Tidal Energy Dissipation Research Articles

Orbital evolution of Saturn’s mid-sized moons and the tidal heating of Enceladus

The formation and orbital evolution of Saturn’s inner mid-sized moons – Rhea, Dione, Tethys, Enceladus, and Mimas – are still debated. The most puzzling aspects are 1) how the Tethys–Dione pair and the Mimas–Enceladus pair passed through their strong 3:2 mean-motion resonances during the tidal orbital evolution, and 2) the current strong heat flow from Enceladus, which is a few orders of magnitude higher than the tidal energy dissipation caused by the present orbital eccentricity of Enceladus. Here we perform N-body simulations of the moons’ orbital evolution from various initial conditions – assuming that the moons were formed from Saturn’s hypothetical massive ring – and investigate possible paths to solve the above difficulties. If the moons remain on nearly circular orbits and the influence of the rings is neglected, we find that the Tethys–Dione pair cannot avoid becoming trapped in the 2:1 and 3:2 mean-motion resonances as they recede from Saturn, and that the Tethys–Enceladus pair cannot avoid collisions after the resonance trapping, in case Saturn’s quality factor is smaller than 15,000. These findings are inconsistent with the current orbital configuration. However, taking into account both the eccentricity excitation and the orbital expansion caused by the ring torque, we find that these resonance captures are avoided. With the relatively high eccentricity pumped up by the torque, Enceladus passes through all the mean-motion resonances with Tethys, and the Dione–Tethys pair passes through their 2:1 resonance and possibly the 3:2 resonance as well. After Enceladus resides beyond the 2:1 resonance with the outer ring edge, the eccentricity can be tidally damped. While this is a promising path of evolution, in most runs, Enceladus collides with Tethys by the excited eccentricity. There is a hint that a ring mass decrease (possibly due to Mimas formation) could avoid the collision between Enceladus and Tethys. The parameter survey taking into account detailed ring evolution and Mimas is left for future study. The heat that was tidally dissipated due to the eccentricity excitation by the ring torque in the past is stored in the moons and slowly radiated away through conductive transfer. The stored heat in Enceladus may account for the current anomalously high heat flow.

Strong tidal currents over two shallow banks in the western subarctic Pacific

The south-flowing waters of the Kamchatka and Oyashio currents are key components of the western subarctic Pacific gyre. The dissipation of tidal energy in shallow and coastal regions of these currents and the attendant mixing are the important processes that affect the upper layer temperature and salinity. Examples of the impact of tidal currents on water temperature and salinity are the persistent tide-driven mixing around the Kashevarov and Kruzenshtern banks. The Kruzenshtern Bank is a shallow submarine bank stretching along the eastern continental slope of the Kuril Islands with the minimum depth of 86 m. Surface drifters observations are used to determine the characteristics of tidal currents and the circulation over these banks. New software that allows more versatility in the harmonic analysis is used for drifter’s data. The two banks have similar features. The variations in current velocities are dominated by the diurnal signals. The K1 and O1 tidal ellipses over the banks are the largest and clockwise. The enhanced tidal currents suggest that the formation of cold and saline water in summer is due to mixing of water column over the banks with intermediate waters. Variations of tidal ellipses over the bank may explain the formation of polynya at the western end of the Kashevarov Bank. We found that the 18.6-year lunar nodal cycle is a significant characteristic of salinity variation at the temperature minimum in the eddies eastward of the Boussole Strait over the period 1990–2015.

Is There a Tectonically Driven Supertidal Cycle?

AbstractEarth is 180 Myr into the current supercontinent cycle, and the next supercontinent is predicted to form in 250 Myr. The continuous changes in continental configuration can move the ocean between resonant states, and the semidiurnal tides are currently large compared to the past 252 Myr due to tidal resonance in the Atlantic. This leads to the hypothesis that there is a “supertidal” cycle linked to the supercontinent cycle. Here this is tested using new tectonic predictions for the next 250 Myr as bathymetry in a numerical tidal model. The simulations support the following hypothesis: a new tidal resonance will appear 150 Myr from now, followed by a decreasing tide as the supercontinent forms 100 Myr later. This affects the dissipation of tidal energy in the oceans, with consequences for the evolution of the Earth‐Moon system, ocean circulation and climate, and implications for the ocean's capacity of hosting and evolving life.

