scholarly journals Tidal dissipation in evolving low-mass and solar-type stars with predictions for planetary orbital decay

2020 ◽  
Vol 498 (2) ◽  
pp. 2270-2294
Author(s):  
A J Barker
Keyword(s):  
Gravity Waves ◽  
Wave Breaking ◽  
Effective Viscosity ◽  
Main Sequence ◽  
Internal Gravity Waves ◽  
Stellar Structure ◽  
Tidal Dissipation ◽  
Dominant Mechanism ◽  
Hot Jupiters ◽  
Orbital Decay

ABSTRACT We study tidal dissipation in stars with masses in the range 0.1–1.6 M⊙ throughout their evolution, including turbulent effective viscosity acting on equilibrium tides and inertial waves (IWs) in convection zones, and internal gravity waves in radiation zones. We consider a range of stellar evolutionary models and incorporate the frequency-dependent effective viscosity acting on equilibrium tides based on the latest simulations. We compare the tidal flow and dissipation obtained with the conventional equilibrium tide, which is strictly invalid in convection zones, finding that the latter typically overpredicts the dissipation by a factor of 2–3. Dissipation of IWs is computed using a frequency-averaged formalism accounting for realistic stellar structure for the first time, and is the dominant mechanism for binary circularization and synchronization on the main sequence. Dissipation of gravity waves in the radiation zone assumes these waves to be fully damped (e.g. by wave breaking), and is the dominant mechanism for planetary orbital decay. We calculate the critical planetary mass required for wave breaking as a function of stellar mass and age, and show that this mechanism predicts destruction of many hot Jupiters but probably not Earth-mass planets on the main sequence. We apply our results to compute tidal quality factors following stellar evolution, and tidal evolutionary time-scales, for the orbital decay of hot Jupiters, and the spin synchronization and circularization of binary stars. We also provide predictions for shifts in transit arrival times due to tidally driven orbital decay of hot Jupiters that may be detected with NGTS, TESS, or PLATO.

scholarly journals Internal wave breaking and the fate of planets around solar-type stars

2010 ◽  
Vol 6 (S271) ◽  
pp. 363-364
Author(s):  
Adrian J. Barker ◽  
Gordon I. Ogilvie
Keyword(s):  
Gravity Waves ◽  
Wave Breaking ◽  
Internal Gravity Waves ◽  
Amplitude Dependence ◽  
Tidal Dissipation ◽  
Short Period ◽  
Central Regions ◽  
Solar Type ◽  
The Waves ◽  
Solar Type Star

AbstractInternal gravity waves are excited at the interface of convection and radiation zones of a solar-type star, by the tidal forcing of a short-period planet. The fate of these waves as they approach the centre of the star depends on their amplitude. We discuss the results of numerical simulations of these waves approaching the centre of a star, and the resulting evolution of the spin of the central regions of the star and the orbit of the planet. If the waves break, we find efficient tidal dissipation, which is not present if the waves perfectly reflect from the centre. This highlights an important amplitude dependence of the (stellar) tidal quality factor Q′, which has implications for the survival of planets on short-period orbits around solar-type stars, with radiative cores.

scholarly journals Numerical and the MU radar estimations of gravity wave enhancement and turbulent ozone fluxes near the tropopause

2004 ◽  
Vol 22 (11) ◽  
pp. 3889-3898 ◽  
Author(s):  
N. M. Gavrilov ◽  
S. Fukao
Keyword(s):  
Gravity Waves ◽  
Wave Breaking ◽  
Internal Gravity Waves ◽  
Vertical Temperature ◽  
Turbulent Diffusion Coefficient ◽  
Middle Latitudes ◽  
Mu Radar ◽  
Different Seasons ◽  
Ozone Fluxes ◽  
Vertical Ozone

Abstract. It is shown with a numerical simulation that a sharp increase in the vertical temperature gradient and Brunt-Väisälä frequency near the tropopause may produce an increase in the amplitudes of internal gravity waves (IGWs) propagating upward from the troposphere, wave breaking and generation of stronger turbulence. This may enhance the transport of admixtures between the troposphere and stratosphere in the middle latitudes. Turbulent diffusion coefficient calculated numerically and measured with the MU radar are of 1-10m2/s in different seasons in Shigaraki, Japan (35° N, 136° E). These values lead to the estimation of vertical ozone flux from the stratosphere to the troposphere of (1-10)x1014, which may substantially add to the usually supposed ozone downward transport with the general atmospheric circulation. Therefore, local enhancements of IGW intensity and turbulence at tropospheric altitudes over mountains due to their orographic excitation and due to other wave sources may lead to the changes in tropospheric and total ozone over different regions.

