Tidal Friction Research Articles

Characteristic Analysis of Vertical Tidal Profile Parameters at Tidal Current Energy Site

Many mathematical models have been proposed to estimate vertical tidal current profiles. However, as previous studies have shown that tidal current energy sites have different characteristics in their vertical tidal current profiles, it is necessary to estimate the profiles from field-measured data for practical purposes. In this study, we measured layered tidal currents over two months using an acoustic Doppler current profiler (ADCP) to analyze the characteristics of vertical tidal current profiles at the Jangjuk Strait, a candidate site for tidal current energy. As a result, the power law parameter α and bed roughness β were estimated as 4.51–12.41 and 0.38–0.42, respectively. Additionally, the maximum roughness length representing seabed roughness in the logarithmic profile was estimated as 0.221 m, and the estimated friction velocity was 0.038–0.194 m/s. Furthermore, a high correlation was observed between the depth-averaged tidal current velocity and friction velocities at all sites during flood and ebb tide conditions. A high correlation was also found between the bed roughness, roughness length, and power law exponent at relatively deeper sites. Tidal current energy sites display distinct characteristics compared to other sea areas. Therefore, it is essential to account for field conditions when conducting numerical modeling and design.

Strong Cosmic Censorship with bounded curvature

Abstract In this paper we propose a weaker version of Penrose’s much heeded Strong Cosmic Censorship (SCC) conjecture, asserting inextendability of maximal Cauchy developments by manifolds with Lipschitz continuous Lorentzian metrics and Riemann curvature bounded in Lp. Lipschitz continuity is the threshold regularity for causal structures, and curvature bounds rule out infinite tidal accelerations, arguing for physical significance of this weaker SCC conjecture. The main result of this paper, under the assumption that no extensions exist with higher connection regularity W1,p loc, proves in the affirmative this SCC conjecture with bounded curvature for p sufficiently large, (p > 4 with uniform bounds, p > 2 without uniform bounds).

The increasingly dominant role of climate change on length of day variations

The melting of ice sheets and global glaciers results in sea-level rise, a pole-to-equator mass transport increasing Earth's oblateness and resulting in an increase in the length of day (LOD). Here, we use observations and reconstructions of mass variations at the Earth's surface since 1900 to show that the climate-induced LOD trend hovered between 0.3 and 1.0 ms/cy in the 20th century, but has accelerated to 1.33 [Formula: see text] 0.03 ms/cy since 2000. We further show that surface mass transport fully explains the accelerating trend in the Earth oblateness observed in the past three decades. We derive an independent measure of the decreasing LOD trend induced by Glacial Isostatic Adjustment (GIA) of [Formula: see text]0.80 [Formula: see text] 0.10 ms/cy, which provides a constraint for the mantle viscosity. The sum of this GIA rate and lunar tidal friction fully explains the secular LOD trend that is inferred from the eclipse record in the past three millennia prior to the onset of contemporary climate change. Projections of future climate warming under high emission scenarios suggest that the climate-induced LOD rate may reach 2.62 [Formula: see text] 0.79 ms/cy by 2100, overtaking lunar tidal friction as the single most important contributor to the long-term LOD variations.

TASTE

The discovery of the first transiting hot Jupiters (HJs), giant planets on orbital periods shorter than P ~ 10 days, was announced more than 20 years ago. As both ground- and space-based follow-up observations are piling up, we are approaching the temporal baseline required to detect secular variations in their orbital parameters. In particular, several recent studies have focused on constraining the efficiency of the tidal decay mechanism to better understand the evolutionary timescales of HJ migration and engulfment. This can be achieved by measuring a monotonic decrease in orbital period dP/dt < 0 due to mechanical energy being dissipated by tidal friction. WASP-12b was the first HJ for which a tidal decay scenario appeared convincing, even though alternative explanations have been hypothesized. Here we present a new analysis based on 28 unpublished high-precision transit light curves gathered over a 12-yr baseline and combined with all the available archival data, and an updated set of stellar parameters from HARPS-N high-resolution spectra, which are consistent with a main-sequence scenario, close to the hydrogen exhaustion in the core. Our values of dP/dt = −30.72 ± 2.67 and Q′* = (2.13 ± 0.18) × 105 are statistically consistent with previous studies, and indicate that WASP-12 is undergoing fast tidal dissipation. We additionally report the presence of excess scatter in the timing data and discuss its possible origin.

