Search

Fluid muds are common in estuarine environments, but their ancient examples have rarely been documented due to poor comprehension of their depositional processes and characteristics. Mudstone layers in the tidally-influenced channel sequences of the middle McMurray Formation are examined in detail through microscopic observations and interpreted on the basis of recent advances in the understanding of flow dynamics of high mud-concentration flows. The mudstone layers, < 1 to 25 mm thick, are classified into three microfacies. Structureless mudstone (Microfacies 1) consists mainly of clay particles with randomly dispersed coarse grains (coarse silt to fine sand). It represents cohesive mud flows with sufficient cohesive forces to support coarse grains (quasi-laminar plug flow). Silt-streaked mudstone (Microfacies 2) is similar to Microfacies 1 in texture, but contains discontinuous streaks of coarse-silt to very-fine-sand grains. It is interpreted as being also deposited by cohesive fluid muds. The silt streaks are, however, suggestive of the presence of weak turbulence under the cohesive plug (upper transitional plug flow). Heterolithic laminated mudstone (Microfacies 3) is characterized by alternations of very thin, silt and clay laminae, which are either parallel or low-angle cross-laminated. It is interpreted as the deposits of low-amplitude bed-waves formed in lower transitional plug flows. These microfacies reflect a range of flow phases of fluid muds, which changed as flow velocities and suspended sediment concentrations fluctuated with tidal cycles. Repeated vertical changes of microfacies are suggestive of an ideal sequence of fluid muds formed during tidal acceleration and deceleration. The sequence comprising microfacies 3, 2 and 1 in ascending order represents deposition from lower transitional plug flows through upper transitional plug flows to quasi-laminar plug flows as suspended sediment concentrations increase with flow deceleration. That of the reversed order of microfacies reflects the reversed change in flow types during acceleration. These results provide the basis for recognizing fluid-mud deposits and tidal signatures in ancient estuarine sequences.

Volcanism powered by tidal forces inside celestial bodies can provide enough energy to keep important solvents for living systems in the liquid phase. Moreover, tidal forces and their environmental consequences may strongly influence habitability of planets and other celestial bodies and may result in special forms of live and living conditions. A prerequisite to calculate such tidal interactions and consequences is depending on simulations for tidal accelerations in a multi-body system. Unfortunately, from measurements in many extrasolar planetary systems only few physical and orbital parameters are well enough known for investigated celestial bodies. For calculating tidal acceleration vectors under missing most orbital parameter exactly, a simulation method is developed that is only based on a few basic parameters, easily measurable even in extrasolar planetary systems. Such a method as being presented here, allows finding a relation between the tidal acceleration vectors and potential heating inside celestial objects. Using values and results of our model approach to our solar system as a “gold standard” for feasibility allowed us to classify this heating in relation to different forms of volcanism. This “gold standard” approach gave us a classification measure for the relevance of tidal heating in other extrasolar systems with a reduced availability of exact physical parameters. We would help to estimate conditions for the identification of potential candidates for further sophisticated investigations by more complex established methods like viscoelastic multi-body theories. As a first example, we applied the procedures developed here to the extrasolar planetary system TRAPPIST-1 as an example to check our working hypothesis.

The biotic and abiotic controls on major shifts in atmospheric oxygen and the persistence of low-oxygen periods over a majority of Earth’s history remain under debate. Explanations of Earth’s stepwise pattern of oxygenation have mostly neglected the effect of changing diel illumination dynamics linked to daylength, which has increased through geological time due to Earth’s rotational deceleration caused by tidal friction. Here we used microsensor measurements and dynamic modelling of interfacial solute fluxes in cyanobacterial mats to investigate the effect of changing daylength on Precambrian benthic ecosystems. Simulated increases in daylength across Earth’s historical range boosted the diel benthic oxygen export, even when the gross photosynthetic production remained constant. This fundamental relationship between net productivity and daylength emerges from the interaction of diffusive mass transfer and diel illumination dynamics, and is amplified by metabolic regulation and microbial behaviour. We found that the resultant daylength-driven surplus organic carbon burial could have shaped the increase in atmospheric oxygen that occurred during the Great and Neoproterozoic Oxidation Events. Our suggested mechanism, which links the coinciding increases in daylength and atmospheric oxygen via enhanced net productivity, reveals a possible contribution of planetary mechanics to the evolution of Earth’s biology and geochemistry. Rotational deceleration has increased daylength on Earth, potentially linking the increased burial of organic carbon by cyanobacterial mats and planetary oxygenation, according to experiments and modelling of Precambrian benthic ecosystems.

All exchanges between the open ocean and the Antarctic continental shelf must cross the Antarctic Slope Current (ASC). Previous studies indicate that these exchanges are strongly influenced by mesoscale and tidal variability, yet the mechanisms responsible for setting the ASC’s transport and structure have received relatively little attention. In this study the roles of winds, eddies, and tides in accelerating the ASC are investigated using a global ocean–sea ice simulation with very high resolution (1/48° grid spacing). It is found that the circulation along the continental slope is accelerated both by surface stresses, ultimately sourced from the easterly winds, and by mesoscale eddy vorticity fluxes. At the continental shelf break, the ASC exhibits a narrow (~30–50 km), swift (>0.2 m s−1) jet, consistent with in situ observations. In this jet the surface stress is substantially reduced, and may even vanish or be directed eastward, because the ocean surface speed matches or exceeds that of the sea ice. The shelfbreak jet is shown to be accelerated by tidal momentum advection, consistent with the phenomenon of tidal rectification. Consequently, the shoreward Ekman transport vanishes and thus the mean overturning circulation that steepens the Antarctic Slope Front (ASF) is primarily due to tidal acceleration. These findings imply that the circulation and mean overturning of the ASC are not only determined by near-Antarctic winds, but also depend crucially on sea ice cover, regionally-dependent mesoscale eddy activity over the continental slope, and the amplitude of tidal flows across the continental shelf break.

