Tidal Coefficients Research Articles

ArcTiCA: Arctic tidal constituents atlas

Tides in the Arctic Ocean affect ocean circulation and mixing, and sea ice dynamics and thermodynamics. However, there is a limited network of available in situ tidal coefficient data for understanding tidal variability in the Arctic Ocean; e.g., the global TICON-3 database contains only 111 sites above 60°N and 21 above 70°N. At the same time, the presence of sea ice and latitude limits of satellite altimetry complicate altimetry-based retrievals of Arctic tidal coefficients. This leads to a reliance on ocean tide models whose accuracy depend on having sufficient in situ data for validation and assimilation. Here, we present a comprehensive new dataset of tidal constituents in the Arctic region, combining analyses of in situ measurements from tide gauges, ocean bottom pressure sensors and GNSS interferometric reflectometry. The new dataset contains 914 measurement sites above 60°N and 399 above 70°N, with each site being quality-assessed and expert guidance provided to help maximise the usage of the dataset. We also compare the dataset to recent tide models.

Vanishing of Black Hole Tidal Love Numbers from Scattering Amplitudes.

We extract the black hole (BH) static tidal deformability coefficients (Love numbers) and their spin-0 and spin-1 analogs by comparing on-shell amplitudes for fields to scatter off a spinning BH in the worldline effective field theory and in general relativity. We point out that the general relativity amplitudes due to tidal effects originate entirely from the BH potential region. Thus, they can be separated from gravitational nonlinearities in the wave region, whose proper treatment requires higher order effective field theory loop calculations. In particular, the elastic scattering in the near field approximation is produced exclusively by tidal effects. We find this contribution to vanish identically, which implies that the static Love numbers of Kerr BHs are zero for all types of perturbations. We also reproduce the known behavior of scalar Love numbers for higher-dimensional BHs. Our results are manifestly gauge invariant and coordinate independent, thereby providing a valuable consistency check for the commonly used off-shell methods.

Dynamical Tidal Love Numbers of Rapidly Rotating Planets and Stars

Abstract Tidal interactions play an important role in many astrophysical systems, but uncertainties regarding the tides of rapidly rotating, centrifugally distorted stars and gaseous planets remain. We have developed a precise method for computing the dynamical, nondissipative tidal response of rotating planets and stars, based on summation over contributions from normal modes driven by the tidal potential. We calculate the normal modes of isentropic polytropes rotating at up to ≃90% of their critical breakup rotation rates, and tabulate fits to mode frequencies and tidal overlap coefficients that can be used to compute the frequency-dependent, nondissipative tidal response (via potential Love numbers k ℓm ). Although fundamental modes (f-modes) possess dominant tidal overlap coefficients at (nearly) all rotation rates, we find that the strong coupling of retrograde inertial modes (i-modes) to tesseral (ℓ > ∣m∣) components of the tidal potential produces resonances that may be relevant to gas giants like Jupiter and Saturn. The coupling of f-modes in rapid rotators to multiple components of both the driving tidal potential and the induced gravitational field also affect the tesseral response, leading to significant deviations from treatments of rotation that neglect centrifugal distortion and high-order corrections. For very rapid rotation rates (≳70% of breakup), mixing between prograde f-modes and i-modes significantly enhances the sectoral (ℓ = ∣m∣) tidal overlap of the latter. The tidal response of very rapidly rotating, centrifugally distorted planets or stars can also be modified by resonant sectoral f-modes that are secularly unstable via the Chandrasekhar–Friedman–Schutz mechanism.

On the vanishing of Love numbers for Kerr black holes

It was shown recently that the static tidal response coefficients, called Love numbers, vanish identically for Kerr black holes in four dimensions. In this work, we confirm this result and extend it to the case of spin-0 and spin-1 perturbations. We compute the static response of Kerr black holes to scalar, electromagnetic, and gravitational fields at all orders in black hole spin. We use the unambiguous and gauge-invariant definition of Love numbers and their spin-0 and spin-1 analogs as Wilson coefficients of the point particle effective field theory. This definition also allows one to clearly distinguish between conservative and dissipative response contributions. We demonstrate that the behavior of Kerr black hole responses to spin-0 and spin-1 fields is very similar to that of the spin-2 perturbations. In particular, static conservative responses vanish identically for spinning black holes. This implies that vanishing Love numbers are a generic property of black holes in four-dimensional general relativity. We also show that the dissipative part of the response does not vanish even for static perturbations due to frame-dragging.