PIONEERS: a 6DoF motion sensor to measure rotation and tides in the Solar System

Observation of rotation variations and tides provides constraints on the interior properties of celestial bodies. Both can be precisely measured with a 6DoF (Degrees of Freedom) motion sensor placed on their surface. This type of instrument measures rotation rates and linear accelerations in a large frequency band, which includes the frequencies involved in the tides and rotation variations. A novel sensor under development aims to measure rates and accelerations with an amplitude spectral density of 2μrads-1Hz-1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${2}\\,\\upmu \ extrm{rad}\\, \ extrm{s}^{-1} \ extrm{H}\ extrm{z}^{-1/2}$$\\end{document} and 20μms-2Hz-1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${20}\\,\\upmu \ extrm{m}\\,\ extrm{s}^{-2} \ extrm{H}\ extrm{z}^{-1/2}$$\\end{document} respectively in its compact version and three orders of magnitude better (5nrads-1Hz-1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${5}\\,\ extrm{nrad}\\, \ extrm{s}^{-1} \ extrm{H}\ extrm{z}^{-1/2}$$\\end{document} and 10pms-2Hz-1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${10}\\,\ extrm{pm}\\,\ extrm{s}^{-2} \ extrm{H}\ extrm{z}^{-1/2}$$\\end{document}, respectively) with its high-performance version. Here, we compare these instrument performances with the precision required to measure rotation and tides in order to improve our knowledge of the interior of nine celestial bodies identified as targets for future space missions: Dimorphos, Phobos, Europa, Io, Titan, Enceladus, Triton, the Moon and Mars. Results indicate that Phobos, the Moon, and Mars cannot be investigated with the compact model, but that the interior of the other bodies can be constrained through measurements of rotation rate, and/or centrifugal acceleration, and/or tidal acceleration. We also find that the high-performance prototype instrument is suitable for acceleration measurements for all nine bodies, but not adequate for inferring interior constraints from rotation rate measurements for Triton, the Moon, and Mars. The signatures of the interior in the rotation rate and centrifugal and tidal accelerations also provide scientific requirements for future developments of 6DoF motion sensors for these nine bodies.Graphical

Back to the present: A general treatment for the tidal field from the wake of dynamical friction

Context. Dynamical friction can be a valuable tool for inferring dark matter properties that are difficult to constrain by other methods. Most applications of dynamical friction calculations are concerned with the long-term angular momentum loss and orbital decay of the perturber within its host. This, however, assumes knowledge of the unknown initial conditions of the system. Aims. We advance an alternative methodology to infer the host properties from the perturber’s shape distortions induced by the tides of the wake of dynamical friction, which we refer to as the tidal dynamical friction. Methods. As the shape distortions rely on the tidal field that has a predominantly local origin, we present a strategy to find the local wake by integrating the stellar orbits back in time along with the perturber, then removing the perturber’s potential and re-integrating them back to the present. This provides perturbed and unperturbed coordinates and hence a change in coordinates, density, and acceleration fields, which yields the back-reaction experienced by the perturber. Results. The method successfully recovers the tidal field of the wake based on a comparison with N-body simulations. We show that similar to the tidal field itself, the noise and randomness of the dynamical friction force due to the finite number of stars is also dominated by regions close to the perturber. Stars near the perturber influence it more but are smaller in number, causing a high variance in the acceleration field. These fluctuations are intrinsic to dynamical friction. We show that a stellar density of 0.0014 M⊙ kpc−3 yields an inherent variance of 10% to the dynamical friction. Conclusions. The current method extends the family of dynamical friction methods that allow for the inference of host properties from tidal forces of the wake. It can be applied to specific galaxies, such as Magellanic Clouds, with Gaia data.

The maximum mass of a black hole which can tidally disrupt a star: measuring black hole spins with tidal disruption events

ABSTRACT The tidal acceleration experienced by an object at the event horizon of a black hole decreases as one over the square of the black hole’s mass. As such there is a maximum mass at which a black hole can tidally disrupt an object outside of its event horizon and potentially produce observable emission. This maximum mass is known as the ‘Hills mass’, and in full general relativity is a function of both the black hole’s spin a• and the inclination angle of the incoming object’s orbit with respect to the black hole’s spin axis ψ. In this paper, we demonstrate that the Hills mass can be represented by a simple analytical function of a• and ψ, the first general solution of this problem. This general solution is found by utilizing the symmetries of a class of critical Kerr metric orbits known as the innermost bound spherical orbits. Interestingly, at fixed black hole spin the maximum Hills mass can lie at incoming orbital inclinations outside of the black hole’s equatorial plane ψ ≠ π/2. When compared to previous results in the literature this effect can lead to an increase in the maximum Hills mass (at fixed spin) by as much as a factor of $\sqrt{11/5} \simeq 1.48$ for a maximally rotating black hole. We then demonstrate how Bayesian inference, coupled with an estimate of the mass of a black hole in a tidal disruption event, can be used to place conservative constraints on that black hole’s spin. We provide a publicly available code tidalspin which computes these spin distributions.