Critical Latitude in Tidal Dynamics Using the Kara Sea as an Example

It is well known that, within the linear nonviscous equations of tidal dynamics, the amplitudes of oscillations of the barotropic and baroclinic tidal velocity components unlimitedly increase when approaching the critical latitude. It is also known that the linear equations of tidal dynamics with a constant and specified vertical eddy viscosity indicate the occurrence of significant tidal velocity shears in the near-bottom layer, which are responsible for increasing the baroclinic tidal energy dissipation, the turbulent kinetic energy, and the thickness of the bottom boundary layer. The first circumstance—the growth of the amplitudes of oscillations of the barotropic and baroclinic tidal velocity components—is due to the elimination in the original equations of small terms, which are small everywhere except for the critical latitude zone. The second circumstance—the occurrence of significant tidal velocity shears—is due to the fact that internal tidal waves, which induce the dissipation of the baroclinic tidal energy and the diapycnal diffusion, are either not taken into account or described inadequately. It is suggested that diapycnal diffusion can lead to the degeneration (complete or partial) of tidal velocity shears, with all the ensuing consequences. The aforesaid is confirmed by simulation results obtained using the QUODDY-4 high-resolution three-dimensional finite-element hydrostatic model along the 66.25° E section, which passes in the Kara Sea across the critical latitude.

Dynamical Formation of Close Binaries during the Pre-main-sequence Phase

Abstract Solar-type binaries with short orbital periods ( days; a ≲ 0.1 au) cannot form directly via fragmentation of molecular clouds or protostellar disks, yet their component masses are highly correlated, suggesting interaction during the pre-main-sequence (pre-MS) phase. Moreover, the close binary fraction of pre-MS stars is consistent with that of their MS counterparts in the field ( ). Thus, we can infer that some migration mechanism operates during the early pre-MS phase (τ ≲ 5 Myr) that reshapes the primordial separation distribution. We test the feasibility of this hypothesis by carrying out a population synthesis calculation which accounts for two formation channels: Kozai–Lidov (KL) oscillations and dynamical instability in triple systems. Our models incorporate (1) more realistic initial conditions compared to previous studies, (2) octupole-level effects in the secular evolution, (3) tidal energy dissipation via weak-friction equilibrium tides at small eccentricities and via non-radial dynamical oscillations at large eccentricities, and (4) the larger tidal radius of a pre-MS primary. Given a 15% triple-star fraction, we simulate a close binary fraction from KL oscillations alone of after τ = 5 Myr, which increases to by τ = 5 Gyr. Dynamical ejections and disruptions of unstable coplanar triples in the disk produce solitary binaries with slightly longer periods P ≈ 10–100 days. The remaining ≈60% of close binaries with outer tertiaries, particularly those in compact coplanar configurations with log (days) ≈ 2–5 ( au), can be explained only with substantial extra energy dissipation due to interactions with primordial gas.

Global Tidal Impacts of Large‐Scale Ice Sheet Collapses

AbstractRecent studies show that the glaciers draining both the West Antarctic and the Greenland Ice Sheets are experiencing an accelerated ice loss, highlighting the possibility of large‐scale ice sheet retreat and sea level rise in the coming centuries and millennia. These sea level changes would vary spatially and could significantly alter global tides as the latter are highly dependent on bathymetry (or water column thickness under ice shelves) and basin shape. This paper investigates how the principal semidiurnal (M2) tidal amplitudes and energy dissipation respond to the nonuniform sea level changes induced by complete ice sheet collapses. The sea level changes are calculated using gravitationally self‐consistent sea level theory, and the tides are simulated using an established tidal model. Results from the simulations show global and spatially heterogeneous changes in tidal amplitudes. In addition, pronounced changes in tidal energy dissipation occur in both the open ocean and in shelf‐seas, also altering the location of tidal mixing fronts. These changes have the potential to impact ocean mixing, and hence large‐scale currents and climate patterns, and the contribution of shelf‐sea to the global carbon cycle. The new results highlight the importance of considering changes in the tides in predictions of future climate and reconstructions of past climate phases such as the Last Interglacial.

