Excitation Of Gravity Waves Research Articles

Tidal Spin-up of Subdwarf B Stars

Hot subdwarf B (sdB) stars are stripped helium-burning stars that are often found in close binaries, where they experience strong tidal interactions. The dissipation of tidally excited gravity waves alters their rotational evolution throughout the sdB lifetime. While many sdB binaries have well-measured rotational and orbital frequencies, there have been few theoretical efforts to accurately calculate the tidal torque produced by gravity waves. In this work, we directly calculate the tidal excitation of internal gravity waves in realistic sdB stellar models and integrate the coupled spin–orbit evolution of sdB binaries. We find that for canonical sdB (M sdB = 0.47 M ⊙) binaries, the transitional orbital period below which they could reach tidal synchronization in the sdB lifetime is ∼0.2 day, with weak dependence on the companion masses. For low-mass sdBs (M sdB = 0.37 M ⊙) formed from more massive progenitor stars, the transitional orbital period becomes ∼0.15 day. These values are very similar to the tidal synchronization boundary (∼0.2 day) evident from observations. We discuss the dependence of tidal torques on stellar radii, and we make predictions for the rapidly rotating white dwarfs formed from synchronized sdB binaries.

Mesoscale weather influenced by auroral gravity waves contributing to conditional symmetric instability release?

Abstract. We consider possible influence on severe weather occurrence in the context of solar wind coupling to the magnetosphere–ionosphere–atmosphere system, mediated by aurorally excited atmospheric gravity waves. Solar wind high-speed streams from coronal holes cause intensifications of ionospheric currents at high latitudes launching gravity waves propagating in the upper and lower atmosphere. While these gravity waves reach the troposphere with much attenuated amplitudes, they can contribute to conditional symmetric instability release and intensification of storms. Severe weather events, including winter storms and heavy rainfall causing floods and flash floods, show a tendency to follow arrivals of solar wind high-speed streams from coronal holes. The ERA5 re-analysis is used to evaluate slantwise convective available potential energy and vertically integrated extent of realizable symmetric instability to assess the likelihood of slantwise convection in frontal zones of extratropical cyclones during severe snowstorms and flash floods. The observed low-level southerly winds and high wind shears in these regions are favorable conditions for over-reflection of down-going aurorally excited gravity waves potentially contributing to conditional symmetric instability release leading to slantwise convection and high-rate precipitation.

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.

A parametric large-eddy simulation study of wind-farm blockage and gravity waves in conventionally neutral boundary layers

We present a suite of large-eddy simulations (LES) of a wind farm operating in conventionally neutral boundary layers. A fixed 1.6 GW wind farm is considered for 40 different atmospheric stratification conditions to investigate effects on wind-farm efficiency and blockage, as well as related gravity-wave excitation. A tuned Rayleigh damping layer and a wave-free fringe-region method are used to avoid spurious excitation of gravity waves, and a domain-size study is included to evaluate and minimize effects of artificial domain blockage. A fully neutral reference case is also considered, to distinguish between a case with hydrodynamic blockage only, and cases that include hydrostatic blockage induced by the air column above the boundary layer and the excitation of gravity waves therein. We discuss in detail the dependence of gravity-wave excitation, flow fields and wind-farm blockage on capping-inversion height, strength and free-atmosphere lapse rate. In all cases, an unfavourable pressure gradient is present in front of the farm, and a favourable pressure gradient in the farm, with hydrostatic contributions arising from gravity waves at least an order of magnitude larger than hydrodynamic effects. Using respectively non-local and wake efficiencies $\eta _{nl}$ and $\eta _{w}$ , we observe a strong negative correlation between the unfavourable upstream pressure rise and $\eta _{nl}$ , and a strong positive correlation between the favourable pressure drop in the farm and $\eta _{w}$ . Using a simplified linear gravity-wave model, we formulate a simple scaling for the ratio $(1-\eta _{nl})/\eta _{w}$ , which matches reasonably well with the LES results.

Repeated Cyclogenesis on Hot-Exoplanet Atmospheres with Deep Heating.