Updated universal relations for tidal deformabilities of neutron stars from phenomenological equations of state

Equation of state (EOS) insensitive relations, so-called universal relations, between the neutron star (NS) compactness, its multipolar tidal deformability coefficients, and between the tidal parameters for binary systems are essential to break degeneracies in gravitational wave data analysis. Here, we validate and recalibrate these universal relations using a large set of almost 2 million phenomenological EOSs that are consistent with current observations. In doing so, we extend universal relations to a larger region of the EOS parameter space, most notably to softer EOSs and larger compactnesses. We show that waveform models that neglect higher-than-leading-order tidal deformations of the NSs accumulate as much as $3.5$ radians of dephasing from $20\,{\rm Hz}$ to merger. We also perform a full Bayesian parameter estimation of the GW170817 data, and we compare the NS radius constraints produced using universal relations from the literature and the updated fits we propose here. We find that the new fits yield a NS radius that is smaller by about 500 meters. This difference is less than the statistical uncertainty on the radius at the signal-to-noise-ratio of GW170817, but it is significantly larger than the precision anticipated for next-generation detectors.

Sub-daily polar motion from GPS, GLONASS, and Galileo

We derive an empirical model of the sub-daily polar motion (PM) based on the multi-GNSS processing incorporating GPS, GLONASS, and Galileo observations. The sub-daily PM model is based on 3-year multi-GNSS solutions with a 2 h temporal resolution. Firstly, we discuss differences in sub-daily PM estimates delivered from individual GNSS constellations, including GPS, GLONASS, Galileo, and the combined multi-GNSS solutions. Secondly, we evaluate the consistency between the GNSS-based estimates of the sub-daily PM with three independent models, i.e., the model recommended in the International Earth Rotation and Reference Systems Service (IERS) 2010 Conventions, the Desai–Sibois model, and the Gipson model. The sub-daily PM estimates, which are derived from system-specific solutions, are inherently affected by artificial non-tidal signals. These signals arise mainly from the resonance between the Earth rotation period and the satellite revolution period. We found strong spurious signals in GLONASS-based and Galileo-based results with amplitudes up to 30 µas. The combined multi-GNSS solution delivers the best estimates and the best consistency of the sub-daily PM with external geophysical and empirical models. Moreover, the impact of the non-tidal spurious signals in the frequency domain diminishes in the multi-GNSS combination. After the recovery of the tidal coefficients for 38 tides, we infer better consistency of the GNSS-based empirical models with the new Desai–Sibois model than the model recommended in the IERS 2010 Conventions. The consistency with the Desai–Sibois model, in terms of the inter-quartile ranges of tidal amplitude differences, reaches the level of 1.6, 5.7, 6.3, 2.2 µas for the prograde diurnal tidal terms and 1.2/2.1, 2.3/6.0, 2.6/5.5, 2.1/5.1 µas for prograde/retrograde semi-diurnal tidal terms, for the combined multi-GNSS, GPS, GLONASS, and Galileo solutions, respectively.

Gravitomagnetic tidal effects in gravitational waves from neutron star binaries

Gravitational waves emitted by coalescing binary systems containing neutron stars (or other compact objects) carry signatures of the stars' internal equation of state, notably, through the influence of tidal deformations during the binary's inspiral stage. While the leading-order tidal effects for post-Newtonian binaries of compact bodies in general relativity are due to the bodies' mass-quadrupole moments induced by gravitoelectric tidal fields, we consider here the leading effects due to current-quadrupole moments induced by gravitomagnetic tidal fields. We employ an effective action approach to determine the near-zone gravitational field and the conservative orbital dynamics, initially allowing for arbitrary (not just tidally induced) current quadrupoles; our approach significantly reduces the complexity of the calculation compared to previous derivations of the conservative dynamics for arbitrary multipoles. We finally compute the leading contributions from gravitomagnetic tides to the phase and (for the first time) the mode amplitudes of the gravitational waves from a quasicircular binary inspiral, given in terms of the bodies' quadrupolar gravitomagnetic tidal Love numbers (tidal linear response coefficients in an adiabatic approximation). In the phase, gravitomagnetic tides are suppressed by one post-Newtonian order relative to gravitoelectric ones, but this is not always the case for the mode amplitudes. In the $(\ensuremath{\ell},|m|)=(2,1)$ and (3,2) modes, for example, they appear at the same leading orders.