Hydrodynamic and transport responses to land reclamation in different areas of semi-enclosed subtropical bay

Many coastal areas worldwide have been reclaimed to meet the increasing land demand. Understanding the effects of land reclamation on the hydrodynamics and transport processes of a semi-enclosed bay is therefore of significance. From a case study of Deep Bay (DB) in China and referring to idealized bay models, the effects of two types of land reclamation, one that narrows the bay mouth and another that reduces the water area inside the bay, were examined in this study. Simulation results of idealized models show that the current velocity at the bay mouth and the incoming tidal energy flux are negatively correlated with the width of bay mouth, as the tidal prism remains almost constant when the bay mouth width reduces. The bay mouth width reduction would also increase the tidal energy dissipation inside of the bay due to friction increase. In DB, a 30% reduction in the mouth width increased the bay mouth current velocity by up to 5% and the total incoming energy flux by 18%. The narrowed bay mouth also substantially changed the bay's vertical structure of salinity, increasing the stratification strength by 1.7×10−4s−2. For reductions in the water surface area in the head of the bay, results from idealized bay simulations show that the current velocity throughout the bay, the incoming tidal energy flux, and salinity at the inner bay all decrease with water area reduction. Reclaiming 14% of area in DB, the current velocity reduced by 9% at the bay mouth, but increased in the middle and inner parts. The incoming tidal energy flux also increased as the coastline became more streamlined after reclamation, and the salinity at inner bay decreased. Both reclamation types have substantially altered the water and salt transport processes and increased the water exchange ability of the bay with the adjacent sea.

Tidal propagation and its non-linear characteristics in the Head Bay of Bengal

The Head Bay of Bengal is highly vulnerable to flooding events caused due to monsoons, cyclones and sea-level rise, owing to its funnel-like shape, high tidal range, presence of numerous river drainage systems, low-lying topography, and shallow bathymetry. Tides dominate the hydrodynamic behaviour and coastal processes in this region and its propagation is quite distinct. The present study uses ADCIRC hydrodynamic model customized for the Head Bay of Bengal, discretized using unstructured finite elements and validated against limited available observations in this data sparse region. The water-level elevations derived from ADCIRC simulation was used to understand the pattern of non-linear tidal propagation with respect to complex coastal geomorphology prevalent in this region. The study finds a marginal amplification of diurnal tide, nearly double amplification of semi-diurnal components, and existence of a degenerate amphidromic point near Meghna delta consistent with previous studies. The spatial and temporal variability of tidal spectral components were examined by applying the techniques of wavelet, harmonic, and time-series analysis at various locations. Maximum amplification of tides occurs at the head of the bay, along a zone enclosing the mouth of tidal inlets; and for regions northward, the tides decay with progressively increasing phase lags. The study signifies dominance of a forced fortnightly tide and tidal asymmetry leading to flood-dominance in the rivers Hooghly, Meghna, and Tetulia. The non-linear properties of tides have been elucidated, and their origin and spatio-temporal variability in these riverine systems were further investigated. Shallow depth and sharp depth gradients were discerned to be the important conditions for the origin of non-linear components. It has been deduced that non-linear tides are generated in regions where propagating tides are accumulated, and amplified in regions where they are funneled. A study of tidal energetics show that maximum rate of tidal energy dissipation is deep inside the rivers at head of the bay. The spatial variability analysis of tidal form factor shows an overall semi-diurnal dominance in the Head Bay.

Explicitly modelled deep-time tidal dissipation and its implication for Lunar history

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.

Seasonal modulation of M2 tide in the Northern Bay of Bengal

The Northern Bay of Bengal (BoB) with its adjoining Ganges-Brahmaputra-Meghna delta (GBM) forms the largest deltaic region in the world. It is surrounded by a wide area of low-lying land (less than a few meters above mean sea level), very densely populated. It is home to a strong variability of sea level, across all timescales, with ample tides and frequent storm surges. It is also subject to extended river flooding during the monsoon season, with frequent overflows of two of the world's largest rivers (Brahmaputra and Ganges). There is thus a need to understand and predict the various mechanisms responsible for coastal and estuarine water level variability in this area. In this study, we address one of the least understood facets of this variability: the low-frequency modulation of tides. We focus on the seasonal changes of amplitude of the semi-diurnal lunar tide, M2. It is found that M2 amplitude shows marked changes between winter and summer seasons (of order 10cm), incommensurate with most of the world's coastal ocean. We observe contrasted patterns from the open areas of the coastal ocean to the inner part of the GBM estuary. In the coastal ocean and over most of the GBM delta, M2 amplitude is stronger during summer and decreases until winter. Conversely, in the far northern part of GBM estuary, M2 amplitude is stronger during winter and weaker during summer. We make use of a hydrodynamic barotropic tidal model to decipher the processes responsible for this evolution. It is found that throughout the coastal ocean and over most of the GBM delta, this evolution is driven by frictional effects, with a seasonal modulation of bottom dissipation of tidal energy. Our simple barotropic model, however, does not capture the observed range of seasonal modulation of tides in the GBM estuary and at its mouth. Our study advocates for a careful consideration of these processes for a proper representation of the tidal dynamics as well as of the flooding hazard in the Bengal delta.