Most current models of hot-exoplanet atmospheres assume shallow heating, a strong day-night differential heating near the top of the atmosphere. Here we investigate the effects of energy deposition at differing depths in a model tidally locked gas-giant exoplanet. We perform high-resolution atmospheric flow simulations of hot-exoplanet atmospheres forced with idealized thermal heating representative of shallow and deep heating (i.e., stellar irradiation strongly deposited at ∼10^{3} Pa and ∼10^{5} Pa pressure levels, respectively). Unlike with shallow heating, the flow with deep heating exhibits a new dynamic equilibrium state, characterized by repeated generation of giant cyclonic storms that move away westward once formed. The formation is accompanied by a burst of heightened turbulence, leading to the production of small-scale flow structures and large-scale mixing of temperature on a timescale of ∼3 planetary rotations. Significantly, while effects that could be important (e.g., coupled radiative flux and convectively excited gravity waves) are not included, over a timescale of several hundred days the simulations robustly show that the emergent thermal flux depends strongly on the heating type and is distinguishable by current observations.

Tracking Local Sea Ice Extent in the Beaufort Sea Using Distributed Acoustic Sensing and Machine Learning

Abstract Monitoring sea ice extent is critical to understand long-term trends in climate change. Here, we show that ambient noise recorded by fiber-optic sensing technology deployed in an Arctic shallow marine seafloor environment can track sea ice extent. We use a 37.4 km long section of fiber-optic cable deployed offshore of Oliktok Point, Alaska. Data are analyzed for two weeks: one in July 2021 and another in November 2021, when there is incomplete and evolving sea ice coverage. We apply different Machine Learning algorithms to identify types of ambient seismic noise in frequency–time scalogram images. We find evidence for two dominant noise types related to excitation of oceanic gravity waves in open water and the presence of sea ice with sufficient strength to suppress wave action. Comparison of the Distributed Acoustic Sensing (DAS) noise clustering results with satellite-based observations indicates that seafloor DAS can complement sea ice constraints from satellite imagery by locally increasing spatial and temporal resolution and tracking for which ice coverage is sufficient to diminish ocean waves.

3D hydrodynamics simulations of internal gravity waves in red giant branch stars

ABSTRACT We present the first 3D hydrodynamics simulations of the excitation and propagation of internal gravity waves (IGWs) in the radiative interiors of low-mass stars on the red giant branch (RGB). We use the ppmstar explicit gas dynamics code to simulate a portion of the convective envelope and all the radiative zone down to the hydrogen-burning shell of a $1.2\, {\rm M}_{\odot }$ upper RGB star. We perform simulations for different grid resolutions (7683, 15363, and 28803), a range of driving luminosities, and two different stratifications (corresponding to the bump luminosity and the tip of the RGB). Our RGB tip simulations can be directly performed at the nominal luminosity, circumventing the need for extrapolations to lower luminosities. A rich, continuous spectrum of IGWs is observed, with a significant amount of total power contained at high wavenumbers. By following the time evolution of a passive dye in the stable layers, we find that IGW mixing in our simulations is weaker than predicted by a simple analytical prescription based on shear mixing and not efficient enough to explain the missing RGB extra mixing. However, we may be underestimating the efficiency of IGW mixing given that our simulations include a limited portion of the convective envelope. Quadrupling its radial extent compared to our fiducial set-up increases convective velocities by up to a factor 2 and IGW velocities by up to a factor 4. We also report the formation of a $\sim 0.2\, H_P$ penetration zone and evidence that IGWs are excited by plumes that overshoot into the stable layers.

Ocean Surface Gravity Wave Excitation of Flexural Gravity and Extensional Lamb Waves in Ice Shelves

Flexure and extension of ice shelves in response to incident ocean surface gravity waves have been linked to iceberg calving, rift growth, and even disintegration of ice shelves. Most modeling studies utilize a plate bending model for the ice, focusing exclusively on flexural gravity waves. Ross Ice shelf seismic data shows not only flexural gravity waves, with dominantly vertical displacements, but also extensional Lamb waves, which propagate much faster with dominantly horizontal displacements. Our objective is to model the full-wave response of ice shelves, including ocean compressibility, ice elasticity, and gravity. Our model is a 2D vertical cross-section of the ice shelf and sub-shelf ocean cavity. We quantify the frequency-dependent excitation of flexural gravity and extensional Lamb waves and provide a quantitative theory for extensional Lamb wave generation by the horizontal force imparted by pressure changes on the vertical ice shelf edge exerted by gravity waves. Our model predicts a horizontal to vertical displacement ratio that increases with decreasing frequency, with ratio equal to unity at ~0.001 Hz. Furthermore, in the very long period band (<0.003 Hz), tilt from flexural gravity waves provides an order of magnitude larger contribution to seismometer horizontal components than horizontal displacements from extensional Lamb waves.