In this lecture opening the session focused on tides in stellar and planetary systems, I will review the Jean-Paul Zahn's key contributions to the theory of tidal dissipation in stars and fluid planetary layers. I will first recall the general principles of tidal friction in celestial bodies. Then, I will focus on the theories of the stellar equilibrium and dynamical tides founded by Jean-Paul and their predictions for the evolution of binary stars. I will underline their essential legacy for ongoing studies of tidal dissipation in stars hosting planets and in fluid planetary regions. I will also discuss his pioneering work on the turbulent friction applied on tidal flows by stellar convection and the corresponding still unsolved challenging problems. Next, I will present the results we obtained on tidal dissipation in the potential dense rocky/icy core of gaseous giant planets such as Jupiter and Saturn within the Encelade international team. This mechanism provides important keys to interpret the high-precision astrometric measurements of the rates of tidal orbital migration of the moons of these planets, which are found to be larger than expected. This corresponds to a Jovian and Saturnian tidal frictions which are higher by one order of magnitude than the usually used values calibrated on formation scenarios. Finally, I will review the work done by Jean-Paul and Michel Rieutord on potential Ekman boundary layers associated to tidal flows. As a consequence, a coherent physical modeling of tides is now mandatory to understand the properties and the evolution of stellar and planetary systems. To progress on this forefront research subject, we are walking on the path first drawn by Jean-Paul.

Unveiling the fate of ultra-short period (USP) planets may help us understand the qualitative agreement between tidal theory and the observed exoplanet distribution. Nevertheless, due to the time-varying interchange of spin-orbit angular momentum in star-planet systems, the expected amount of tidal friction is unknown and depends on the dissipative properties of stellar and planetary interiors. In this work, we couple structural changes in the star and the planet resulting from the energy released per tidal cycle and simulate the orbital evolution of USP planets and the spin-up produced on their host star. For the first time, we allow the strength of magnetic braking to vary within a model that includes photo-evaporation, drag caused by the stellar wind, stellar mass loss, and stellar wind enhancement due to the in-falling USP planet. We apply our model to the two exoplanets with the shortest periods known to date, NGTS-10b and WASP-19b. We predict they will undergo orbital decay in time-scales that depend on the evolution of the tidal dissipation reservoir inside the star, as well as the contribution of the stellar convective envelope to the transfer of angular momentum. Contrary to previous work, which predicted mid-transit time shifts of $\sim30-190$ s over 10 years, we found that such changes would be smaller than 10 s. We note this is sensitive to the assumptions about the dissipative properties of the system. Our results have important implications for the search for observational evidence of orbital decay in USP planets, using present and future observational campaigns., Accepted for publication in MNRAS. 13 pages, 10 figures

We study further a general relativistic mechanism for the acquisition of tidal energy by free test particles near a gravitationally collapsed configuration. Specifically, we investigate the solutions of timelike geodesic equation in a Fermi normal coordinate system established about the world line of an accelerated observer that remains spatially at rest in the exterior Schwarzschild spacetime. Such static observers in effect define the rest frame of the collapsed source. The gain in tidal energy is due to local spacetime curvature. Previous work in this direction in connection with astrophysical jets involved geodesic motion along the Kerr rotation axis where outward moving particles could be tidally accelerated to almost the speed of light if their initial speed, as measured by the reference observer, is above a certain threshold escape velocity. We focus here for simplicity on the exterior Schwarzschild spacetime and show that the effective tidal acceleration to near the speed of light can occur for geodesic motion in certain radially outward directions. The implications of these results for the physics of gravitationally collapsed systems are briefly discussed., 10 pages, 2 figures; v2: minor adjustments to the source file; v3: section added, presentation improved; v4: minor improvements

We examine the tidal deformation of a nonrotating compact body (material body or black hole) in general relativity. The body's exterior metric is calculated in a simultaneous expansion in powers of the ratio between the distance to the body and three distinct length scales: the radius of curvature of the external spacetime in which the body is inserted, the scale of spatial inhomogeneity of the curvature, and the scale of temporal variation. The metric is valid in the body's immediate neighborhood, which excludes the external matter responsible for the tidal environment. The body's tidal response is encapsulated in four types of relativistic Love numbers: $k_\ell$, the familiar Love number that measures the linear response to a static tidal field, $p_\ell$, which measures the quadratic response to the tidal field, $\dot{k}_\ell$ and $\ddot{k}_\ell$, associated with first and second time derivatives of the tidal field, respectively. The Love numbers acquire an operational meaning through the definition of tidally induced multipole moments. Previously proposed definitions for the moments suffer from ambiguities associated with the subtraction of a "pure tidal field" from the full metric. A robust operational definition is proposed here. It relies on inserting the body's local metric within a global metric constructed in post-Newtonian theory; the global metric includes the external matter responsible for the tidal environment. When viewed in the post-Newtonian spacetime, the compact body appears as a skeletonized object with a specific multipole structure. The tidally induced multipole moments provide a description of this structure. They manifest themselves, for example, in the body's tidal acceleration, which is nonlinear in the tidal field. At leading order in the tidal interaction, the acceleration is proportional to the $k_2$ Love number as calculated in full general relativity., 62 pages, 1 figure. New appendix. This version matches the published article

Using the Andrade-derived Sundberg-Cooper rheology, we apply several improvements to the secular tidal evolution of TRAPPIST-1e and the early history of Pluto-Charon under the simplifying assumption of homogeneous bodies. By including higher-order eccentricity terms (up to and including e20), we find divergences from the traditionally used e2 truncation starting around e=0.1. Order-of-magnitude differences begin to occur for e>0.6. Critically, higher-order eccentricity terms activate additional spin-orbit resonances. Worlds experiencing nonsynchronous rotation can fall into and out of these resonances, altering their long-term evolution. Nonzero obliquity generally does not generate significantly higher heating; however, it can considerably alter orbital and rotational evolution. Much like eccentricity, obliquity can activate new tidal modes and resonances. Tracking the dual-body dissipation within Pluto and Charon leads to faster evolution and dramatically different orbital outcomes. Based on our findings, we recommend future tidal studies on worlds with e≥0.3 to take into account additional eccentricity terms beyond e2. This threshold should be lowered to e>0.1 if nonsynchronous rotation or nonzero obliquity is under consideration. Due to the poor convergence of the eccentricity functions, studies on worlds that may experience very high eccentricity (e≥0.6) should include terms with high powers of eccentricity. We provide these equations up to e10 for arbitrary obliquity and nonsynchronous rotation. Finally, the assumption that short-period, solid-body exoplanets with e≥0.1 are tidally locked in their 1:1 spin-orbit resonance should be reconsidered. Higher-order spin-orbit resonances can exist even at these relatively modest eccentricities, while previous studies have found such resonances can significantly alter stellar-driven climate., The Planetary Science Journal, 2 (1), ISSN:2632-3338