Tidal and subtidal hydrodynamics and energetics in a constricted estuary

The dynamics of coastal plain estuaries are mainly associated with variable tidal forcing and local winds in combination with bathymetric complexity and coastline irregularity. Specific features, such as constricted areas, can potentially affect and energize the hydrodynamics of these types of systems. Particularly, tidal range and tidal currents can be significantly amplified where the incoming tidal wave becomes constricted. In this work, the impact of a narrow constriction on a mesotidal estuary was analysed at tidal and subtidal time scales. Tidal hydrodynamics, energy fluxes and energy dissipation were determined for the entire Cádiz Bay (southwestern Spain) using the Delft3D numerical model. Field observations were used to analyse tidal propagation and energy dissipation along the bay constriction and to calibrate and test the numerical model. The results indicate that the presence of the constriction transformed and distorted the tide and increased the tidal range and flow velocities along the channel, with implications on energy dissipation. The tidal currents were oriented along-channel at the central part of the constriction, although abrupt bathymetric changes at the channel inner boundary provoked a sudden rotation of the flow. Although the energy fluxes were higher for spring tides and were strongly influenced by winds, the energy dissipation was controlled by bed shear stresses and vertical dispersion. The significance of this energy dissipation was that it destabilized the water column, which resulted in a weakly stratified system with implications on water quality. At a subtidal scale, the residual water volume exchange was the result of the combined effects of the neap/spring tides, wind and waves, whereas tides were dominant at the tidal scale.

Viscoelastic tides: models for use in Celestial Mechanics

This paper contains equations for the motion of linear viscoelastic bodies interacting under gravity. The equations are fully three dimensional and allow for the integration of the spin, the orbit, and the deformation of each body. The goal is to present good models for the tidal forces that take into account the possibly different rheology of each body. The equations are obtained within a finite dimension Lagrangian framework with dissipation function. The main contribution is a procedure to associate to each spring–dashpot model, which defines the rheology of a body, a potential and a dissipation function for the body deformation variables. The theory is applied to the Earth (solid part plus oceans) and a comparison between model and observation of the following quantities is made: norm of the Love numbers, rate of tidal energy dissipation, Chandler period, and Earth–Moon distance increase.

Assessing the influence of sea level rise on tidal power output and tidal energy dissipation near a channel

The influence of sea level rise on tidal power output and tidal energy dissipation is investigated by means of numerical simulations. The hydrodynamics in the Taiwan Strait were simulated using a new unstructured-grid, depth-averaged numerical model. Eight tidal constituents (M2, S2, N2, K2, K1, O1, P1, and Q1) were used to specify the open boundary conditions to drive the model. The observed data, including the time-series water level and tidal current, were used to validate the numerical model. The model results were in reasonable agreement with the measured data. The values of root mean square error (RMSE) for water level and tidal current are in the ranges of 0.06–0.19 m and 0.12–0.20 m/s, respectively. Moreover, the modeling amplitudes for eight tidal constituents determined using the present model were also similar to those determined using the regional inverse tidal model. The model predicted results indicated that the Penghu Channel is an appropriate location for deploying a tidal power plant because of its deep water (>100 m) and fast tidal current (>1.5 m/s). Furthermore, four sea level rise (SLR) scenarios were adopted to investigate the influence of SLR on tidal energy dissipation and tidal power output in the Penghu Channel. The simulation results showed that the total tidal energy dissipation was 11.23 GW for the baseline condition and increased corresponding to different SLR scenarios. The mean tidal power output was 42.15 MW when the additional turbine friction coefficient was set to 0.225. The extractable tidal energy increased by 1.62 MW, 2.09 MW, 2.63 MW, and 3.52 MW for SLR values of 0.87 m, 1.11 m, 1.40 m, and 1.90 m, respectively. We found that sea level rise increased tidal energy dissipation and energy output in the Penghu Channel.