Transport by breaking internal gravity waves on slopes

2016 ◽  
Vol 789 ◽  
pp. 93-126 ◽  
Author(s):  
Robert S. Arthur ◽  
Oliver B. Fringer
Keyword(s):  
Gravity Waves ◽  
Wave Breaking ◽  
Internal Gravity Waves ◽  
Length Scale ◽  
Two Dimensional ◽  
Turbulent Diffusivity ◽  
Nepheloid Layer ◽  
Molecular Diffusivity ◽  
Tracking Model ◽  
Offshore Transport

We use the results of a direct numerical simulation (DNS) with a particle-tracking model to investigate three-dimensional transport by breaking internal gravity waves on slopes. Onshore transport occurs within an upslope surge of dense fluid after breaking. Offshore transport occurs due to an intrusion of mixed fluid that propagates offshore and resembles an intermediate nepheloid layer (INL). Entrainment of particles into the INL is related to irreversible mixing of the density field during wave breaking. Maximum onshore and offshore transport are calculated as a function of initial particle position, and can be of the order of the initial wave length scale for particles initialized within the breaking region. An effective cross-shore dispersion coefficient is also calculated, and is roughly three orders of magnitude larger than the molecular diffusivity within the breaking region. Particles are transported laterally due to turbulence that develops during wave breaking, and this lateral spreading is quantified with a lateral turbulent diffusivity. Lateral turbulent diffusivity values calculated using particles are elevated by more than one order of magnitude above the molecular diffusivity, and are shown to agree well with turbulent diffusivities estimated using a generic length scale turbulence closure model. Based on a favourable comparison of DNS results with those of a similar two-dimensional case, we use two-dimensional simulations to extend our cross-shore transport results to additional wave amplitude and bathymetric slope conditions.

scholarly journals Oceanic tides from Earth-like to ocean planets

2018 ◽  
Vol 615 ◽  
pp. A23 ◽  
Author(s):  
P. Auclair-Desrotour ◽  
S. Mathis ◽  
J. Laskar ◽  
J. Leconte
Keyword(s):  
Gravity Waves ◽  
Three Dimensional ◽  
Stable Stratification ◽  
Internal Gravity Waves ◽  
Tidal Dissipation ◽  
Planetary Rotation ◽  
Wide Range ◽  
Oceanic Tides ◽  
3D Effects ◽  
Tidal Response

Context. Oceanic tides are a major source of tidal dissipation. They drive the evolution of planetary systems and the rotational dynamics of planets. However, two-dimensional (2D) models commonly used for the Earth cannot be applied to extrasolar telluric planets hosting potentially deep oceans because they ignore the three-dimensional (3D) effects related to the ocean’s vertical structure. Aims. Our goal is to investigate, in a consistant way, the importance of the contribution of internal gravity waves in the oceanic tidal response and to propose a modelling that allows one to treat a wide range of cases from shallow to deep oceans. Methods. A 3D ab initio model is developed to study the dynamics of a global planetary ocean. This model takes into account compressibility, stratification, and sphericity terms, which are usually ignored in 2D approaches. An analytic solution is computed and used to study the dependence of the tidal response on the tidal frequency and on the ocean depth and stratification. Results. In the 2D asymptotic limit, we recover the frequency-resonant behaviour due to surface inertial-gravity waves identified by early studies. As the ocean depth and Brunt–Väisälä frequency increase, the contribution of internal gravity waves grows in importance and the tidal response becomes 3D. In the case of deep oceans, the stable stratification induces resonances that can increase the tidal dissipation rate by several orders of magnitude. It is thus able to significantly affect the evolution time scale of the planetary rotation.