This study utilized the Singular Spectrum Analysis (SSA) approach to perform time series orthogonalization and demonstrated its use by analyzing vertical tidal acceleration and sea level time series from different deep-ocean locations. This method quantifies astronomical variations by using decomposed vertical tidal acceleration to reconstruct and predict deep-ocean tide. The results show that each decomposed vertical tidal acceleration can be associated with the decomposed sea level having at least 5 astronomical variations. Their associated energies can also be used to diagnose the change of the oceanic tide response to tidal acceleration. Performance evaluation also shows that this method can give comparable reconstruction accuracy and slightly better prediction accuracy compared to the harmonic analysis-based method. It is indicated that the proposed method is accurate enough to be applied in a tsunami detection algorithm. The results also indicate that the proposed method is stable enough to provide unpropagated prediction residuals.

[Context] The method of gyrochronology relates the age of its star to its rotation period. However, recent evidence of deviations from gyrochronology relations has been reported in the literature., [Aims] We study the influence of tidal interaction between a star and its companion on the rotation velocity of the star to explain peculiar stellar rotation velocities., [Methods] We followed the interaction of a star and its planet using a comprehensive numerical framework that combines tidal friction, magnetic braking, planet migration, and detailed stellar evolution models from the GARSTEC grid. We focus on close-in companions from 1 to 20 MJup orbiting low-mass (0.8 − 1 M⊙) main-sequence stars with a broad metallicity of [Fe/H] = − 1 up to solar., [Results] Our simulations suggest that the dynamical interaction between a star and its companion can have different outcomes that depend on the initial semi-major axis and the mass of the planet, as well as on the mass and metallicity of its host star. In most cases, especially in the case of planet engulfment, we find a catastrophic increase in stellar rotation velocity from 1 kms−1 to over 40 kms−1 while the star is still on the main-sequence. The main prediction of our model is that low-mass main-sequence stars with abnormal rotation velocities should be more common at low-metallicity, as lower [Fe/H] favours faster planet engulfment, based on the assumption that the occurrence rate of close-in massive planets is similar at all metallicities., [Conclusions] Our scenario explains peculiar rotation velocities of low-mass main-sequence stars by the tidal interaction between the star and its companion. Current observational samples are too narrow and incomplete, and, thus, they are not sufficient for our model to be tested., L. C. acknowledges support by the DFG Grant CA 1795/3. We acknowledge support by the Collaborative Research centre SFB 881 (projects A5, A10), Heidelberg University, of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation). A. S. is partially supported by MICINN grants ESP2017-82674-R and PID2019-108709GB-I00, and Grant 2017-SGR-1131 from Generalitat of Catalunya

Thermal, orbital, and rotational dynamics of tidally loaded exoplanets are interconnected by intricate feedback. The rheological structure of the planet determines its susceptibility to tidal deformation and, as a consequence, participates in shaping its orbit. The orbital parameters and the spin state, conversely, control the rate of tidal dissipation and may lead to substantial changes of the interior. We investigate the coupled thermal-orbital evolution of differentiated rocky exoplanets governed by the Andrade viscoelastic rheology. The coupled evolution is treated by a semi-analytical model, 1d parametrized heat transfer and self-consistently calculated tidal dissipation. First, we conduct several parametric studies, exploring the effect of the rheological properties, the planet's size, and the orbital eccentricity on the tidal locking and dissipation. These tests show that the role of tidal locking into high spin-orbit resonances is most prominent on low eccentric orbits, where it results in substantially higher tidal heating than the synchronous rotation. Second, we calculate the long-term evolution of three currently known low-mass exoplanets with nonzero orbital eccentricity and absent or yet unknown eccentricity forcing (namely GJ 625 b, GJ 411 b, and Proxima Centauri b). The tidal model incorporates the formation of a stable magma ocean and a consistently evolving spin rate. We find that the thermal state is strongly affected by the evolution of eccentricity and spin state and proceeds as a sequence of thermal equilibria. Final despinning into synchronous rotation slows down the orbital evolution and helps to maintain long-term stable orbital eccentricity., 44 pages, 13 figures; to be published in ApJ

Paper on the creep tide theory and its applications to satellites and planets with emphasis on a new set of differential equations allowing easier numerical studies. The creep tide theory is a new paradigm that does not fix a priori the tidal deformation of the body, but considers the deformation as a low-Reynolds-number flow. The evolution under tidal forces is ruled by an approximate solution of the Navier-Stokes equation depending on the body's viscosity with no ad hoc assumptions on its shape and orientation. It reproduces closely the results of Darwinian theories in the case of gaseous planets and stars, but the results are completely different in the case of stiff satellites and planets. It explains the tidal dissipations of Enceladus and Mimas. The extension of the theory to nonhomogeneous icy satellites with a subsurface ocean allows the amplitude of the forced oscillations around synchronization (librations) to be better determined., Comment: 27 pages, 8 figures

We will review the physical mechanisms involved in the dynamical evolution of Trans-Neptunian binaries (TNBs). They include: gravitational encounters with massive objects, the impulse transferred in the collisions with objects of the background population of Trans-Neptunian objects, Kozai oscillations of the binary mutual orbit induced by the Sun and planets, and tidal friction on both the primary and the secondary component of the binary and perturbations due to their nonsphericity. Then, we will show that, acting together, all these effects seem to explain most of the orbital characteristics of the known binary systems. Given the number of surviving binaries after 4.5 Gyr of dynamical evolution and the binary fraction observed today, it is plausible to suggest that all the planetesimals in the outer solar system should have been born as binaries or multiple systems. TNB belonging to the Centaur population have short dynamical lifetimes. In the frame of the present understanding of binary evolution in the outer solar system, binary Jupiter Family Comets would be found mainly in the form of contact binaries. If a population of binary systems survived to the instability phase of the outer solar system as Neptune Trojans, we would have at present a considerable fraction of them already in the Trojan Clouds. The observational evidence does not rule out this possibility. As the dynamical evolution of TNB involves strong diffusive mechanisms that could erase much of their primordial orbital structure, it would be necessary to accumulate more observational data and the computations of mutual orbits, to impose definitive constraints on the proposed formation mechanisms.

