Tidal Resonance Research Articles

Numerical modeling of tidal propagation and frequency responses in the Guadalquivir estuary (SW, Iberian Peninsula)

A three-dimensional numerical model, based on Delft3D code, has been implemented and calibrated in the mesotidal Guadalquivir Estuary (Spain), a tidally-driven estuary due to the reduced freshwater discharges (25 m3s-1 year-round average), which are subject to human regulation at the dam located at its head. The model has been applied to study in detail some estuarine features for low freshwater discharges: the first one is the non-linear interaction of semidiurnal constituents, which results in a tidal amplification factor (ratio of local amplitude to the amplitude at the mouth) that depends on the spring-neap tidal cycle, with markedly larger values during neap tides. The second one is the analysis of tidal resonance in the estuary, extending previous studies on the topic, which shows that resonance occurs at near-diurnal frequencies. The peak of resonance decreases in magnitude and shifts towards lower frequencies as friction increases, either by increasing the friction coefficient itself or the amplitude of the tide.

Did atmospheric thermal tides cause a daylength locking in the Precambrian? A review on recent results

After the initial suggestion by Zahnle and Walker (1987) that the torque accelerating the spin rate of the Earth and produced by the heating of the atmosphere by the Sun could counteract the braking luni-solar gravitational torque in the Precambrian, several authors have recently revisited this hypothesis. In these studies, it is argued that the geological evidence of the past spin state of the Earth plays in favor of this atmospheric tidal locking of the length of the day (LOD). In the present review of the recent literature, we show that the drawn conclusions critically depend on LOD estimates based on stromatolite growth band data of Panella at 1.88 and 2.0 Ga which are subject to large uncertainties. When only the most robust cyclostatigraphic estimates of the LOD are retained, the LOD locking hypothesis is not supported. Moreover, our consideration of the published General Circulation Model numerical simulations and of a new analytical model for the thermal atmospheric tides suggest that the atmospheric tidal resonance, which is the crucial ingredient for the LOD locking in the Precambrian, was never of sufficiently large amplitude to allow for this tidal LOD lock.

Tidal Resonance: A Factor Worth Considering in the Orbital Evolution of Heartbeat Stars

Heartbeat star systems have been reported to exhibit two distinct different orbital dynamic evolution processes: apsidal precession (e.g., KIC 4544587) and orbital decay (e.g., KIC 3766353). While experiencing similar dynamic tidal interactions, these binary systems display different dynamical behaviors, which is a puzzling phenomenon. In this work, we deduced a theoretical relation between the timescale of stellar pulsation Ppul and orbital periods Porb of heartbeat stars based on the resonance criteria representing the orbital local low-energy configuration. The theoretical relation shows that when the ratio of Porb to Ppul is an integer, the specific orbital period is captured in the resonance state, resulting in resonance locking. The resonance criteria are verified by periodograms of the pulsations and orbits of the two systems KIC 4544587 and KIC 3766353 from observations. KIC 4544587 is an apsidal precession heartbeat star with eight observed resonant frequencies available from observations and has an almost integer ratio of Ppul/Porb=67.968. On the contrary, KIC 3766353 is undergoing the process of orbital shrinkage with only three weak pulsation–orbital resonance frequencies available and shows a non-integer ratio of Ppul/Porb=83.163. Given the results, the theoretical relation is a potential proxy to distinguish between apsidal precession and orbital decay binary systems. Furthermore, we predict that the orbital period of KIC 3766353 will be reduced to 2.492 days, at which time it will be transformed into apsidal precession.