A note on breaking waves

1988 ◽  
Vol 419 (1857) ◽  
pp. 323-335 ◽  
Keyword(s):  
Phase Velocity ◽  
Gravity Waves ◽  
Turbulent Mixing ◽  
Wave Breaking ◽  
Richardson Number ◽  
Breaking Waves ◽  
Internal Gravity Waves ◽  
Time Interval ◽  
Wave Groups ◽  
Surface Gravity Waves

Some simple general properties of wave breaking are deduced from the known behaviour of surface gravity waves in deep water, on the assumption that breaking occurs in association with wave groups. In particular we derive equations for the time interval, ז, between the onset of breaking of successive waves: ז ═ T / |1 – ( c ⋅ c g )/ c 2 |, and for the propagation vector c b (referred to as the ‘wave-breaking vector’) of the position at which breaking, once initiated, will proceed: c b ═ c (1 – c ⋅ c g / c 2 )+ c g . Here c is the phase velocity, and c g the group velocity, of waves of period T . Interfacial waves, internal gravity waves, inertial waves and planetary waves are considered as particular examples. The results apply not only to wave breaking, but to the movement of any property (e. g. fluid acceleration, gradient Richardson number) that is carried through a medium in association with waves. One application is to describe the distribution, in space and time, of regions of turbulent mixing, or transitional phenomena, in the oceans or atmosphere.

Excitation and breaking of internal gravity waves by parametric instability

1998 ◽  
Vol 374 ◽  
pp. 117-144 ◽  
Author(s):  
DOMINIQUE BENIELLI ◽  
JOËL SOMMERIA
Keyword(s):  
Gravity Waves ◽  
Wave Breaking ◽  
Parametric Instability ◽  
Excitation Frequency ◽  
Vertical Plane ◽  
Excitation Amplitude ◽  
Internal Gravity Waves ◽  
Stratified Medium ◽  
Primary Wave ◽  
Maximum Slope

We study the dynamics of internal gravity waves excited by parametric instability in a stably stratified medium, either at the interface between a water and a kerosene layer, or in brine with a uniform gradient of salinity. The tank has a rectangular section, and is narrow to favour standing waves with motion in the vertical plane. The fluid container undergoes vertical oscillations, and the resulting modulation of the apparent gravity excites the internal waves by parametric instability.Each internal wave mode is amplified for an excitation frequency close to twice its natural frequency, when the excitation amplitude is sufficient to overcome viscous damping (these conditions define an ‘instability tongue’ in the parameter space frequency-amplitude). In the interfacial case, each mode is well separated from the others in frequency, and behaves like a simple pendulum. The case of a continuous stratification is more complex as different modes have overlapping instability tongues. In both cases, the growth rates and saturation amplitudes behave as predicted by the theory of parametric instability for an oscillator. However, complex friction effects are observed, probably owing to the development of boundary-layer instabilities.In the uniformly stratified case, the excited standing wave is unstable via a secondary parametric instability: a wave packet with small wavelength and half the primary wave frequency develops in the vertical plane. This energy transfer toward a smaller scale increases the maximum slope of the iso-density surfaces, leading to local turning and rapid growth of three-dimensional instabilities and wave breaking. These results illustrate earlier stability analyses and numerical studies. The combined effect of the primary excitation mechanism and wave breaking leads to a remarkable intermittent behaviour, with successive phases of growth and decay for the primary wave over long timescales.

A study of the occurrence of dynamically unstable conditions in the middle atmosphere

1984 ◽  
Vol 62 (10) ◽  
pp. 963-967 ◽  
Author(s):  
Kevin Hamilton
Keyword(s):  
Gravity Waves ◽  
Wave Breaking ◽  
Middle Atmosphere ◽  
Internal Gravity Waves ◽  
Small Scale ◽  
Simple Analysis ◽  
Quantitative Estimates ◽  
Shear Instabilities ◽  
Vertically Propagating ◽  
The Tropics