Several white dwarfs with atmospheric metal pollution have been found to host small planetary bodies (planetesimals) orbiting near the tidal disruption radius. We study the physical properties and dynamical origin of these bodies under the hypothesis that they underwent high-eccentricity migration from initial distances of several astronomical units. We examine two plausible mechanisms for orbital migration and circularization: tidal friction and ram-pressure drag in a compact disc. For each mechanism, we derive general analytic expressions for the evolution of the orbit that can be rescaled for various situations. We identify the physical parameters that determine whether a planetesimal's orbit can circularize within the appropriate time-scale and constrain these parameters based on the properties of the observed systems. For tidal migration to work, an internal viscosity similar to that of molten rock is required, and this may be naturally produced by tidal heating. For disc migration to operate, a minimal column density of the disc is implied; the inferred total disc mass is consistent with estimates of the total mass of metals accreted by polluted WDs., Comment: 17 pages, 13 figures, 2 appendices

Tidal dissipation due to convective turbulent viscosity shapes the evolution of a variety of astrophysical binaries. For example, this type of dissipation determines the rate of orbital circularization in a binary with a post-main sequence star that is evolving toward a common envelope phase. Viscous dissipation can also influence binaries with solar-type stars, or stars with a close-in giant planet. In general, the effective viscosity in a convective stellar envelope depends on the tidal forcing frequency $\omega_{\rm tide}$; when $\omega_{\rm tide}$ is larger than the turnover frequency of convective eddies, the viscosity is reduced. Previous work has focused on binaries in nearly circular orbits. However, for eccentric orbits, the tidal potential has many forcing frequencies. In this paper, we develop a formalism for computing tidal dissipation that captures the effect of frequency-dependent turbulent viscosity and is valid for arbitrary binary eccentricities. We also present an alternative simpler formulation that is suitable for very high eccentricities. We apply our formalisms to a giant branch (GB) star model and a solar-type star model. We find that a range of pseudosynchronous rotation rates are possible for both stellar models, and the pseudosynchronous rate can differ from the prediction of the commonly-used weak tidal friction theory by up to a factor of a few. We also find that tidal decay and circularization due to turbulent viscosity can be a few orders of magnitude faster than predicted by weak tidal friction in GB stars on eccentric, small pericentre orbits, but is suppressed by a few orders of magnitude in solar-type stars due to viscosity reduction., Comment: 15 pages, 11 figures

It is a well-established fact that the Earth’s rate of daily rotation is decreasing at a current rate of 6 × 10−22 rad s−2. Initially, it was proposed that the angular momentum of the spinning Earth is being transferred to the orbiting Moon due to the friction between the tidal bulge and the Earth. This causes the Earth to slow down, and the increased momentum of the Moon causes it to recede from the Earth. There is no way to directly estimate the magnitude of the torque due to tidal friction; if this mechanism is assumed to be responsible for the slowdown of the Earth, it leads to a serious problem of the close proximity of the Moon in the past for which no evidence has been found. Most of the experts on the subject are, therefore, of the opinion that the tidal friction cannot be accepted as the sole mechanism. Quite a few other exotic mechanisms have been suggested but not with complete success. Since the orbital motion of the Moon and the daily rotation rates are linked by the number of days in a lunar month, the relation between the length of the lunar month and the length of a year can reveal if the whole of the angular momentum of the Earth is being transferred to the Moon or not. Geological and paleontological data do not agree with a purely tidal friction theory. An earlier work, based on a very approximate analysis, indicated that a mechanism based on velocity dependent inertial induction could explain a major part of this slowdown without causing Moon’s close approach problem. In this article, the analysis is not only a more accurate one, but a combined model has been proposed that take care of both the tidal friction and inertial induction. It has been shown in the article that a combination of inertial induction and tidal friction can explain the phenomenon better. A detailed analysis of the interaction of Mars with the Sun has also been worked out, and it has been found out that Mars should also possess a secular retardation of magnitude 1.1 × 10−22 rad s−2 due to inertial induction though there is no major satellite to pick up the angular momentum lost by Mars. Unfortunately, the subject has not received much attention in the recent times but deserves to be taken up more seriously.

Geophysical data from the Cassini spacecraft imply the presence of a global ocean underneath the ice shell of Enceladus 1 , only a few kilometres below the surface in the South Polar Terrain 2–4 . Chemical analyses indicate that the ocean is salty 5 and is fed by ongoing hydrothermal activity 6–8 . In order to explain these observations, an abnormally high heat power (>20 billion watts) is required, as well as a mechanism to focus endogenic activity at the south pole 9,10 . Here, we show that more than 10 GW of heat can be generated by tidal friction inside the unconsolidated rocky core. Water transport in the tidally heated permeable core results in hot narrow upwellings with temperatures exceeding 363 K, characterized by powerful (1–5 GW) hotspots at the seafloor, particularly at the south pole. The release of heat in narrow regions favours intense interaction between water and rock, and the transport of hydrothermal products from the core to the plume sources. We are thus able to explain the main global characteristics of Enceladus: global ocean, strong dissipation, reduced ice-shell thickness at the south pole and seafloor activity. We predict that this endogenic activity can be sustained for tens of millions to billions of years. Tidal forcing within a very porous (unconsolidated) core can generate enough energy to drive all the observed global features of Enceladus. This activity can be sustained up to several billion years.