Tidally excited gravity waves in the cores of solar-type stars: resonances and critical-layer formation

ABSTRACT We simulate the propagation and dissipation of tidally induced non-linear gravity waves in the cores of solar-type stars. We perform hydrodynamical simulations of a previously developed Boussinesq model using a spectral-element code to study the stellar core as a wave cavity that is periodically forced at the outer boundary with a given azimuthal wavenumber and an adjustable frequency. For low-amplitude forcing, the system exhibits resonances with standing g modes at particular frequencies, corresponding to a situation in which the tidal torque is highly frequency-dependent. For high-amplitude forcing, the excited waves break promptly near the centre and spin up the core so that subsequent waves are absorbed in an expanding critical layer (CL), as found in previous work, leading to a tidal torque with a smooth frequency-dependence. For intermediate-amplitude forcing, we find that linear damping of the waves gradually spins up the core such that the resonance condition can be altered drastically. The system can evolve towards or away from g-mode resonances, depending on the difference between the forcing frequency and the closest eigenfrequency. Eventually, a CL forms and absorbs the incoming waves, leading to a situation similar to the high-amplitude case in which the waves break promptly. We study the dependence of this process on the forcing amplitude and frequency, as well as on the diffusion coefficients. We emphasize that the small Prandtl number in the centre of solar-like stars facilitates the development of a differentially rotating core owing to the non-linear feedback of waves. Our simulations and analysis reveal that this important mechanism may drastically change the phase of gravity waves and thus the classical picture of resonance locking in solar-type stars needs to be revised.

Stochastic excitation of internal gravity waves in rotating late F-type stars: A 3D simulation approach

Context. There are no strong constraints placed thus far on the amplitude of internal gravity waves (IGWs) that are stochastically excited in the radiative interiors of solar-type stars. Late F-type stars have relatively thin convective envelopes with fast convective flows and tend to be fast rotators compared to solar-type stars of later spectral types. These two elements are expected to directly impact the IGW excitation rates and properties. Aims. We want to estimate the amplitude of stochastically excited gravity modes (g-modes) in F-type stars for different rotational regimes. Methods. We used the ASH code to perform 3D simulations of deep-shell models of 1.3 M⊙ F-type solar-type stars, including the radiative interior and the shallow convective envelope. Results. We found different differential rotation regimes in the convective zone, depending on the rotation rate we imposed on the stellar models. We find that the convective structures and the overshoot properties are affected by rotation. The IGWs are excited by interface interactions between convective plumes and the top of the radiative interior. We were able to characterise the IGWs and g-mode properties in the radiative interior, and we compared these properties using the computation from the 1D oscillation code GYRE. The amplitude of low-frequency modes is significantly higher in fast-rotating models and the evolution of the period spacing of consecutive modes exhibits evidence of a behaviour that is modified by the influence of the Coriolis force. For our fastest rotating model, we were able to detect the intermediate degree g-mode signature near the top of the simulation domain. Nevertheless, the predicted luminosity perturbations from individual modes still remain at small amplitudes. Conclusions. We obtained mode amplitudes that are several orders of magnitude higher than those of prior 3D simulations of solar models. Our simulations suggest that g-mode signatures could be detectable in late F-type stars, which are the hottest main-sequence solar-type pulsating stars. We therefore emphasise that they constitute object of primary importance for improving our understanding of internal stellar dynamics.

Toward fully compressible numerical simulations of stellar magneto-convection with the RAMSES code