Gamma-ray burst precursors from tidally resonant neutron star oceans: potential implications for GRB 211211A

ABSTRACT Precursors have been observed seconds to minutes before some short gamma-ray bursts. While the precursor origins remain unknown, one explanation relies on the resonance of neutron star pulsational modes with the tidal forces during the inspiral phase of a compact binary merger. In this paper, we present a model for short gamma-ray burst precursors that relies on tidally resonant neutron star oceans. In this scenario, the onset of tidal resonance in the crust–ocean interface mode ignites the precursor flare, possibly through the interaction between the excited neutron star ocean and the surface magnetic fields. From just the precursor total energy, the time before the main event, and a detected quasi-periodic oscillation frequency, we may constrain the binary parameters and neutron star ocean properties. Our model can immediately distinguish neutron star–black hole mergers from binary neutron star mergers without gravitational wave detection. We apply our model to GRB 211211A, the recently detected long duration short gamma-ray burst with a quasi-periodic precursor, and explore the parameters of this system. The precursor of GRB 211211A is consistent with a tidally resonant neutron star ocean explanation that requires an extreme mass ratio neutron star–black hole merger and a high-mass neutron star. While difficult to reconcile with the main gamma-ray burst and associated kilonova, our results constrain the possible precursor mechanisms in this system. A systematic study of short gamma-ray burst precursors with the model presented here can test precursor origin and probe the possible connection between gamma-ray bursts and neutron star–black hole mergers.

Late Pleistocene Evolution of Tides and Tidal Dissipation

AbstractStudies of the Last Glacial Maximum (LGM; 26.5–19 ka) tides showed strong enhancements in open ocean tidal amplitudes and dissipation rates; however, changes prior to the LGM remain largely unexplored. Using two different ice sheet and sea level reconstructions, we explicitly simulate the evolution of the leading semi‐diurnal and diurnal tidal constituents (M2, S2, K1, and O1) over the last glacial cycle with a global tide model. Both sets of simulations show that global changes, dominated by the Atlantic, take place for the semi‐diurnal constituents, while changes for the diurnal constituents are mainly regional. Irrespective of the reconstruction, open ocean dissipation peaks during the sea level lowstands of MIS 2 (∼20 ka) and MIS 4 (∼60 ka), although dissipation values prior to MIS 2 are sensitive to differences in reconstructed ice sheet extent. Using the statistically significant relationship between global mean sea level and dissipation, we apply regression analysis to infer open ocean and shelf dissipation, respectively, over the last four glacial cycles back to 430 ka. Our analysis shows that open ocean tidal energy was probably increased for most of this period, peaking during glacial maxima, and returning to near‐present‐day values during interglacials. Due to tidal resonance during glacial phases, small changes in bathymetry could have caused large changes in tidal amplitudes and dissipation, emphasizing the need for accurate ice margin reconstructions. During glacial phases, once global mean sea level decreased by more than ∼100 m, the amount of open ocean tidal energy available for ocean mixing approximately doubled.

Mid-Proterozoic day length stalled by tidal resonance

We present statistical analysis of a compilation of observational constraints on the Precambrian length of day and find that the day length stalled at about 19 h for about 1 billion years during the mid-Proterozoic. We suggest that the accelerative torque of atmospheric thermal tides from solar energy balanced the decelerative torque of lunar oceanic tides, temporarily stabilizing Earth’s rotation. This stalling coincides with a period of relatively limited biological evolution known as the boring billion.

Evolution of Global Ocean Tide Levels Since the Last Glacial Maximum

AbstractThis study addresses the evolution of global tidal dynamics since the Last Glacial Maximum focusing on the extraction of tidal levels that are vital for the interpretation of geologic sea‐level markers. For this purpose, we employ a truly‐global barotropic ocean tide model which considers the non‐local effect of Self‐Attraction and Loading. A comparison to a global tide gauge data set for modern conditions yields agreement levels of 65%–70%. As the chosen model is data‐unconstrained, and the considered dissipation mechanisms are well understood, it does not have to be re‐tuned for altered paleoceanographic conditions. In agreement with prior studies, we find that changes in bathymetry during glaciation and deglaciation do exert critical control over the modeling results with minor impact by ocean stratification and sea ice friction. Simulations of 4 major partial tides are repeated in time steps of 0.5–1 ka and augmented by 4 additional partial tides estimated via linear admittance. These are then used to derive time series from which the tidal levels are determined and provided as a global data set conforming to the HOLSEA format. The modeling results indicate a strengthened tidal resonance by M2, but also by O1, under glacial conditions, in accordance with prior studies. Especially, a number of prominent changes in local resonance conditions are identified, that impact the tidal levels up to several meters difference. Among other regions, resonant features are predicted for the North Atlantic, the South China Sea, and the Arctic Ocean.