Surface gravity from tidal acceleration

Surface gravity from tidal acceleration

Impact of tidal friction on the motion of lithospheric plates and earthquake activity

AbstractThis paper draws attention to the contribution of tidal friction (TF) to plate tectonic processes. Our proposed model supports recent geodetic observations and geodynamic models highlighting exogenous local contributions to plate motions. The TF has a westward effect on lithospheric plates and the lithosphere as a whole. To determine the extent of this effect, we use the asthenospheric viscosity estimated using the Eötvös force. We also show that TF has a detectable impact on the latitudinal distribution of earthquake activity.

Tidal Angular Momentum in Close Binary Systems in presence of Wind Driven Non-conservative Mass Transfer with Uniform Mass Accretion Rate

A very well-known property of close binary stars is that they usually rotate slowly than a similar type single star. Massive stars in close binary systems are supposed to experience an exchange of mass and angular momentum via mass transfer and tidal interaction, and thus the evolution of binary stars becomes more complex than that of individual stars. In recent times, it has become clear that a large number of massive stars interact with binary companions before they die. The observation also reveals that in close pairs the rotation tends to be synchronized with the orbital motion and the companions are naturally tempted to invoke tidal friction. We here introduce the effect of tidal angular momentum in the model of wind driven non-conservative mass transfer taking mass accretion rate as uniform with respect to time. To model the angular momentum evolution of a low mass main sequence companion star can be a challenging task. So, to make the present study more interesting, we have considered initial masses of the donor and gainer stars at the proximity of bottom-line main sequence stars and they are taken with lower angular momentum. We have produced a graphical profile of the rate of change of tidal angular momentum and the variation of tidal angular momentum with respect to time under the present consideration.

Deviation of geodesics and particle trajectories in a gravitational wave of the Bianchi type VI universe

For the Bianchi type VI universe, exact solutions of the equation of geodesic deviation in a strong primordial gravitational wave in a privileged coordinate system are obtained. The solutions refer to Shapovalov’s gravitational-wave models of spacetime and allow the existence of complete integrals of the Hamilton–Jacobi equation for test particles. For all the solutions obtained, the analytical form of the tidal acceleration vector in a strong primordial gravitational wave is obtained. An explicit form of the coordinate transformation, an explicit form of the metric of the primordial gravitational wave of the Bianchi type VI universe, and the form of the tidal acceleration vector in the laboratory synchronous coordinate system are obtained. The synchronous coordinate system is associated with a freely falling observer and allows the observer to separate time and spatial coordinates, as well as to synchronize time at different points in space. The presented mathematical approach can be applied both in the general theory of relativity and in modified theories of gravity.

Deviation of Geodesics, Particle Trajectories and the Propagation of Radiation in Gravitational Waves in Shapovalov Type III Wave Spacetimes

A class of exact (non-perturbative) models of strong gravitational waves based on Shapovalov type III spacetimes and Einstein’s vacuum equations is obtained. Exact solutions are found for the trajectories of particles and radiation in a gravitational wave in privileged coordinate systems. Exact solutions are obtained for the equations of geodesic deviation and tidal acceleration of particles in a gravitational wave in privileged coordinate systems. An explicit analytical law of transition from a privileged coordinate system to a synchronous reference system associated with a freely falling observer with an explicit selection of time and spatial coordinates is obtained. An explicit form of the metric of a gravitational wave in a synchronous frame of reference is obtained. For a synchronous frame of reference, the trajectories of particles and radiation, the deviation of geodesics, and tidal accelerations in a gravitational wave are obtained. The presented methods and approaches are applicable both to Einstein’s general theory of relativity and to modified theories of gravity.

Shallow water tides induced by frictional nonlinearity in the Bohai and Yellow Seas

In shallow waters, tidal friction at seabed is proportional to the square of tidal current velocity, and can induce shallow water tides. M2, S2 and N2 are the most important semi-diurnal constituents in the Bohai and Yellow Seas, and their interaction through the frictional nonlinearity can induce shallow water tides, with 2MS2 and 2MN2 being the most representative constituents. In this paper, we analyze the observed hourly records at 27 tidal stations along the coast of the Bohai and Yellow Seas and obtain harmonic constants of μ2 and L2 constituents, which can be separated into astronomical parts μ2′ and L2′, and frictional nonlinearity-induced parts, 2MS2 and 2MN2, respectively. A numerical model is also performed to simulate the constituents 2MS2 and 2MN2. It shows a fairly good agreement between the model and observations in the harmonic constants of constituents 2MS2 and 2MN2. The cotidal charts of 2MS2 and 2MN2 are presented. It is found that the frictional nonlinearity-induced shallow water tides can significantly reduce the main fortnightly and monthly modulations.