Role of bioclimate conditions on cerebral aneurysm rupture in the Brittany region of France

IntroductionSubarachnoid hemorrhage (SAH) from intracranial aneurysm rupture is an unpredictable event responsible for significant morbidity and mortality. Despite inconsistencies, some studies suggest a potential role of climate conditions in SAH onset. The purpose of this study was to determine the impact of climatic and lunar factors on onset of SAH in an oceanic climate such as that of Brittany, France. MethodsAll adults with SAH admitted to the neurosurgery department and intensive care unit of the University Hospital of Rennes (France) between January 1st, 2011 and December 31st, 2012 were included. Meteorological variables, their variations, lunar phases and tidal coefficients were compared between days with and without SAH. ResultsWe retrospectively included 295 patients with SAH. Mean minimum temperature was significantly lower during days with SAH (7.7±4.7°C versus 8.3±4.6°C; P=0.039); temperature variation between 2 successive days was significantly greater for days with SAH (8.6±4.1°C versus 7.9±3.8°C; P<0.01). Multivariate analysis showed that a 2-day temperature drop greater than or equal to 8°C was associated with 35% increased risk of SAH (odds ratio 1.35 [1.03–1.77]). There were no significant effects of other meteorological variables, lunar phase or tidal coefficient on SAH occurrence. ConclusionLow temperature and sudden temperature drop were associated with increased occurrence of SAH in Brittany, France.

A NOVEL HIGH-RESOLUTION STORM SURGE FORECAST FOR THE GERMAN BIGHT

Storm surges are one of the most dangerous natural hazards in coastal areas and have the ability to cause great damages including fatalities. To be prepared when another storm surge hits the coast, reliable storm surge forecasts are indispensable. Storm surge warnings are routinely provided for selected tide gauge locations along a coastline through state-of-the-art forecast systems. In Germany, the Federal Maritime and Hydrographic Agency (BSH) (in cooperation with the German Weather Service (DWD)) have the responsibility for storm surge forecasts and warnings along the German North and Baltic Sea coastlines. The operational system in place for the North Sea consists of numerical weather forecast systems, a surge model and model output statistics. It provides accurate high frequency water level forecasts up to six days ahead at selected tide gauge sites (Müller-Navarra and Knüpfer, 2010), but not for the coastline in between. Spatial forecasts are, however, currently not available for two reasons: first, the shallow coast with complex morphological structures leads to strong non-linearities between individual sites hampering simple interpolation schemes (Arns et al. 2015). Second, tidal predictions are limited to tide gauge locations, which do not fall dry during low tide, since the traditional estimation of tidal coefficients requires complete time series covering both low and high waters.

An Analytical Solution of Groundwater Flow in Wedge-shaped Aquifers with Estuarine Boundary Conditions

The issue of the groundwater fluctuation due to tidal effect in a two-dimensional coastal leaky aquifer system has attracted much attention in recent years. The predictions of head fluctuation play an important role in dealing with groundwater managements and contaminant remediation problems in costal aquifers. This article presents a two-dimensional analytical model describing the groundwater flow in a coastal leaky aquifer of wedge shape affected by the tides and bounded by two estuarine rivers with an arbitrary included angle. The solution of the model is derived in the Polar coordinates by the Hankel transform and finite sine transform. The head fluctuation predicted by this new solution is compared with that by an existing solution for groundwater flow in a non-L shaped tidal aquifer. The groundwater fluctuation due to the joint effect of estuarine tides is explored based on the present solution. Moreover, the influences of the parameters such as diffusion (Di), included angle (Ф), and tidal river coefficients (K1, K2) on the head fluctuation in the aquifer are also assessed and discussed. The results demonstrate that those parameters have significant effects on the head fluctuation in the leaky confined aquifer system. Moreover, the effect of Di increases with Ф, and the effects of K1 and K2 on the normalized amplitude and phase lag of the groundwater fluctuation are significant when both parameter values are larger than 10−5.

