfrequencies are determined for both the ideal and dissipative cases. These eigenmodes are formed from linear combinations of the Galerkin expansion basis functions. The system is truncated to numerically study inertial wave structure, varying the number of eigenmodes. The largest system considered in detail is a 25 eigenmode system and a graphical depiction is presented of the five lowest dissipation eigenmodes, all of which are non-oscillatory. These results may be useful in understanding data produced by numerical simulations of fluid and magnetofluid turbulence in a spherical shell that use a Galerkin, toroidal–poloidal basis as well as qualitative features of liquids confined by a spherical shell.

Flow structures in spanwise rotating plane Poiseuille flow based on thermal analogy

The analogy between rotating shear flow and thermal convection suggests the existence of plumes, inertial waves and plume currents in plane Poiseuille flow under spanwise rotation. The existence of these flow structures is examined with the results of three-dimensional and two-dimensional three-component direct numerical simulations. The dynamics of plumes near the unstable side is embodied in a truncated exponential distribution of turbulent fluctuations. For large rotation numbers, inertial waves are identified near the stable side, and these can be used to explain the abnormal flow statistics, such as the large root-mean-square of the streamwise velocity fluctuation and the nearly negligible Reynolds shear stress. For small or medium rotation numbers, plumes generated from the unstable side form large-scale plume currents and the patterns of the plume currents show different capabilities in scalar transport.

Inertial Gyro Wave Energy Conversion Nonlinear Modeling and Power-Index Predictive Control for Autonomous Ship

The complex marine environment and the high energy consumption of shipboard equipment pose challenges to the long-term navigation of autonomous unmanned ships. In wave-induced motion, inertial gyro antirolling technology is used to offset the energy transmitted by waves, but the massive consumption of energy is not conducive to long-term navigation of the unmanned ships. This paper attempts to exploit the wave energy transmitted by the gyro to improve the power supply of the unmanned ship. Firstly, a nonlinear coupling model of the gyro antirolling device and the unmanned ship is established. Secondly, considering various model constraints and physical constraints of the equipment, the energy evaluation objective function of nonlinear model predictive control (NMPC) is designed. In the simulation, the proposed control method can effectively extract electric energy from different waves.

Mesoscale influences on the development of a dryline in Argentina: A modelling case study

Drylines are a frequent feature of the atmospheric circulation in Argentina. Recent work described their climatological characteristics and synoptic-scale processes associated with their formation. However, little is known about the mesoscale processes that are relevant for their life cycle. In this paper, we investigate the influence of these mechanisms on the formation and movement using a case-study approach. Also, the relationship between these mechanisms and convective initiation near the dryline is investigated. A typical northern Patagonia dryline is simulated using the Weather Research and Forecasting (WRF) with an horizontal resolution of 3 km. The FLEXible PARTicle dispersion-WRF is also used to study some of the processes from a Lagrangian perspective. During the quiescent period corresponding to dryline formation and intensification, the dryline strengthens along the axis of a thermally-induced surface trough that promotes differential moisture advection. Also, convergence along the dryline is enhanced during night-time by the inertial oscillation ahead of the dryline and by the development of a thermally-driven circulation between the elevated terrain in northern Patagonia and the adjacent plains. These two mechanisms contribute to enhancing the intensity of the moisture gradient and to trigger deep moist convection. Under a period of stronger synoptic forcing, the dryline intensifies in response to the confluence induced by the deepening surface trough and moves away from the terrain elevations. Its movement during this period is driven by horizontal dry advection and the vertical mixing enhanced by the entrainment into the boundary layer of extremely dry air, whose origin can be traced back to the mid-levels over the Pacific Ocean. When the magnitude of the low-level westerly winds increase, moister air from lower levels cross the barrier, contributing to weakening the moisture gradient at the dryline.

On the Diurnal Cycle of Heavy Rainfall over the Sichuan Basin during 10\u201318 August 2020

A sustained heavy rainfall event occurred over the Sichuan basin in southwest China during 10–18 August 2020, showing pronounced diurnal rainfall variations with nighttime peak and afternoon minimum values, except on the first day. Results show that the westward extension of the anomalously strong western Pacific subtropical high was conducive to the maintenance of a southerly low-level jet (LLJ) in and to the southeast of the basin, which favored continuous water vapor transport and abnormally high precipitable water in the basin. The diurnal cycle of rainfall over the basin was closely related to the periodic oscillation of the LLJ in both wind speed and direction that was caused by the combination of inertial oscillation and terrain thermal forcing. The nocturnally enhanced rainfall was produced by moist convection mostly initiated during the evening hours over the southwest part of the basin where high convective available potential energy with moister near-surface moist air was present. The convective initiation took place as cold air from either previous precipitating clouds from the western Sichuan Plateau or a larger-scale northerly flow met a warm and humid current from the south. It was the slantwise lifting of the warm, moist airflow above the cold air, often facilitated by southwest vortices and quasi-geostrophic ascent, that released the convective instability and produced heavy rainfall.

Responses of the atmospheric boundary layer to a low‐latitude mesoscale SST front

AbstractThe responses of the atmospheric boundary layer at low latitudes (20°N) to forcing by an ocean‐mesoscale sea surface temperature (SST) front are investigated under the conditions that the background wind intersects with the SST front (i.e., there are cross‐frontal and along‐frontal wind components) through ideal numerical experiments. The simulation results show that the responses of the atmospheric boundary layer are sensitive to the background wind speed and its direction relative to the SST front. The type of convergence and divergence of Ekman transport and that of the background wind can be constructive or destructive, depending on the relative orientation of the background wind and the SST front. When the two kinds of convergence and divergence are constructive, they can cause strong convergence and divergence in the boundary layer near the SST front; further, the unbalanced state forced over the SST front will excite inertial gravity waves propagating into the free atmosphere. The vertical velocity excited in this case is much greater than that when there is only a cross‐frontal background wind component with an equivalent magnitude. On the contrary, when the two kinds of convergence and divergence are destructive, the resultants of convergence and divergence are reduced significantly, and the interaction between the boundary layer and the aloft atmosphere decays rapidly with height. The significance of the results obtained for the analysis of coastal precipitation are discussed.

Flow structures, nonlinear inertial waves and energy transfer in rotating spheres

We investigate flow structures, nonlinear inertial waves and energy transfer in a rotating fluid sphere, using a Galerkin spectral method based on helical-wave decomposition (HWD). Numerical simulations of flows in a sphere are performed with different system rotation rates, where a large-scale forcing is employed. For the case without system rotation, the intense vortex structures are tube-like. When a weak rotation is introduced, small-scale structures are reduced and vortex tubes tend to align with the rotation axis. As the rotation rate increases, a large-scale anticyclonic vortex structure is formed near the rotation axis. The structure is shown to be led by certain geostrophic modes. When the rotation rate further increases, a cyclone and an anticyclone emerge from the top and bottom of the boundary, respectively, where two quasi-geostrophic equatorially symmetric inertial waves dominate the flow. Based on HWD, effects of spherical confinement on rotating turbulence are systematically studied. It is found that the forward cascade becomes weaker as the rotation increases. When the rotation rate becomes larger than some critical value, dual energy cascades emerge, with an inverse cascade at large scales and a forward cascade at small scales. Finally, the flow behavior near the boundary is studied, where the average boundary layer thickness gets smaller when system rotation increases. The flow behavior in the boundary layer is closely related to the interior flow structures, which create significant mass flux between the boundary layer and the interior fluid through Ekman pumping.