The origin of an overpopulation of contact binary plutinos

ABSTRACT In the trans-Neptunian region, 10–25 per cent of binary objects are contact binaries. However, the amplitude of the light curves of a sample of plutinos indicates that this fraction could reach 50 per cent or even more. This remarkable difference cannot be explained by the single action of the Kozai cycles and tidal friction (KCTF), nor it can be assumed that it is due to a formation mechanism different from the one that gave rise to the binaries of the other hot populations. In this work, we present numerical simulations showing that a superabundance of contact binaries occurs as a natural consequence of the coupling between the dynamical evolution of the mutual orbit of the binaries subject to the action of KCTF and the variation of the heliocentric orbit of the binary centre of mass due to the perturbations of the giant planets. This same mechanism affects the other populations, but to a lesser extent, because the variations of the heliocentric orbits are much smaller for them than for objects that are within the 3:2 mean motion resonance with Neptune. This mechanism also increases the fraction of tight binaries in the plutino population, where it could reach $\sim 30~{{\ \rm per\ cent}}$.

Self-consistent Spin, Tidal, and Dynamical Equations of Motion in the REBOUNDx Framework

We introduce self-consistent spin, tidal, and dynamical equations of motion into REBOUNDx, a library of additional effects for the popular N-body integrator REBOUND. The equations of motion used are derived from the constant time lag approximation to the equilibrium tide model of tidal friction. These effects will allow the study of a variety of systems of which the full dynamical picture cannot be encapsulated by point particle dynamics. We provide several test cases and benchmark the code’s performance against analytic predictions. The open-source code is available in the most recent release of REBOUNDx.

Tidal drag and westward drift of the lithosphere

Tidal forces are generally neglected in the discussion about the mechanisms driving plate tectonics despite a worldwide geodynamic asymmetry also observed at subduction and rift zones. The tidal drag could theoretically explain the westerly shift of the lithosphere relative to the underlying mantle. Notwithstanding, viscosity in the asthenosphere is apparently too high to allow mechanical decoupling produced by tidal forces. Here, we propose a model for global scale geodynamics accompanied by numerical simulations of the tidal interaction of the Earth with the Moon and the Sun. We provide for the first time a theoretical proof that the tidal drag can produce a westerly motion of the lithosphere, also compatible with the slowing of the Earth’s rotational spin. Our results suggest a westerly rotation of the lithosphere with a lower bound of ω≈(0.1-0.2)°/Myr in the presence of a basal effective shear viscosity η≈1016 Pa·s, but it may rise to ω>1°/Myr with a viscosity of η≲3×1014 Pa·s within the Low-Velocity Zone (LVZ) atop the asthenosphere. This faster velocity would be more compatible with the mainstream of plate motion and the global asymmetry at plate boundaries. Based on these computations, we suggest that the super-adiabatic asthenosphere, being vigorously convecting, may further reduce the viscous coupling within the LVZ. Therefore, the combination of solid Earth tides, ultra-low viscosity LVZ and asthenospheric polarized small-scale convection may mechanically satisfy the large-scale decoupling of the lithosphere relative to the underlying mantle. Relative plate motions are explained because of lateral viscosity heterogeneities at the base of the lithosphere, which determine variable lithosphere-asthenosphere decoupling and plate interactions, hence plate tectonics.

The effect of the giant planets on the dynamical evolution of the mutual orbits of trans-Neptunian binaries

ABSTRACT The action of tidal friction, coupled with the Kozai cycles, drastically changed the original orbits of trans-Neptunian binaries (TNBs). The dynamics of the Kozai mechanism is driven by the solar torque on the mutual orbit, so that the orientation of the latter relative to the heliocentric orbital plane plays a fundamental role in this process, both in the magnitude and in the characteristic of the cycles. In this way, any effect that makes this relative orientation vary may be relevant in the dynamics of the process. In this paper, we will focus on the effect that the perturbations of the giant planets on the heliocentric orbit of TNBs have on the dynamics of the Kozai cycles and tidal friction. For this task, we have performed numerical simulations of the evolution of a synthetic population of TNBs subject to Kozai cycles and tidal friction adding planetary perturbation on their heliocentric orbits. We found that in a non-negligible fraction of cases (∼25 per cent), this additional perturbation produces substantial changes in the orbital evolution. The slow precession of the heliocentric orbit and the variation of its inclination can make the dynamical evolution of the mutual orbits very irregular, completely changing the morphology of the Kozai cycles. When these variations are coupled to tidal friction, the lifetime of the TNBs can change substantially.