Tidal effects on the LAGEOS–LARES satellites and the LARASE program

The effects of solid and ocean tides have been computed on the right ascension of the ascending node of the two LAGEOS and LARES satellites and on the argument of pericenter of LAGEOS II. Their effects—together with the possible mis-modeling related to systematic errors in the estimate of the tidal coefficients, especially in the case of ocean tides—are quite important to be well established for the key role of the LAGEOS satellites, as well as of the newly LARES, in space geodesy and geophysics as well as in fundamental physics measurements. In the case of the measurement of the Lense–Thirring effect, the mis-modeling of long-period tides may mimic a secular effect on the cited orbital elements, thus producing a degradation in the measurement of the relativistic precession. A suitable combination of the orbital elements of the three satellites can help in avoiding the effects of the long-period tides of degree $$\ell =2$$ (as for the Lunar solid tides with periods of 18.6 and 9.3 years) and $$\ell =4$$ , but other long-period tides, as the ocean $$K_1$$ tide, which has the same periodicities of the right ascension of the ascending node $$\varOmega $$ of the satellites, may strongly influence the measurement, especially if it is performed over a relatively short time span. These results are particularly important in the case of LARES, since they are new and because of the role that the orbit of LARES, and especially of its ascending node right ascension, will have in a new measurement of the Lense–Thirring effect by the joint analysis of its orbit with that of the two LAGEOS.

Integration of tidal range energy with undersea pumped storage

Abstract The deployment of tidal technology is affected by the general bottlenecks associated with all new renewables in respect of finance and integration with the grid. In this research, a development strategy is defined for tidal range projects based on geodynamics, civil engineering, and economics with the aim of assisting policy makers and industry. Criteria related to hydrodynamics, bathymetry, marine structure safety and cost recovery apply to relevant sites and to real data power prices. The case study described is that of the Bay of Bourgneuf on the French Atlantic coast, where a tidal range power plant of 900 MW could optimally be built with respect to sedimentation, water depth, and tidal coefficients. It has been determined that a 30 m-high artificial dam could maximise the harvestable energy (3 TWh). Numerical simulations show that a tidal plant sized at just 700 MW would be cost-efficient, due to the constraints of the grid and to high power curtailment rates (30%). The expected value of the Levelised Cost of Electricity would be around 200€2016/MWh. Integration into the grid could be improved through addition of an innovative underwater energy storage system, rated to one third of the size of the tidal plant. The economics would improve (the LCOE would drop to 170€2016/MWh) due to lower curtailment and to price arbitrage opportunities. Issues related to missing investor money (>3Bln€2016) and unquantifiable positive externalities such as flood protection, energy independency, and clean energy provision are discussed, underpinning the need for regulator support.

Resonant tidal excitation of oscillation modes in merging binary neutron stars: Inertial-gravity modes

In coalescing neutron star (NS) binaries, tidal force can resonantly excite low-frequency (< 500 Hz) oscillation modes in the NS, transferring energy between the orbit and the NS. This resonant tide can induce phase shift in the gravitational waveforms, and potentially provide a new window of studying NS interior using gravitational waves. Previous works have considered tidal excitations of pure g-modes (due to stable stratification of the star) and pure inertial modes (due to Coriolis force), with the rotational effect treated in an approximate manner. However, for realistic NSs, the buoyancy and rotational effects can be comparable, giving rise to mixed inertial-gravity modes. We develop a non-perturbative numerical spectral code to compute the frequencies and tidal coupling coefficients of these modes. We then calculate the phase shift in the gravitational waveform due to each resonance during binary inspiral. We adopt polytropic NS models with a parameterized stratification. We derive relevant scaling relations and survey how the phase shift depends on various properties of the NS. We find that for canonical NSs (with mass M = 1.4M_sun and radius R = 10 km) and modest rotation rates (< 300 Hz), the gravitational wave phase shift due to a resonance is generally less than 0.01 radian. But the phase shift is a strong function of R and M, and can reach a radian or more for low-mass NSs with larger radii (R > 15 km). Significant phase shift can also be produced when the combination of stratification and rotation gives rise to a very low frequency (< 20 Hz in the inertial frame) modified g-mode. We also find that some inertial modes can be strongly affected by stratification, and that the m = 1 r-mode, previously identified to have a small but finite inertial-frame frequency based on the Cowling approximation, in fact has essentially zero frequency, and therefore cannot be excited.