Context. Numerical simulations of magneto-convection have greatly expanded our understanding of stellar interiors and stellar magnetism. Recently, fully compressible hydrodynamical simulations of full-star models have demonstrated the feasibility of studying the excitation and propagation of pressure and internal gravity waves in stellar interiors, which would allow for a direct comparison with asteroseismological measurements. However, the impact of magnetic fields on such waves has not been taken into account yet in three-dimensional simulations. Aims. We conduct a proof of concept for the realization of three-dimensional, fully compressible, magneto-hydrodynamical numerical simulations of stellar interiors with the RAMSES code. Methods. We adapted the RAMSES code to deal with highly subsonic turbulence, typical of stellar convection, by implementing a well-balanced scheme in the numerical solver. We then ran and analyzed three-dimensional hydrodynamical and magneto-hydrodynamical simulations with different resolutions of a plane-parallel convective envelope on a Cartesian grid. Results. Both hydrodynamical and magneto-hydrodynamical simulations develop a quasi-steady, turbulent convection layer from random density perturbations introduced over the initial profiles. The convective flows are characterized by small-amplitude fluctuations around the hydrodynamical equilibrium of the stellar interior, which is preserved over the whole simulation time. Using our compressible well-balanced scheme, we were able to model flows with Mach numbers as low as ℳ ∼ 10−3, but even lower Mach number flows are possible in principle. In the magneto-hydrodynamical runs, we observe an exponential growth of magnetic energy consistent with the action of a small-scale dynamo. The weak seed magnetic fields are amplified to mean strengths of 37% relative to the kinetic equipartition value in the highest resolution simulation. Since we chose a compressible approach, we see imprints of pressure and internal gravity waves propagating in the stable regions above and beneath the convection zone. In the magneto-hydrodynamical case, we measured a deficit in acoustic and internal gravity wave power with respect to the purely hydrodynamical counterpart of 16% and 13%, respectively. Conclusions. The well-balanced scheme implemented in RAMSES allowed us to accurately simulate the small-amplitude, turbulent fluctuations of stellar (magneto-)convection. The qualitative properties of the convective flows, magnetic fields, and excited waves are in agreement with previous studies in the literature. The power spectra, profiles, and probability density functions of the main quantities converge with resolution. Therefore, we consider the proof of concept to be successful. The deficit of acoustic power in the magneto-hydrodynamical simulation shows that magnetic fields must be included in the study of pressure waves in stellar interiors. We conclude by discussing future developments.

Impact of radial truncation on global 2D hydrodynamic simulations for a Sun-like model

ABSTRACT Stellar convection is a non-local process responsible for the transport of heat and chemical species. It can lead to enhanced mixing through convective overshooting and excitation of internal gravity waves (IGWs) at convective boundaries. The relationship between these processes is still not well understood and requires global hydrodynamic simulations to capture the important large-scale dynamics. The steep stratification in stellar interiors suggests that the radial extent of such simulations can affect the convection dynamics, the IGWs in the stably stratified radiative zone, and the depth of the overshooting layer. We investigate these effects using 2D global simulations performed with the fully compressible stellar hydrodynamics code music. We compare eight different radial truncations of the same solar-like stellar model evolved over approximately 400 convective turnover times. We find that the location of the inner boundary has an insignificant effect on the convection dynamics, the convective overshooting, and the travelling IGWs. We relate this to the background conditions at the lower convective boundary which are unaffected by the truncation, as long as a significantly deep radiative layer is included in the simulation domain. However, we find that extending the outer boundary by only a few per cent of the stellar radius significantly increases the velocity and temperature perturbations in the convection zone, the overshooting depth, the power and the spectral slope of the IGWs. The effect is related to the background conditions at the outer boundary, which are determined in essence by the hydrostatic stratification and the given luminosity.

Numerical Convergence of 2D Solar Convection in Implicit Large-eddy Simulations

Abstract Large-eddy simulations (LES) and implicit LES (ILES) are wise and affordable alternatives to the unfeasible direct numerical simulations of turbulent flows at high Reynolds (Re) numbers. However, for systems with few observational constraints, it is a formidable challenge to determine if these strategies adequately capture the physics of the system. Here, we address this problem by analyzing numerical convergence of ILES of turbulent convection in 2D, with resolutions between 642 and 20482 grid points, along with the estimation of their effective viscosities, resulting in effective Reynolds numbers between 1 and ∼104. The thermodynamic structure of our model resembles the solar interior, including a fraction of the radiative zone and the convection zone. In the convective layer, the ILES solutions converge for the simulations with ≥5122 grid points, as evidenced by the integral properties of the flow and its power spectra. Most importantly, we found that even a resolution of 1282 grid points, Re ∼ 10 , is sufficient to capture the dynamics of the large scales accurately. This is a consequence of the ILES method allowing the energy contained in these scales to be the same in simulations with low and high resolution. Special attention is needed in regions with a small density scale height driving the formation of fine structures unresolved by the numerical grid. In the stable layer, we found the excitation of internal gravity waves, yet high resolution is needed to capture their development and interaction.