The mountains of Jupiter's volcanic moon Io are tall, steep, and tectonic in origin, yet their precise modes of formation and their associations with volcanic paterae are not fully understood. Global spatial statistics of paterae and mountains and their associated lineations reveal that both types of features are more common at low latitudes and tectonic lineations have preferred orientations, whereas straight patera margins are randomly oriented. Additionally, structurally controlled lineations tend to cluster with each other, and in areas of high concentrations these tectonic lineations are shorter in length than their global average. These results indicate that global-scale (rather than local or regional) processes are involved in forming Io's tectonic structures, but that the diversity of mountain characteristics and the collapse of paterae adjacent to mountain complexes are more locally controlled. Regional structural mapping of the Hi'iaka, Shamshu, Tohil, and Zal regions reveals Io's mountains reside in large, fault-bounded crustal blocks that have undergone modification through local responses of subsurface structures to variable stresses. Strike-slip motion along reactivated faults led to the formation of transpressional and transtensional features, creating tall peaks and low basins, some of which are now occupied by paterae. We propose Io's mountains result from a combination of crustal stresses involving global and local-scale processes, dominantly volcanic loading and tidal flexing. These stresses sometimes are oriented at oblique angles to pre-existing faults, reactivating them as reverse, normal, or strike-slip faults, modifying the large, cohesive crustal blocks that many of Io's mountains reside in. Further degradation of mountains and burial of faults has occurred from extensive volcanism, mass wasting, gravitational collapse, and erosion by sublimation and sapping of sulfur-rich layers. This model of fault-bounded blocks being modified by global stresses and local structural response accounts for the variation and patterns of mountain sizes, shapes, and orientations, along with their isolation and interactions with other features. It also provides a context for the operation and extent of global and regional stresses in shaping Io's surface.

The frictional influence of the seabed on the tidal flow in shelf seas and estuaries is usually modelled via a prescribed, spatially/temporally invariant drag coefficient. In practice, the seabed exhibits considerable variability, particularly spatially, that should in principle be included in simulations. Local variations in the seabed roughness (ks) alter the flow strength and, hence, local sediment transport rates. The effect of using a spatially/temporally varying ks is assessed here with reference to a tidal channel (Menai Strait, N. Wales) in which the variability of the bedforms has been monitored using multi-beam surveying. The channel not only exhibits strong tidal flow, but also a residual induced flow that is used here as diagnostic to assess various bed roughness formulations tested in a Telemac model. Tidal simulations have been carried out with both constant and temporally/spatially variable ks, and the predicted residual flow is shown to be sensitive to these representations. For a mean spring-neap (SN) cycle with variable ks, the average residual flow is calculated to be 525 m3 s− 1, consistent with observations. This residual flow can be recovered using imposed, constant values of ks in the range 0.15 m to 0.3 m. The results suggest that the overall, effective roughness of the seabed is less than half of the maximum local roughness due to the dunes in mid-channel, but more than the spatially-averaged ks value in the channel as a whole by about 50%. Simulations carried out with an M2-alone tide using variable ks produce a somewhat smaller (by 7%) residual flow of 491 m3 s− 1. The use of an ‘equivalent M2’ tide of amplitude enhanced by 7.3% reconciles these estimates. The main contribution to ks is made by dunes which are modelled using Van Rijn's (2007) formulation subject to an additional ‘history effect’. The modelled ks is found to equal approximately the observed height of the dunes along mid-channel transects rather than half the height as expected. This is attributed to the non-equilibrium nature of the bedforms in the reversing tidal flow, which exhibited shorter wavelength and more symmetrical profiles than dunes in steady flow.

The majority of confirmed terrestrial exoplanets orbits close to their host stars and their evolution was likely altered by tidal interaction. Nevertheless, due to their viscoelastic properties on the tidal frequencies, their response cannot be described exactly by standardly employed constant-lag models. We therefore introduce a tidal model based on the numerical evaluation of a continuum mechanics problem describing the deformation of viscoelastic (Maxwell or Andrade) planetary mantles subjected to external force. We apply the method on a model Earth-size planet orbiting a low-mass star and study the effect of the orbital eccentricity, the mantle viscosity and the chosen rheology on the tidal dissipation, the complex Love numbers and the tidal torque. The number of stable spin states (i.e., zero tidal torque) grows with increasing mantle viscosity, similarly to the analytical model of Correia et al. (Astron Astrophys 571:A50, 2014) for homogeneous bodies. This behavior is only slightly influenced by the rheology used. Similarly, the Love numbers do not distinctly depend on the considered rheological model. The increase in viscosity affects the amplitude of their variations. The tidal heating described by the Maxwell rheology attains local minima associated with low spin-orbit resonances, with depth and shape depending on both the eccentricity and the viscosity. For the Andrade rheology, the minima at low resonances are very shallow and the tidal heating for all viscosities resembles a “fluid limit.” The tidal heating is the quantity influenced the most by the rheology, having thus possible impact on the internal thermal evolution.

Tidal interactions between Planet and its satellites are known to be the main phenomena, which are determining the orbital evolution of the satellites. The modern ansatz in the theory of tidal dissipation in Saturn was developed previously by the international team of scientists from various countries in the field of celestial mechanics. Our applying to the theory of tidal dissipation concerns the investigating of the system of ODE-equations (ordinary differential equations) that govern the orbital evolution of the satellites; such an extremely non-linear system of 2 ordinary differential equations describes the mutual internal dynamics for the eccentricity of the orbit along with involving the semi-major axis of the proper satellite into such a monstrous equations. In our derivation, we have presented the elegant analytical solutions to the system above; so, the motivation of our ansatz is to transform the previously presented system of equations to the convenient form, in which the minimum of numerical calculations are required to obtain the final solutions. Preferably, it should be the analytical solutions; we have presented the solution as a set of quasi-periodic cycles via re-inversing of the proper ultra-elliptical integral. It means a quasi-periodic character of the evolution of the eccentricity, of the semi-major axis for the satellite orbit as well as of the quasi-periodic character of the tidal dissipation in the Planet.