Geometric polarization of plasmas and Love numbers of AdS black branes

We use AdS/CFT holography to study how a strongly-coupled plasma polarizes when the geometry where it resides is not flat. We compute the linear-response polarization coefficients, which are directly related to the static two-point correlation function of the stress-energy tensor. In the gravitational dual description, these parameters correspond to the tidal deformation coefficients — the Love numbers — of a black brane. We also compute the coefficients of static electric polarization of the plasma.

Tropospheric delays in ground‐based GNSS multipath reflectometry—Experimental evidence from coastal sites

AbstractRecent studies have demonstrated the utility of ground‐based Global Navigation Satellite Systems‐Multipath Reflectometry (GNSS‐MR) for sea level studies. Typical root‐mean‐square (RMS) differences of GNSS‐MR‐derived sea level time series with respect to nearby tide gauges are on the order of 6–40 cm, sufficiently accurate to estimate tidal and secular sea level variations but are possibly biased due to delay of the signal through the troposphere. In this study we investigate the tropospheric effect from more than 20 GNSS coastal sites located from several meters up to 280 m above sea level. We find a bias in the estimated heights that is elevation and height dependent and can reach orders of 1 m for a 90 m site. Without correcting for tropospheric delay we find that GNSS‐MR‐estimated tidal coefficients will be smaller than their true amplitudes by around 2% while phases seem unaffected. Correcting for the tropospheric delay also improves leveling results as a function of reflector height. Correcting for the tropospheric delay in GNSS‐MR for sea level studies is therefore highly recommended for all sites no matter the height of the antenna above the sea surface as it manifests as a scale error.

The effect of tidal torques on the structure and evolution of rotating stars

The tide is a very important physical factor which can affect significantly the structure and evolution of stars. Tidal coefficients in three theoretical models have been explored in this paper. Basing on the equations of angular momentum transport and chemical elements mixing, we can investigate the effect of tidal coefficients on the structure and mixing of chemical elements. It is shown that the tidal coefficient is related to stellar masses, metal abundances, and evolutionary stages. The tidal coefficient E 2 increases with stellar mass but decreases metal abundance and evolutionary time. The bigger tidal coefficient is, the higher efficiency of processes which the orbital angular momentum transforms into the spin angular momentum will be. Furthermore, angular momentum transports efficiently inside the star. Tidal torques can enhance the helium and nitrogen at the stellar surface and enlarge the convective core which can cause the star to shift toward high luminosity. Comparing model M1 with M3, we find that rotational mixing induced by tidal torque can reduce the opacity, and radiative temperature gradient but it can inhibit the hydrodynamic effects of centrifugal force which can increase the radiative temperature gradient. Therefore, tidally induced rotational mixing can decrease the convective core. Furthermore, rotational mixing induced by tidal torque can increase both the number density of hydrogen in stellar core and the efficiency of nuclear reactions. This physical process may increase central temperatures and cause the star to expand greatly. The star will have a large moment of inertia. It is of significance to investigate the tidal mixing in close binary systems.

Comparison of Regression Methods to Compute Atmospheric Pressure and Earth Tidal Coefficients in Water Level Associated with Wenchuan Earthquake of 12 May 2008

The earth tide, atmospheric pressure, precipitation and earthquake fluctuations, especially earthquake greatly impacts water well levels, thus anomalous co-seismic changes in ground water levels have been observed. In this paper, we have used four different models, simple linear regression (SLR), multiple linear regression (MLR), principal component analysis (PCA) and partial least squares (PLS) to compute the atmospheric pressure and earth tidal effects on water level. Furthermore, we have used the Akaike information criterion (AIC) to study the performance of various models. Based on the lowest AIC and sum of squares for error values, the best estimate of the effects of atmospheric pressure and earth tide on water level is found using the MLR model. However, MLR model does not provide multicollinearity between inputs, as a result the atmospheric pressure and earth tidal response coefficients fail to reflect the mechanisms associated with the groundwater level fluctuations. On the premise of solving serious multicollinearity of inputs, PLS model shows the minimum AIC value. The atmospheric pressure and earth tidal response coefficients show close response with the observation using PLS model. The atmospheric pressure and the earth tidal response coefficients are found to be sensitive to the stress–strain state using the observed data for the period 1 April–8 June 2008 of Chuan 03# well. The transient enhancement of porosity of rock mass around Chuan 03# well associated with the Wenchuan earthquake (Mw = 7.9 of 12 May 2008) that has taken its original pre-seismic level after 13 days indicates that the co-seismic sharp rise of water well could be induced by static stress change, rather than development of new fractures.