Sensitivity of palaeotidal models of the northwest European shelf seas to glacial isostatic adjustment since the Last Glacial Maximum

Abstract The spatial and temporal distribution of relative sea-level change over the northwest European shelf seas has varied considerably since the Last Glacial Maximum, due to eustatic sea-level rise and a complex isostatic response to deglaciation of both near- and far-field ice sheets. Because of the complex pattern of relative sea level changes, the region is an ideal focus for modelling the impact of significant sea-level change on shelf sea tidal dynamics. Changes in tidal dynamics influence tidal range, the location of tidal mixing fronts, dissipation of tidal energy, shelf sea biogeochemistry and sediment transport pathways. Significant advancements in glacial isostatic adjustment (GIA) modelling of the region have been made in recent years, and earlier palaeotidal models of the northwest European shelf seas were developed using output from less well-constrained GIA models as input to generate palaeobathymetric grids. We use the most up-to-date and well-constrained GIA model for the region as palaeotopographic input for a new high resolution, three-dimensional tidal model (ROMS) of the northwest European shelf seas. With focus on model output for 1 ka time slices from the Last Glacial Maximum (taken as being 21 ka BP) to present day, we demonstrate that spatial and temporal changes in simulated tidal dynamics are very sensitive to relative sea-level distribution. The new high resolution palaeotidal model is considered a significant improvement on previous depth-averaged palaeotidal models, in particular where the outputs are to be used in sediment transport studies, where consideration of the near-bed stress is critical, and for constraining sea level index points.

The influence of human activities on morphodynamics and alteration of sediment source and sink in the Changjiang Estuary

Several works have discussed the morphological evolution in the Changjiang Estuary (CJE) in recent years. The erosion of its subaqueous delta in recent decades has been ascribed to a decline in fluvial sediment input. However, the interaction between the reduction of riverine sediment load and human activities in the estuary that could have caused morphological change has not been considered. In this work we provide evidence on the morphological evolution around the delta front zone since 1986 and use a numerical model to explore the correlation between the change in hydrodynamics and the evolution pattern. Bathymetric data analysis suggests a decrease of net accretion rate from 16.7mm/year (1986–1997) to 9.1mm/year (1997–2010) in the study area. Spatially, the tidal flats accreted whereas the subaqueous delta switched from deposition between 1986 and 1997 to erosion between 1997 and 2010. We used two indicators, tidal energy dissipation and erosion rate, to quantify the change in hydrodynamics and found that the erosion of the subaqueous delta in recent decades can readily be explained by the alteration of the hydrodynamics. The newly built navigation training works in the North Passage had a significant effect on the estuarine hydrodynamics, resulting in a local morphological adjustment. This erosion generated a new source of sediments to maintain the high suspended sediment concentration and tidal flat progradation. The erosion of the subaqueous delta may continue and gradually slow down until the altered hydrodynamics and morphology reach an equilibrium state in the future.

Hydrodynamic effects at the entry of tidal waves into estuaries

The phenomenon of an increase in tidal wave height in cone-shaped estuaries is studied. The effect of estuary narrowing in the direction of tidal wave propagation (the hydrodynamic effect of confusor) is among the factors amplifying the tide. An opposite effect of turbulent friction, whose manifestation increases with decreasing bay’s depth, conversely, reduces tide amplitude because of the dissipation of tidal wave energy. Stokes diffusion layer also plays a significant role in the formation of wave transformation regime. In an estuary with a median depth, which is much greater than the Stokes layer thickness, the confusor effect is stronger and tide amplitude increases at estuary head. At depths lesser than Stokes layer thickness, the turbulent friction dominates over the confusor effect and the amplitude of tidal wave decreases at the head of the estuary. The depths of the order of Stokes layer thickness cause an interesting intermediate phenomenon—at the entrance into the estuary, first the effect of friction manifests itself, resulting in a decrease in the amplitude of tidal wave, but later, the effect of confusor starts dominating, and the amplitude of tidal wave again increases toward estuary head. When the period of tidal wave coincides with seiche period, a resonance enhancement of seiche oscillations takes place in the estuary.