The observed masses, radii and temperatures of 60 medium- to long-period binaries, most of which contain a cool, evolved star and a hotter less-evolved one, are compared with theoretical models which include (a) core convective overshooting, (b)mass loss, possibly driven by dynamo action as in RS CVn binaries, and (c) tidal friction, including its effect on orbital period through magnetic braking. A reasonable fit is found in about 42 cases, but in 11 other cases the primaries appear to have lost either more mass or less mass than the models predict, and in 4 others the orbit is predicted to be either more or less circular than observed. Of the remaining 3 systems, two ($\gamma$ Per and HR 8242) have a markedly `over-evolved' secondary, our explanation being that the primary component is the merged remnant of a former short-period sub-binary in a former triple system. The last system (V695 Cyg) defies any agreement at present. Mention is also made of three other systems (V643 Ori, OW Gem and V453 Cep), which are relevant to our discussion.

Dissipation of tidal energy causes the Moon to recede from the Earth. The currently measured rate of recession implies that the age of the Lunar orbit is 1500 My old, but the Moon is known to be 4500 My old. Consequently, it has been proposed that tidal energy dissipation was weaker in the Earth's past, but explicit numerical calculations are missing for such long time intervals. Here, for the first time, numerical tidal model simulations linked to climate model output are conducted for a range of paleogeographic configurations over the last 252 My. We find that the present is a poor guide to the past in terms of tidal dissipation: the total dissipation rates for most of the past 252 My were far below present levels. This allows us to quantify the reduced tidal dissipation rates over the most resent fraction of lunar history, and the lower dissipation allows refinement of orbitally-derived age models by inserting a complete additional precession cycle.

High-eccentricity migration is an important channel for the formation of hot Jupiters (HJs). In particular, Lidov-Kozai (LK) oscillations of orbital eccentricity/inclination induced by a distant planetary or stellar companion, combined with tidal friction, have been shown to produce HJs on Gyr timescales, provided that efficient tidal dissipation operates in the planet. We re-examine this scenario with the inclusion of dynamical tides. When the planet's orbit is in a high-eccentricity phase, the tidal force from the star excites oscillatory f-modes and r-modes in the planet. For sufficiently large eccentricity and small pericentre distance, the mode can grow chaotically over multiple pericentre passages and eventually dissipate non-linearly, drawing energy from the orbit and rapidly shrinking the semi-major axis. We study the effect of such chaotic tides on the planet's orbital evolution. We find that this pathway produces very eccentric ($e\gtrsim 0.9$) warm Jupiters (WJs) on short timescales (a few to 100 Myrs). These WJs efficiently circularize to become HJs due to their persistently small pericentre distances. Chaotic tides can also save some planets from tidal disruption by truncating the LK eccentricity oscillations, significantly increasing the HJ formation fraction for a range of planet masses and radii. Using a population synthesis calculation, we determine the characteristics of WJs and HJs produced in this scenario, including the final period distribution, orbital inclinations and stellar obliquities. Chaotic tides endow LK migration with several favorable features to explain observations of HJs. We expect that chaotic tides are also important in other flavours of high-$e$ migration.

The population of giant planets on short-period orbits can potentially be explained by some flavours of high-eccentricity migration. In this paper we investigate one such mechanism involving "secular chaos", in which secular interactions between at least three giant planets push the inner planet to a highly eccentric orbit, followed by tidal circularization and orbital decay. In addition to the equilibrium tidal friction, we incorporate dissipation due to dynamical tides that are excited inside the giant planet. Using the method of Gaussian rings to account for planet-planet interactions, we explore the conditions for extreme eccentricity excitation via secular chaos and the properties of hot Jupiters formed in this migration channel. Our calculations show that once the inner planet reaches a sufficiently large eccentricity, dynamical tides quickly dissipate the orbital energy, producing an eccentric warm Jupiter, which then decays in semi-major axis through equilibrium tides to become a hot Jupiter. Dynamical tides help the planet avoid tidal disruption, increasing the chance of forming a hot Jupiter, although not all planets survive the process. We find that the final orbital periods generally lie in the range of 2-3 days, somewhat shorter than those of the observed hot Jupiter population. We couple the planet migration to the stellar spin evolution to predict the final spin-orbit misalignments. The distribution of the misalignment angles we obtain shows a lack of retrograde orbits compared to observations. Our results suggest that high-eccentricity migration via secular chaos can only account for a fraction of the observed hot Jupiter population., Comment: 17 pages, 14 figures, submitted to MNRAS

With the discovery of TRAPPIST-1 and its seven planets residing within 0.06 au, it is becoming increasingly necessary to carry out correct treatments of tidal interactions. The eccentricity, rotation, and obliquity of the planets of TRAPPIST-1 do indeed result from the tidal evolution over the lifetime of the system. Tidal interactions can also lead to tidal heating in the interior of the planets (as for Io), which may then be responsible for volcanism or surface deformation. In the majority of studies aimed at estimating the rotation of close-in planets or their tidal heating, the planets are considered as homogeneous bodies and their rheology is often taken to be a Maxwell rheology. Here, we investigate the impact of taking into account a multi-layer structure and an Andrade rheology in the way planets dissipate tidal energy as a function of the excitation frequency. We use an internal structure model, which provides the radial profile of structural and rheological quantities (such as density, shear modulus, and viscosity) to compute the tidal response of multi-layered bodies. We then compare the outcome to the dissipation of a homogeneous planet (which only take a uniform value for shear modulus and viscosity). We find that for purely rocky bodies, it is possible to approximate the response of a multi-layer planet by that of a homogeneous planet. However, using average profiles of shear modulus and viscosity to compute the homogeneous planet response leads to an overestimation of the averaged dissipation. We provide fitted values of shear modulus and viscosity that are capable of reproducing the response of various types of rocky planets. However, we find that if the planet has an icy layer, its tidal response can no longer be approximated by a homogeneous body because of the very different properties of the icy layers (in particular, their viscosity), which leads to a second dissipation peak at higher frequencies. We also compute the tidal heating profiles for the outer TRAPPIST-1 planets (e to h).