Wake properties and power output of very large wind farms for different meteorological conditions and turbine spacings: a large-eddy simulation case study for the German Bight

Abstract. Germany's expansion target for offshore wind power capacity of 40 GW by the year 2040 can only be reached if large portions of the Exclusive Economic Zone in the German Bight are equipped with wind farms. Because these wind farm clusters will be much larger than existing wind farms, it is unknown how they will affect the boundary layer flow and how much power they will produce. The objective of this large-eddy simulation study is to investigate the wake properties and the power output of very large potential wind farms in the German Bight for different turbine spacings, stabilities and boundary layer heights. The results show that very large wind farms cause flow effects that small wind farms do not. These effects include, but are not limited to, inversion layer displacement, counterclockwise flow deflection inside the boundary layer and clockwise flow deflection above the boundary layer. Wakes of very large wind farms are longer for shallower boundary layers and smaller turbine spacings, reaching values of more than 100 km. The wake in terms of turbulence intensity is approximately 20 km long, in which longer wakes occur for convective boundary layers and shorter wakes for stable boundary layers. Very large wind farms in a shallow, stable boundary layer can excite gravity waves in the overlying free atmosphere, resulting in significant flow blockage. The power output of very large wind farms is higher for thicker boundary layers because thick boundary layers contain more kinetic energy than thin boundary layers. The power density of the energy input by the geostrophic pressure gradient limits the power output of very large wind farms. Because this power density is very low (approximately 2 W m−2), the installed power density of very large wind farms should be small to achieve a good wind farm efficiency.

On gravity wave parameterisation in vicinity of low‐level blocking

AbstractThis note is framed as an open question to the community regarding parameterisation schemes using the blocking layer depth to reduce the orographic gravity wave drag. It is the purpose of this note to argue that the current orographic gravity wave drag parameterisation in the vicinity of blocking is inadequate. Reducing the gravity wave amplitude (and thereby reducing the gravity wave drag) by assuming an effective mountain height dependent on the blocking depth is not realistic. The arguments given here will hopefully spark a debate and new considerations, ultimately leading to improvements in current orographic gravity wave drag parameterisations. This note illustrates that low‐level blocking can induce more gravity waves or gravity waves with a higher momentum flux (compared to the current parameterisation schemes). More realistic parameterisation schemes are likely to improve the models' performance. However, the fact is complex theories are needed to describe gravity wave excitation by orography so that it is difficult to represent gravity wave nature by a ‘too simple’ parameterisation scheme.

Non-linear tidal excitation of superharmonic gravity waves in main-sequence stars in binary and exoplanetary systems

ABSTRACT We study the role of non-linear effects on tidally excited internal gravity waves in stellar radiation zones in exoplanetary or binary systems. We are partly motivated to study tides due to massive short-period hot Jupiters, which preferentially orbit stars with convective cores, for which wave breaking near the stellar centre cannot operate. We develop a theory (and test it with numerical calculations) for the non-linear excitation of superharmonic ‘secondary’ waves (with frequencies 2ωp) by a ‘primary’ tidal wave (with frequency ωp) near the interface between the radiation zone and convective envelope. These waves have the same horizontal phase speeds to leading order, and this non-linear effect could contribute importantly to tidal dissipation if the secondary waves can efficiently damp the primary. We derive criteria involving the orbital and stellar parameters required to excite these secondary waves to large amplitudes using a local model of the radiative/convective interface, which we convert to apply to tides in a spherical star. We numerically evaluate the critical amplitudes required for this new non-linear effect to become important using stellar models, comparing them to the ‘conventional’ criteria for wave breaking in radiative cores and the application of WKBJ theory near convective cores. The criteria for this new effect are easier to satisfy than the conventional measures of non-linearity in 1.4 and $2\, {\rm M}_\odot$ stars on the main sequence. We predict non-linear effects to be important even for planetary-mass companions around the latter, but this effect is probably less important in stars with radiative cores.

Stratospheric Gravity Waves Excited by a Propagating Rossby Wave Train—A DEEPWAVE Case Study

Abstract Stratospheric gravity waves observed during the DEEPWAVE research flight RF25 over the Southern Ocean are analyzed and compared with numerical weather prediction (NWP) model results. The quantitative agreement of the NWP model output and the tropospheric and lower-stratospheric observations is remarkable. The high-resolution NWP models are even able to reproduce qualitatively the observed upper-stratospheric gravity waves detected by an airborne Rayleigh lidar. The usage of high-resolution ERA5 data—partially capturing the long internal gravity waves—enabled a thorough interpretation of the particular event. Here, the observed and modeled gravity waves are excited by the stratospheric flow past a deep tropopause depression belonging to an eastward-propagating Rossby wave train. In the reference frame of the propagating Rossby wave, vertically propagating hydrostatic gravity waves appear stationary; in reality, of course, they are transient and propagate horizontally at the phase speed of the Rossby wave. The subsequent refraction of these transient gravity waves into the polar night jet explains their observed and modeled patchy stratospheric occurrence near 60°S. The combination of both unique airborne observations and high-resolution NWP output provides evidence for the one case investigated in this paper. As the excitation of such gravity waves persists during the quasi-linear propagation phase of the Rossby wave’s life cycle, a hypothesis is formulated that parts of the stratospheric gravity wave belt over the Southern Ocean might be generated by such Rossby wave trains propagating along the midlatitude waveguide.