Secular tidal changes in lunar orbit and Earth rotation

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.

Computing the geobiosphere emergy baseline: A novel approach

We demonstrate a new and novel approach to calculate Earth's geobiosphere emergy baseline (GEB). In this method we use gravitational potential energy dissipated in the generation of Earth's main renewable energy sources. From this gravitational perspective, we recognize three refinements to our understanding of Earths driving energies. First we acknowledge the recent literature suggests that Earth's geothermal energy is from two separate sources, decay of radioisotopes and primordial heat, thus warranting separate solar equivalence ratios (SERs). Second, tidal energy dissipation can be viewed as the loss of Earth's rotational kinetic energy (KE), due to gravitational interaction between Earth/Moon/Sun and frictional forces in Earth's oceans. Seen in this way we draw an equivalence between loss of Earth rotational KE and tidal energy dissipated. Third, Earth's rotational KE and primordial heat are coupled processes of the gravitationally induced accretion of Earth.The four sources of available energy to the geobiosphere, solar radiation, tidal energy dissipation, primordial heat, and radiogenic heat, are expressed as a ratio of gravitational emergy needed to produce them. After all four sources are expressed by their gravitational transformities, solar equivalences are computed by dividing their gravitational transformity by the gravitational transformity of solar radiation, resulting in solar equivalent ratios. Using solar equivalences, we combine the four sources to express the emergy driving all planetary phenomena. The method yields four different baselines depending on the allocation procedure used to assign gravitational exergy of Earth's accretion to it is rotational KE and primordial heat. The GEBs ranged between 11.1E+24seJJ−1 and 13.8E+24seJJ−1.

Tidal dissipation in creeping ice and the thermal evolution of Europa

Abstract The thermal and mechanical evolution of Europa and comparable icy satellites—the physics behind creating and sustaining a subsurface water ocean—depends almost entirely on the mechanical dissipation of tidal energy in ice to produce heat, the mechanism(s) of which remain poorly understood. In deformation experiments, we combine steady–state creep and low-frequency, small-strain periodic loading, similar conditions in which tectonics and tidal flexing are occurring simultaneously. The data reveal that the relevant, power-law attenuation in ice (i) is non-linear, depending on strain amplitude, (ii) is independent of grain size, and (iii) exceeds in absorption the prediction of the Maxwell solid model by an order of magnitude. The Maxwell solid model is widely used to model the dynamics of planetary ice shells, so this discrepancy is important. The prevalent understanding of damping in the geophysical context is that it is controlled by chemical diffusion on grain boundaries, which renders attenuation strongly dependent on grain size. In sharp contrast, our results indicate instead the importance of intracrystalline dislocations and their spatial interactions as the critical structural variable affecting dissipation. These dislocation structures are controlled by stress and realized by accumulated plastic strain. Thus, tectonics and attenuation are coupled, which, beyond the icy satellite/subsurface ocean problem, has implications also for understanding the attenuation of seismic waves in deforming regions of the Earth's upper mantle.

Resonance locking as the source of rapid tidal migration in the Jupiter and Saturn moon systems

The inner moons of Jupiter and Saturn migrate outwards due to tidal energy dissipation within the planets, the details of which remain poorly understood. We demonstrate that resonance locking between moons and internal oscillation modes of the planet can produce rapid tidal migration. Resonance locking arises due to the internal structural evolution of the planet and typically produces an outward migration rate comparable to the age of the solar system. Resonance locking predicts a similar migration timescale but a different effective tidal quality factor $Q$ governing the migration of each moon. It also predicts nearly constant migration timescales a function of semi-major axis, such that effective $Q$ values were larger in the past. Recent measurements of Jupiter and Saturn's moon systems find effective $Q$ values that are smaller than expected (and are different between moons), and which correspond to migration timescales of $\sim$10 Gyr. If confirmed, the measurements are broadly consistent with resonance locking as the dominant source of tidal dissipation in Jupiter and Saturn. Resonance locking also provides solutions to several problems posed by current measurements: it naturally explains the exceptionally small $Q$ governing Rhea's migration, it allows the large heating rate of Enceladus to be achieved in an equilibrium eccentricity configuration, and it resolves evolutionary problems arising from present-day migration/heating rates.