Development of a GNSS/INS buoy array in preparation for SWOT validation in Bass Strait

In preparation for validation of the swath-based altimetry mission (Surface Water Oceanography Topography, SWOT), we developed a buoy array, equipped with Global Navigation Satellite System/Inertial Navigation System, capable of accurately observing sea surface height (SSH), wave information and tropospheric delay. Here we present results from an 8-day trial deployment at five locations along a Sentinel-6 Michael Freilich (S6MF) ground track in Bass Strait. A triplet buoy group including two new buoys (Mk-VI) and a single predecessor (Mk-IV) were deployed in proximity to the historic Jason-series comparison point. SSH solutions compared against an in-situ mooring suggest the new buoys were working at an equivalent precision of ~1.5 cm to the previous design (MK-IV). At 10-km spacing along the S6MF track, the buoy array was shown to observe the progression of oceanographic and meteorological phenomena. Tidal analysis of the buoy array indicated moderate spatial variability in the shallow water tidal constituents, with differences in the instantaneous tidal height of up to ~0.2 m across the 40-km track. Further, tidal resonance within Bass Strait was observed to vary, most probably modulated by atmospheric conditions, yet only partially captured by an existing dynamic atmospheric correction product. A preliminary investigation into the spatial scale of the buoy error based on observed/inferred geostrophic currents with our present buoy array configuration suggests that the signal-noise ratio of the array became significant at 20-km spacing in Bass Strait. Finally, as an illustrative comparison between the buoy array and high resolution S6MF data, a single cycle was compared. The wet tropospheric delay observed by the S6MF radiometer exhibited some potential land contamination in the deployed area, while the 1-Hz and 20-Hz significant wave height from S6MF appeared within mission requirements. Generally good agreement between buoy and altimeter SSH was observed. However, subtle differences between the altimeter and the buoy sea level anomaly series warrants further investigation with additional cycles from a sustained deployment in the area. We conclude that the buoy array offers a useful geodetic tool to help quantify and understand intra-swath variability in the context of the SWOT mission.

Resonant jumps induced by stationary tidal perturbation: a two-for-one deal

Extreme-mass-ratio inspirals (EMRIs) are promising target sources for space-based interferometers such as LISA, Taiji, and Tianqin. Depending on the astrophysical environment, such as close perturbers or an accretion disk, EMRI orbital evolution may deviate from the predictions of general relativity in vacuum. In particular, we focus on the resonance jumps, i.e. the changes of the conserved quantities induced by a stationary perturbation to the background Kerr geometry. Using Hamiltonian formulation, we provide a closed relation between the jump in Carter constant and that in the axial component of angular momentum. It is also shown that the obtained relation is consistent with the fitting formulae computed for the tidal resonance in previous works.