Analysis of Ionospheric Disturbance Response to the Heavy Rain Event

Meteorological activities in the troposphere would affect electron concentrations and distributions in the ionosphere, thereby exciting ionospheric disturbance. To explore the ionospheric anomalies during severe convective weather, the ionospheric phenomenon during the heavy rainfall in Sichuan Province on 9 July 2013 was analyzed based on GNSS data. The Total Electron Content (TEC) are evaluated by carrier phase smoothed pseudoranges. Then, the dTEC (detrend TEC) sequences are obtained by using the cubic smoothing spline. They show obvious N-shaped ionospheric disturbances and have propagation characteristics, with the maximum of 0.4 TECU. Frequency domain analysis using continuous wavelet transform (CWT) also reached similar conclusions—that there are obvious ionospheric disturbances with different frequencies and intensity. Based on the isotropic assumption and feature points method, the horizontal propagation velocity of the disturbances in the ionosphere is estimated to be approximately 150 m/s. Then, Sichuan Province is divided into 1° × 1° grids, and the disturbance trigger source is determined via the grid searching method to be the central of Sichuan Province. Finally, the mechanisms causing ionospheric disturbance are discussed. During the heavy rainfall, the strong convection may excite gravity waves (GWs), which are driven by terrain and background wind fields to propagate upwards to the ionosphere and release energy, causing ionospheric disturbances.

Radiation-induced instability of a finite-chord Nemtsov membrane

We consider a problem of stability of a membrane of an infinite span and a finite chord length, submerged in a uniform flow of finite depth with free surface. In the shallow water approximation, Nemtsov [“Flutter effect and emission in the region of anomalous and normal Doppler effects,” Radiophys. Quantum Electron. 28(12), 1076–1079 (1985)] has shown that an infinite-chord membrane is susceptible to flutter instability due to the excitation of long gravity waves on the free surface if the velocity of the flow exceeds the phase velocity of the waves and related this phenomenon with the anomalous Doppler effect. In the present work, we derive a full nonlinear eigenvalue problem for an integrodifferential equation for the finite-chord Nemtsov membrane in the finite-depth flow. In the shallow- and deep-water limits, we develop a perturbation theory in the small added mass ratio parameter acting as an effective dissipation to find explicit analytical expressions for the frequencies and the growth rates of the membrane modes coupled to the surface waves. We find an intricate pattern of instability pockets in the parameter space and describe it analytically. The case of an arbitrary depth flow with free surface requires numerical solution of a new non-polynomial nonlinear eigenvalue problem. We propose an original approach combining methods of complex analysis and residue calculus, Galerkin discretization, Newton method, and parallelization techniques implemented in MATLAB to produce high-accuracy stability diagrams within an unprecedented wide range of a system's parameters. We believe that the Nemtsov membrane plays the same paradigmatic role for understanding radiation-induced instabilities as the Lamb oscillator coupled to a string has played for understanding radiation damping.

Orbital Decay of Short-period Exoplanets via Tidal Resonance Locking

Abstract A large fraction of known exoplanets have short orbital periods where tidal excitation of gravity waves within the host star causes the planets’ orbits to decay. We study the effects of tidal resonance locking, in which the planet locks into resonance with a tidally excited stellar gravity mode. Because a star’s gravity mode frequencies typically increase as the star evolves, the planet’s orbital frequency increases in lockstep, potentially causing much faster orbital decay than predicted by other tidal theories. Due to nonlinear mode damping, resonance locking in Sun-like stars likely only operates for low-mass planets (M ≲ 0.1 M Jup), but in stars with convective cores it can likely operate for all planetary masses. The orbital decay timescale with resonance locking is typically comparable to the star’s main-sequence lifetime, corresponding to a wide range in effective stellar quality factor (103 ≲ Q′ ≲ 109), depending on the planet’s mass and orbital period. We make predictions for several individual systems and examine the orbital evolution resulting from both resonance locking and nonlinear wave dissipation. Our models demonstrate how short-period massive planets can be quickly destroyed by nonlinear mode damping, while short-period low-mass planets can survive, even though they undergo substantial inward tidal migration via resonance locking.