There has recently been a great deal of interest in the possibility that vertically propagating internal gravity waves may be dissipated by small-scale convective or shear instabilities in the upper stratosphere and mesosphere. In the present study, a very simple analysis of about 3000 rocket soundings of temperature and wind at several stations between 8°N and 59°N was conducted in order to obtain quantitative estimates of the frequency of occurrence of dynamically unstable conditions as a function of height, latitude, and season. It was found that in about one-third of the profiles, the local Richardson number dropped below 0.25 at some level near the stratopause. From the results, it appears that gravity wave "breaking" generally occurs at considerably higher altitudes in the tropics than in midlatitudes. There is also a fairly clear indication of higher wave breaking levels in summer than in winter, at least at high latitudes.

scholarly journals Photometric detection of internal gravity waves in upper main-sequence stars

2019 ◽  
Vol 621 ◽  
pp. A135 ◽  
Author(s):  
D. M. Bowman ◽  
C. Aerts ◽  
C. Johnston ◽  
M. G. Pedersen ◽  
T. M. Rogers ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Gravity Waves ◽  
Main Sequence ◽  
Low Frequency ◽  
Internal Gravity Waves ◽  
Main Sequence Stars ◽  
Photometric Detection ◽  
F Stars ◽  
Low Frequency Power ◽  
Frequency Power

Context. Main sequence stars with a convective core are predicted to stochastically excite internal gravity waves (IGWs), which effectively transport angular momentum throughout the stellar interior and explain the observed near-uniform interior rotation rates of intermediate-mass stars. However, there are few detections of IGWs, and fewer still made using photometry, with more detections needed to constrain numerical simulations. Aims. We aim to formalise the detection and characterisation of IGWs in photometric observations of stars born with convective cores (M ≳ 1.5 M⊙) and parameterise the low-frequency power excess caused by IGWs. Methods. Using the most recent CoRoT light curves for a sample of O, B, A and F stars, we parameterised the morphology of the flux contribution of IGWs in Fourier space using an MCMC numerical scheme within a Bayesian framework. We compared this to predictions from IGW numerical simulations and investigated how the observed morphology changes as a function of stellar parameters. Results. We demonstrate that a common morphology for the low-frequency power excess is observed in early-type stars observed by CoRoT. Our study shows that a background frequency-dependent source of astrophysical signal is common, which we interpret as IGWs. We provide constraints on the amplitudes of IGWs and the shape of their detected frequency spectrum across a range of mass, which is the first ensemble study of stochastic variability in such a diverse sample of stars. Conclusions. The evidence of a low-frequency power excess across a wide mass range supports the interpretation of IGWs in photometry of O, B, A and F stars. We also discuss the prospects of observing hundreds of massive stars with the Transiting Exoplanet Survey Satellite (TESS) in the near future.

scholarly journals Radiative hydrodynamic simulations of turbulent convection and pulsations of Kepler target stars

2013 ◽  
Vol 9 (S301) ◽  
pp. 193-196
Author(s):  
Irina N. Kitiashvili
Keyword(s):  
Gravity Waves ◽  
Main Sequence ◽  
Energy Transport ◽  
Turbulence Modeling ◽  
Internal Gravity Waves ◽  
Turbulent Convection ◽  
Hydrodynamic Simulations ◽  
Stellar Pulsations ◽  
Excitation Mechanisms ◽  
Scale Turbulence

AbstractThe problem of interaction of stellar pulsations with turbulence and radiation in stellar convective envelopes is central to our understanding of excitation mechanisms, oscillation amplitudes and frequency shifts. Realistic (“ab initio”) numerical simulations provide unique insights into the complex physics of pulsation-turbulence-radiation interactions, as well as into the energy transport and dynamics of convection zones, beyond the standard evolutionary theory. 3D radiative hydrodynamics simulations have been performed for several Kepler target stars, from M- to A-class along the main sequence, using a new ‘StellarBox’ code, which takes into account all essential physics and includes subgrid scale turbulence modeling. The results reveal dramatic changes in the convection and pulsation properties among stars of different mass. For relatively massive stars with thin convective envelopes, the simulations allow us to investigate the dynamics the whole envelope convection zone including the overshoot region, and also look at the excitation of internal gravity waves. Physical properties of the turbulent convection and pulsations, and the oscillation spectrum for two of these targets are presented and discussed in this paper. In one of these stars, with mass 1.47 M⊙, we simulate the whole convective zone and investigate the overshoot region at the boundary with the radiative zone.

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