Dynamical history of the Galilean satellites for a fast migration of Callisto

Abstract The dynamics of the innermost Galilean satellites (Io, Europa, and Ganymede) is characterized by a chain of mean motion resonances, called Laplace resonance, and by a strong tidal dissipation that causes wide variations of their semimajor axes over large time-scales. The precise history of energy dissipation in the Jovian system is not known, but several theories have been proposed. Tidal resonance locking states that big outer moons can also migrate fast. If this is the case for Callisto, then it should have crossed the 2:1 mean motion resonance with Ganymede in the past, affecting the motion of all four Galilean satellites. Therefore, we aim to determine whether a fast migration for Callisto is compatible with the current orbital configuration of the system. Due to the chaotic nature of the resonant crossing, different outcomes are possible. A small portion of our simulations shows that Callisto can cross the 2:1 resonance with Ganymede without being captured and preserving the Laplace resonance. However, in most cases, we found that Callisto is captured into resonance, despite its divergent migration. As Callisto continues to migrate fast outwards, the moons depart substantially from the exact 8:4:2:1 commensurability, while still maintaining the resonant chain. Callisto can eventually escape it by crossing a high-order mean motion resonance with Ganymede. Afterwards, the moons’ system is able to relax to its current configuration for suitable dissipation parameters of the satellites. Therefore, it is possible, although challenging, to build a self-consistent picture of the past history of the Galilean satellites for a fast migration of Callisto.

Resonant shattering flares in black hole-neutron star and binary neutron star mergers

ABSTRACT Resonant shattering flares (RSFs) are bursts of gamma-rays expected to be triggered by tidal resonance of a neutron star (NS) during binary inspiral. They are strongly dependent on the magnetic field strength at the surface of the NS. By modelling these flares as being the result of multiple colliding relativistic shells launched during the resonance window, we find that the prompt non-thermal gamma-ray emission may have luminosity up to a few $\times 10^{48}\rm{ erg\,s}^{-1}$, and that a broad-band afterglow could be produced. We compute the expected rates of detectable RSFs using the BPASS population synthesis code, with different assumptions about the evolution of surface magnetic field strengths before merger. We find the rate of detectable RSFs to be ∼0.0001–5 per year for BHNS mergers and ∼0.0005–25 per year for NSNS mergers, with the lower bound corresponding to surface-field decay consistent with magneto-thermal evolution in purely crustal fields, while the upper bounds are for systems that have longer lived surface magnetic fields supported by flux frozen into the superconducting core. If some of the observed SGRB precursor flares are indeed RSFs, this suggests the presence of a longer lived surface field for some fraction of the NS population, and that we could expect RSFs to be the most common detectable EM counterpart to GW detections of BHNS mergers. The non-detection of an RSF prior to GRB170817A provides an upper bound on the magnetic fields of the progenitor NSs of Bsurf ∼ 1013.5G.

Tidal dynamics in palaeo‐seas in response to changes in physiography, tidal forcing and bed shear stress

AbstractSimulating hydrodynamic conditions in palaeo‐ocean basins is needed to better understand the effects of tidal forcing on the sedimentary record. When combined with sedimentary analyses, hydrodynamic modelling can help inform complex temporal and spatial variability in the sediment distribution of tide‐dominated palaeo‐ocean basins. Herein, palaeotidal modelling of the epicontinental Upper Jurassic (160 Ma, lower Oxfordian) Sundance and Curtis seas of North America reveals possible regional‐scale variations in tidal dynamics in response to changes in ocean tidal forcing, physiographic configuration and bottom drag coefficient. A numerical model forced with an M2 tidal constituent at the open boundary shows that the magnitude and location of tidal amplification, and the variability in current velocity and bed shear stress in the basin, were controlled by palaeophysiography. Numerical results obtained using a depth of 600 m at the ocean boundary of the system enable the prediction of major facies trends observed in the lower Curtis Formation. The simulation results also highlight that certain palaeophysiographic configurations can either permit or prevent tidal resonance, leading to an overall amplification or dampening of tides across the basin. Furthermore, some palaeophysiographic configurations generated additional tidal harmonics in specific parts of the basins. Consequently, similar sedimentary successions can emerge from a variety of relative sea‐level scenarios, and a variety of sedimentary successions may be deposited in different parts of the basin in any given relative sea‐level scenario. These results suggest that the interpretation of sedimentary successions deposited in strongly tide‐influenced basins should consider changes in tidal dynamics in response to changing sea level and basin physiography.

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.