Presence of liquid water during the evolution of exomoons orbiting ejected free-floating planets

AbstractFree-floating planets (FFPs) can result from dynamical scattering processes happening in the first few million years of a planetary system's life. Several models predict the possibility, for these isolated planetary-mass objects, to retain exomoons after their ejection. The tidal heating mechanism and the presence of an atmosphere with a relatively high optical thickness may support the formation and maintenance of oceans of liquid water on the surface of these satellites. In order to study the timescales over which liquid water can be maintained, we perform dynamical simulations of the ejection process and infer the resulting statistics of the population of surviving exomoons around FFPs. The subsequent tidal evolution of the moons’ orbital parameters is a pivotal step to determine when the orbits will circularize, with a consequential decay of the tidal heating. We find that close-in ($a \lesssim 25$RJ) Earth-mass moons with carbon dioxide-dominated atmospheres could retain liquid water on their surfaces for long timescales, depending on the mass of the atmospheric envelope and the surface pressure assumed. Massive atmospheres are needed to trap the heat produced by tidal friction that makes these moons habitable. For Earth-like pressure conditions (p0= 1 bar), satellites could sustain liquid water on their surfaces up to 52 Myr. For higher surface pressures (10 and 100 bar), moons could be habitable up to 276 Myr and 1.6 Gyr, respectively. Close-in satellites experience habitable conditions for long timescales, and during the ejection of the FFP remain bound with the escaping planet, being less affected by the close encounter.

Is the Growth of the Astronomical Unit Caused by the Allais Eclipse Effect?

In addition to the Pioneer anomaly and the Earth flyby anomaly for spacecraft, other unexplained anomalies disrupt the solar system dynamics, like the astronomical unit. We show in this paper that the Allais eclipse effect causes the major part of the growth of the length scale for the entire solar system. It is the rough disturbance on the barycenter Earth-Moon implying the Sun that was recorded in the movement of the paraconical pendulum. Earth and Moon revolve around their common center of gravity, which in turn orbits the Sun, and the perturbation of the eclipse hits this double, coupled Kepler’s movements. The thesis of the tidal friction supports that oceanic tidal friction transfers the angular momentum of the Earth to the Moon and slows down the rotation of the Earth while taking away the Moon. However, we think that there are not enough shallow seas to sanction this interpretation. The Earth-Moon tidal system might be inaccurate or unreliable in determining the Earth’s actual rotational spin-down rate. Our assertion is that the change in the Earth’s rotation is caused by a repulsive gravitational interaction during solar eclipse. The perturbation would submit to variations and distortions the region of the barycenter of the Earth-Moon system which revolves around the Sun, with the dual secular effects that the Moon spirals outwards and that the Earth-Moon system goes away from the Sun.

Constraints on Moon's Orbit 3.2 Billion Years Ago From Tidal Bundle Data

AbstractThe angular momentum of the Earth‐Moon system was initially dominated by Earth's rotation with a short solar day of around 5 hr duration. Since then, Earth gradually transferred angular momentum through tidal friction to the orbit of the Moon, resulting in an increasing orbital radius and a deceleration of Earth's rotation. Geologic observations of tidal deposits can be used to verify and constrain models of lunar orbital evolution. In this work we reexamine the oldest tidal record suitable for analysis from the Moodies Group, South Africa, with an age of 3.22 billion years. Time frequency analysis of the series of thicknesses of the sandstone‐shale layers yields a periodicity of 15.0 layers, taking into account the possibility of missing laminae. Assuming a mixed tidal system, the duration of two neap‐spring‐neap cycles was 30.0 lunar days for dominant semidiurnal or 30.0 sidereal days for dominant diurnal tides. We derive the relationship between this observation and the past Earth‐Moon distance and re‐visit related published work. We find that the Earth‐Moon distance 3.2 billion years ago was about 70% of today's value. The Archean solar day was around 13 hr long. The ratio of solar to lunar tide‐raising torque controls the leakage of angular momentum from the Earth‐Moon system, but deviation from the assumed ratio of 0.211 results in only moderate changes. A duration of a postulated 21‐hr atmospheric resonance shorter than 200 million years would be consistent with our observation; it would significantly alter the Earth‐Moon distance.