Tidal deformations of spinning black holes in Bowen–York initial data

We study the tidal deformations of the shape of a spinning black hole horizon due to a binary companion in the Bowen–York initial data set. We use the framework of quasi-local horizons and identify a black hole by marginally outer trapped surfaces. The intrinsic horizon geometry is specified by a set of mass and angular-momentum multipole moments and , respectively. The tidal deformations are described by the change in these multipole moments caused by an external perturbation. This leads us to define two sets of dimensionless numbers, the tidal coefficients for and , which specify the deformations of a black hole with a binary companion. We compute these tidal coefficients in a specific model problem, namely the Bowen–York initial data set for binary black holes. We restrict ourselves to axisymmetric situations and to small spins. Within this approximation, we analytically compute the conformal factor, the location of the marginally trapped surfaces, and finally the multipole moments and the tidal coefficients.

Barometric and tidal-induced aquifer water level fluctuation near the Ariake Sea.

Observations of water levels in coastal aquifers and corresponding tides coupled with meteorological variances near the Ariake Sea show that groundwater in this area mainly fluctuates with atmospheric and tidal variations. Tidal effects occur with semi-monthly, diurnal, or semi-diurnal periodicity, whereas the barometric influences commonly act in the low-frequency domain. Tidal and barometric effects in water levels are separable using wavelet techniques and can be evaluated statistically. Results show the following. (1) The tidal coefficients are 0.002-0.154, attenuating roughly exponentially from the seashore. The time lags in water levels increase linearly approximately with increasing inshore distance. Relations between tidal coefficients and time lags and the inshore distance indicate higher hydraulic diffusivity in the south aquifer, which was confirmed by the hydraulic property calibrations in analytical simulations. (2) Water levels related to meteorological phenomena fluctuate inversely according to barometric loading variation with time lags of 2-3h. The effective barometric efficiencies are 0.022-0.12. Lower barometric influences were found in the south aquifer.

Dynamic processes in earth’s rotation parameters and tidal deformations on a rotating geoid

Amplitude-frequency analysis of the Earth's rotaryoscillatory motion due to lunisolar gravita� tional and tidal perturbing torques is performed using methods of classical mechanics. Dynamic processes that occur in Earth's rotation parameters (ERP) and Earth's potential due to tidal deformations lead to distortions in Earth's shape and fluctuations in the gravitational field (1, 2). The results of the numerical modeling of oscillatory processes in the Earth's pole motion and variations in the second zonal harmonic δc20 of the geopotential are discussed. The amplitude and phase of oscillations of the Earth's pole are determined using the dynamic Euler-Liou� ville equations. The power spectral densities of the time series of Earth's polar coordinates are compared with those of δc20 variations in the geopotential. This harmonic is found to be a function of the amplitude and phase of the oscillatory process of the Earth's pole. 1. The study of temporal variations in the geopo� tential (2, 3) due to Earth's rotaryoscillatory motion is of scientific and practical interest. The observed ERP variations and variations in the Earth's gravita� tional field are highly interrelated; dynamic processes that lead to appreciable changes in both ERPs and geophysical phenomena have acquired the most detailed reflection in diurnal oscillations (4). The refinement of the Earth's gravitational field involves replacing the statistical geoid by a geoid that corresponds to the deformable shape of the Earth (due to oceanic and rigidbody tides and other factors). Due to increasing demands on the accuracy of the coordinatetime maintenance of navigation systems, investigations related to the refinement of the gravita� tional field and the shape of the Earth have developed intensively (2). Note that the modeling of tidal deformations on a rotating geoid can be used to reach high characteristics of atomic clock synchronization (the stability of atomic frequency is 10 -14 ) for objects that are located on different continents of the globe. Differential equations of the Earth's rotaryoscilla� tory motions with allowance for the harmonic struc� ture of the tidal coefficients were derived from the dynamic Euler-Liouville equations in the problem considering "a deformable Earth-Moon" system in the solar gravitational field (4):