Importance of tidal resonances in extreme-mass-ratio inspirals

Extreme mass ratio inspirals (EMRIs) will be important sources for future space-based gravitational-wave detectors. In recent work, tidal resonances in binary orbital evolution induced by the tidal field of nearby stars or black holes have been identified as being potentially significant in the context of extreme mass-ratio inspirals. These resonances occur when the three orbital frequencies describing the orbit are commensurate. During the resonance, the orbital parameters of the small body experience a jump leading to a shift in the phase of the gravitational waveform. In this paper, we treat the tidal perturber as stationary and restricted to the equatorial plane, and present a first study of how common and important such resonances are over the entire orbital parameter space. We find that a large proportion of inspirals encounter a low-order resonance in the observationally important regime. While the instantaneous effect of a tidal resonance is small, its effect on the accumulated phase of the gravitational waveform of an EMRI system can be significant due to its many cycles in band; we estimate that the effect is detectable for a significant fraction of sources. We also provide fitting formulae for the induced change in the constants of motion of the orbit due to the tidal resonance for several low-order resonances.

Sensitivity of tides and tidal components to sea-level-rise in the Radial Sand Ridges

Sea-level-rise (SLR) induced by global climate would by changing tidal dynamics in the deltaic and coastal regimes aggravate inundation risks. In order to have a thorough understanding of the tidal responses to SLR in the RSR of the South Yellow Sea, a comprehensive analysis on the tidal and tidal components’ responses to SLR are conducted. Spatial variations of tides and tidal components between SLR scenarios and present-day scenario are examined. Strong spatial variation in tidal responses to SLR occurs over the RSR. Further investigation reveals it is the semidiurnal tide (S2) in control of the tidal range evolution under SLR in this area. Strong spatial variability in the primary tidal amplitudes’ evolution is found between northern Dongsha shoal and southern Lansha-yang channel in the RSR. The significantly enhanced shallow water tidal components, M4 and MS4, lead to increase tidal distortion(flood-dominant) in the nearshore under SLR. In addition, the natural period for tidal resonance in the RSR tends to be smaller and the amplification due to resonance enhances. The evolution in tidal asymmetry and tidal resonance adjusts the timing and height of the local high-water levels. Therefore, conclusion in this study can be used for reference to future high-water level prediction in the RSR.

Gravitational-wave Asteroseismology with f-modes from Neutron Star Binaries at the Merger Phase

Abstract Gravitational-wave signals from coalescing binary neutron stars (BNSs) can yield important information about the properties of nuclear-matter equation of state. We investigate a direct link between the frequency of the quadrupolar 2 f-mode oscillation (f 2f ) of nonrotating and rotating neutron stars calculated by a nonlinear hydrodynamics code in the conformally flat approximation and the gravitational-wave frequency associated with the peak amplitude ( f max ) of binary neutron stars from a set of publicly available simulations. We find that f max and f 2f differ by about 1%, on average, across 45 equal-mass systems with different total mass and equations of state. Interestingly, assuming that the gravitational-wave frequency is still approximately equal to twice the orbital frequency f orb near the merger, the result indicates that the condition for tidal resonance ( ∣ m ∣ f orb ) m = 2 = f 2 f is satisfied to high accuracy near the merger. Moreover, the well-established universal relation between f max and the tidal deformability of equal-mass binary systems can now be explained by a similar relation between f 2f and the tidal deformability of isolated neutron stars. For unequal-mass binaries, f max increasingly deviates from f 2f of the two stars as the mass ratio decreases from unity. Therefore, it is possible to relate the gravitational-wave signal at the merger of a BNS system directly to the fundamental oscillation modes and the mass ratio. This work potentially brings gravitational-wave asteroseismology to the late-inspiral and merger phases of BNSs.