Small tidal forces in the Earth–Moon system cause detectable changes in the orbit. Tidal energy dissipation causes secular rates in the lunar mean motion n, semimajor axis a, and eccentricity e. Terrestrial dissipation causes most of the tidal change in n and a, but lunar dissipation decreases eccentricity rate. Terrestrial tidal dissipation also slows the rotation of the Earth and increases obliquity. A tidal acceleration model is used for integration of the lunar orbit. Analysis of lunar laser ranging (LLR) data provides two or three terrestrial and two lunar dissipation parameters. Additional parameters come from geophysical knowledge of terrestrial tides. When those parameters are converted to secular rates for orbit elements, one obtains dn/dt = $$-25.97\pm 0.05 ''/$$ cent $$^{2}$$ , da/dt = 38.30 ± 0.08 mm/year, and di/dt = −0.5 ± 0.1 $$\upmu $$ as/year. Solving for two terrestrial time delays and an extra de/dt from unspecified causes gives $$\sim $$ $$3\times 10^{-12}$$ /year for the latter; solving for three LLR tidal time delays without the extra de/dt gives a larger phase lag of the N2 tide so that total de/dt = $$(1.50 \pm 0.10)\times 10^{-11}$$ /year. For total dn/dt, there is $$\le $$ 1 % difference between geophysical models of average tidal dissipation in oceans and solid Earth and LLR results, and most of that difference comes from diurnal tides. The geophysical model predicts that tidal deceleration of Earth rotation is $$-1316 ''$$ /cent $$^{2}$$ or 87.5 s/cent $$^{2}$$ for UT1-AT, a 2.395 ms/cent increase in the length of day, and an obliquity rate of 9 $$\upmu $$ as/year. For evolution during past times of slow recession, the eccentricity rate can be negative.

We revisit the global modes and instabilities of homogeneous rotating ellipsoidal fluid masses, which are the simplest global models of rotationally and tidally deformed gaseous planets or stars. The tidal flow in a short-period planet may be unstable to the elliptical instability, a hydrodynamic instability that can drive tidal evolution. We perform a global (and local WKB) analysis to study this instability using the elegant formalism of Lebovitz & Lifschitz. We survey the parameter space of global instabilities with harmonic orders $\ell\leq 5$, for planets with spins that are purely aligned (prograde) or anti-aligned (retrograde) with their orbits. In general, the instability has a much larger growth rate if the planetary spin and orbit are anti-aligned rather than aligned. We have identified a violent instability for anti-aligned spins outside of the usual frequency range for the elliptical instability (when $\frac{n}{\Omega}\lesssim -1$, where $n$ and $\Omega$ are the orbital and spin angular frequencies, respectively) if the tidal amplitude is sufficiently large. We also explore the instability in a rigid ellipsoidal container, which is found to be quantitatively similar to that with a realistic free surface. Finally, we study the effect of rotation and tidal deformation on mode frequencies. We find that larger rotation rates and larger tidal deformations both decrease the frequencies of the prograde sectoral surface gravity modes. This increases the prospect of their tidal excitation, potentially enhancing the tidal response over expectations from linear theory. In a companion paper, we use our results to interpret global simulations of the elliptical instability., Comment: 16 pages, 10 figures, accepted for publication in MNRAS (2016 March 22)

The dynamical evolution of the Earth–Moon system due to tidal friction is treated here. George H. Darwin used Laplace planes (also called proper planes) in his study of tidal evolution. The Laplace plane approach is adapted here to the formalisms of W.M. Kaula and P. Goldreich. Like Darwin, the approach assumes a three-body problem: Earth, Moon, and Sun, where the Moon and Sun are point-masses. The tidal potential is written in terms of the Laplace plane angles. The resulting secular equations of motion can be easily integrated numerically assuming the Moon is in a circular orbit about the Earth and the Earth is in a circular orbit about the Sun. For Earth–Moon distances greater than ∼10 Earth radii, the Earth’s approximate tidal response can be characterized with a single parameter, which is a ratio: a Love number times the sine of a lag angle divided by another such product. For low parameter values it can be shown that Darwin’s low-viscosity molten Earth, M. Ross’s and G. Schubert’s model of an Earth near melting, and Goldreich’s equal tidal lag angles must all give similar histories. For higher parameter values, as perhaps has been the case at times with the ocean tides, the Earth’s obliquity may have decreased slightly instead of increased once the Moon’s orbit evolved further than 50 Earth radii from the Earth, with possible implications for climate. This is contrast to the other tidal friction models mentioned, which have the obliquity always increasing with time. As for the Moon, its orbit is presently tilted to its Laplace plane by 5.2°. The equations do not allow the Moon to evolve out of its Laplace plane by tidal friction alone, so that if it was originally in its Laplace plane, the tilt arose with the addition of other mechanisms, such as resonance passages.

In most cases, the velocity profiles of tidal currents are expressed by the classical logarithmic (log) law, through which various important friction parameters, such as the friction velocity and roughness length, can be obtained conveniently. However, the power law is not used as much as the log law in tidal current surveys because of the difficulty in obtaining the friction parameters as well as the lack of a theoretical basis. Through theoretical improvements of the power law in recent years, its advantages have been validated based on measurements in pipe and river flows. For a better understanding of the power law in tidal flow, an assessment of the power law from three aspects, namely, the mean velocity profiles, the velocity gradient distribution and the Reynolds shearing stress distribution, is performed through a comparison with measurements within a tidal cycle, which are collected from some previous literature. The power law demonstrates a better correlation with the near-bed velocity profiles and gradient distribution compared with the log law. The auxiliary shearing stress distribution caused by tidal acceleration and deceleration can also be well described by the power law. Moreover, the relationships between the power index and other parameters, such as roughness length, Reynolds number and friction velocity, are investigated according to the tidal current profiles.