On the evolution of global ocean tides

We apply Laplace's tidal theory to the evolution of lunar and solar tides on the geologic timescale of Earth's rotation and study the tidal resonance. We study the global tide in the mid-ocean far away from continents. On the short timescale, a linear relationship of tidal height and Earth's rotation is obtained. On the long timescale, the tide is less than 1 metre at present but it was 5 metres in the past and will reach 8 metres in the future because of resonances of tidal wave and Earth's rotation. We conclude that the Earth–Moon orbital separation and the slowdown of Earth's rotation are faster than expected before.

Tidal Resonance in the Adriatic Sea: Observational Evidence

AbstractTides in the Adriatic Sea are anomalously strong in comparison with most of other parts of the Mediterranean Sea. Consequently, tides play a fundamental role in the hydrodynamics of this sea and in the formation of destructive floods in its northernmost part. The resonant character of the Adriatic tides is evident, but the exact mechanism of their formation has never been thoroughly examined. In the present study, we used multidecadal tide gauge data from 10 stations located along the basin's coastline to examine the spectral properties of the Adriatic Sea and to provide high‐resolution tidal analysis. Our results demonstrate that both diurnal and semidiurnal tidal harmonics are resonantly amplified due to the proximity of tidal periods to the periods of the fundamental (21.5 hr) and first (10.9 hr) Adriatic eigen modes, respectively. The constructed resonance models were found to closely describe specific features of the observed tides in the Adriatic Sea, including both major and minor harmonics, and therefore help to explain the dominant physical mechanism driving the floods in the northernmost part of the basin, including the Venice Lagoon.

Excitation of f -modes during mergers of spinning binary neutron star

Tidal effects have important imprints on gravitational waves (GWs) emitted during the final stage of the coalescence of binaries that involve neutron stars (NSs). Dynamical tides can be significant when NS oscillations become resonant with orbital motion; understanding this process is important for accurately modeling GW emission from these binaries, and for extracting NS information from GW data. In this paper, we carry out a systematic study on the tidal excitation of fundamental modes of spinning NSs in coalescencing binaries, focusing on the case when the NS spin is anti-aligned with the orbital angular momentum-where the tidal resonance is most likely to take place. We first expand NS oscillations into stellar eigen-modes, and then obtain a Hamiltonian that governs the tidally coupled orbit-mode evolution. We next find a new approximation that can lead to analytic expressions of tidal excitations to a high accuracy, and are valid in all regimes of the binary evolution: adiabatic, resonant, and post-resonance. Using the method of osculating orbits, we obtain semi-analytic approximations to the orbital evolution and GW emission; their agreements with numerical results give us confidence in on our understanding of the system's dynamics. In particular, we recover both the averaged post-resonance evolution, which differs from the pre-resonance point-particle orbit by shifts in orbital energy and angular momentum, as well as instantaneous perturbations driven by the tidal motion. Finally, we use the Fisher matrix technique to study the effect of dynamical tides on parameter estimation. We find that the dynamical tides may potentially provide an additional channel to study the physics of NSs. The method presented in this paper is generic and not restricted to f mode; it can also be applied to other types of tide.

Modification of tidal resonance in the Severn Estuary by a barrage and lagoon

The Bristol Channel/Severn Estuary has some of the largest tides in the world with a mean spring tidal range of 12.2 m. Numerous proposals have been made to exploit this for energy extraction. However, the large tidal range is partially driven by tidal resonance and such systems can be sensitive to small changes. Thus, it is important to understand the impact of a barrage on the resonance of the system which in turn leads to an understanding of the environmental impact of building a barrage. In this paper, we examine the resonant response of the Bristol Channel system, with and without a barrage structure deployed, using a depth-averaged numerical model. We find that the barrage can alter the response of the Bristol Channel to excitation with higher frequencies than 12 h. However, the barrage causes very little change to the resonant response for longer periods including for the semi-diurnal periods which dominate the tides in the region. We also briefly examine the Swansea Lagoon scheme and find that this is too small to have a significant impact on the resonant response of the channel.