The volume and style of volcanism change periodically, with cycles of three main scales, which have different causes and effects. Short cycles of volcanic activity last from tens to thousands of years and are associated with periodic accumulation of magma in shallow chambers and its subsequent eruptions. The eruptions either have internal causes or are triggered externally by variations in solar activity, tidal friction, and Earth’s rotation speed. Medium-scale cycles, hundreds of thousands to millions of years long, are due to changes in spreading and subduction rates. Long cycles (30–120 Ma) are related to ascent of mantle plumes, which take away material and heat from the core–mantle boundary and change the convection rate. These appear to be the major controls of the average periodicity. Acceleration of asthenospheric convection caused by periodic plume activity pulses can change spreading rates and, correspondingly, the relative positions of moving plates. The medium-scale periodicity of volcanism is illustrated by the examples of Kamchatka and Japan, where the intensity of subduction magmatism changes periodically in response to the opening of back-arc basins (Shikoku, Sea of Japan, and South Kurile basin).

Relativistic tidal equations are formulated with respect to the rest frame of a central gravitational source and their solutions are studied. The existence of certain relativistic critical tidal currents are thereby elucidated. Specifically, observers that are spatially at rest in the exterior Kerr spacetime are considered in detail; in effect, these fiducial observers define the rest frame of the Kerr source. The general tidal equations for the free motion of test particles are worked out with respect to the Kerr background. The analytic solutions of these equations are investigated and the existence of a tidal acceleration mechanism is emphasized., 26 pages; v2: minor improvements, invited contribution to appear in Universe; v3: two errant numerical coefficients in equation (15) corrected. These errors propagated to Section IV; hence, equations (35), (38), (40), (43), (44), (46), (47), (61) and (62) have also been corrected, main results and conclusions remain unchanged

The 500 km long Far Northern Great Barrier Reef (FNGBR) is a semi-enclosed sea with little connectivity with the rest of the GBR further South. Its mean circulation is controlled by the prevailing southeasterly (northwestward) wind that generates a wind-driven mean longshore flow that is enabled by an inflow of oceanic water in the South. From an examination of single-point, mid-depth current meter data at ten sites over one year, it appears that there is no net current during calm weather, which implies that the northward North Queensland Coastal Current in the adjoining Coral Sea does not intrude in the FNGBR. Only about 20–40% of the wind-driven longshore transport continues northward to exit the FNGBR through Torres Strait because of blockage by reefs, shoals and islands and by the tidal friction effect in shallow waters. The remaining 60–80% of the flow appears to be deflected seaward to the Coral Sea in the North, an observation that appears to be supported by oceanographic modelling. This situation differs from that in the central and southern Great Barrier Reef where the southward flowing East Australian Current intrudes on the shelf and generates a net current even during calm weather.

Deep-sea currents in the Northeast Pacific Ocean are examined using observations at Station M, located on the abyssal plain 220 km offshore of central California. Collected near the seabed at ~4000 m depth from October 2014–October 2018, the current meter observations supplement long-term investigations of deep-sea benthic ecology at this site. To investigate mechanisms for variability at different time scales, the observed currents are separated into low-frequency fluctuations with periods of 1.4–60 days, fluctuations that are coherent with astronomical tidal forcing, and other high-frequency fluctuations. These motions contribute similarly to the overall variability at this location. Low-frequency currents exhibit elevated energy at periods of ~30 days, consistent with previous observations elsewhere in the abyssal North Pacific. However, unlike some other observations in the deep ocean, there is no consistent seasonal cycle in the variability of low-frequency motion. The theoretical prediction of Sverdrup balance between transport and local wind stress curl does not explain the timing or the magnitude of low frequency currents, suggesting that they are driven by remote winds or eddy dynamics. The non-tidal high-frequency fluctuations show evidence of a near-inertial peak and clockwise rotary motion, consistent with theoretical expectations for the internal gravity wave spectrum. Like the low-frequency currents, interannual variability of internal wave energy appears to be stronger than seasonal variability. Observations of the vertical structure 2.5–17.5 m above bottom are used to characterize the interactions between currents and the seabed. Observational estimates of diurnal and semidiurnal tidal ellipses are consistent with results from an analytical model that incorporates the effects of the Earth's rotation and tidal acceleration. A numerical model of the time dependent boundary layer provides estimates of bottom roughness and friction velocity that are consistent with previous observations at this site. This study shows that the strength, time scale and polarization of the near-bottom currents at Station M vary significantly between years, demonstrating the value of multi-year records in studies of the lateral transport of organic matter, sediment and organisms at this abyssal site.

Sea level rise (SLR) poses a hazard to assets, ecosystems, and economies in coastal zones, including over 600 million people worldwide who currently reside near estuaries. SLR implications include more frequent oceanic inundation, shoreline erosion, and the failure of stormwater and drainage infrastructure. To predict and manage these potential impacts, a comprehensive understanding of SLR on estuarine hydrodynamics was assessed via a review of existing theory and available literature. The review highlighted that the most common method of assessing SLR impacts in estuaries has been via simplistic static approaches, such as elevation-based water level projections, that are of limited value as they do not include fundamental hydrodynamic responses to estuarine entrance restriction, geometry, bathymetry, friction, and floodplain connectivity. A much smaller number of studies have conducted hydrodynamic modelling of SLR in estuaries showing that estuarine shape, bathymetry, friction, reflection and resonance have a strong influence on estuarine hydrodynamic parameters such as tidal range and asymmetry, saltwater intrusion, and mixing. The majority of the existing SLR estuarine hydrodynamic literature has focused on the influence of estuarine tidal parameters providing conflicting results in terms of influence of SLR on estuarine tidal dynamics and patterns. For most studies, the saltwater intrusion length of the estuary was shown to increase under SLR, whereas very few studies examined the influence of SLR on estuary entrance condition, friction, reflection, resonance, and mixing. A significant knowledge gap identified was the lack of a generic framework to conceptualise how different estuary types respond to SLR based on shape, bathymetry, and entrance condition. To this aim, several conceptual models are introduced to highlight the role of tidal friction, resonance and tidal wave penetration in estuaries under SLR.