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Secular changes of the M2 tide in the Gulf of Maine

Analyses of long time series of hourly tide-gauge data at four stations in the Gulf of Maine reveal that the amplitude of the M2 tide underwent a nearly linear secular increase throughout most of the twentieth century. In the early 1980s, however, the amplitude of M2 abruptly dropped. Sea level changes alone appear inadequate to explain either the long-term trend or the recent trend discontinuity. Tidal models that account for Holocene sea level rise do predict an amplification of M2, but much smaller than the currently observed trends. Nor do recent annual mean sea levels correlate with the recent trend discontinuity. Some unknown fraction of the open Atlantic may be similarly affected, since the M2 discontinuity, but not the long-term secular increase in the tide, is evident also at Halifax.

Ray, Richard D.

Mercury-T: A New Code to Study Tidally Evolving Multi-Planet Systems. Applications to Kepler-62

A large proportion of observed planetary systems contain several planets in a compact orbital configuration, and often harbor at least one close-in object. These systems are then most likely tidally evolving. We investigate how the effects of planet-planet interactions influence the tidal evolution of planets. We introduce for that purpose a new open-source addition to the Mercury N-body code, Mercury-T, which takes into account tides, general relativity and the effect of rotation-induced flattening in order to simulate the dynamical and tidal evolution of multi-planet systems. It uses a standard equilibrium tidal model, the constant time lag model. Besides, the evolution of the radius of several host bodies has been implemented (brown dwarfs, M-dwarfs of mass 0:1 M(sub ⨀), Sun-like stars, Jupiter). We validate the new code by comparing its output for one-planet systems to the secular equations results. We find that this code does respect the conservation of total angular momentum. We applied this new tool to the planetary system Kepler-62. We find that tides influence the stability of the system in some cases. We also show that while the four inner planets of the systems are likely to have slow rotation rates and small obliquities, the fifth planet could have a fast rotation rate and a high obliquity. This means that the two habitable zone planets of this system, Kepler-62e ad f are likely to have very different climate features, and this of course would influence their potential at hosting surface liquid water..

Dynamical evolution and stability

Dwarf Galaxies at Cosmic Noon: New JWST Constraints on Satellite Models and Subhalo Tidal Evolution

The advent of JWST has revolutionized the study of faint satellite galaxies at z ≳ 1, enabling statistical constraints on galaxy evolution and the galaxy–halo connection in a previously unexplored mass and redshift regime. We compare satellite abundances at 1 < z < 3.5 from recent JWST observations with predictions from cosmological dark-matter-only zoom-in simulations. We identify and quantify several sources of biases that can impact theoretical satellite counts, finding that assumptions about subhalo tidal evolution introduce the largest uncertainty in predictions for the satellite mass function. Using a flexible galaxy disruption model, we explore a range of disruption scenarios, spanning hydrodynamically motivated and idealized prescriptions, to bracket plausible physical outcomes. We show that varying galaxy durability can change the predicted satellite mass functions by a factor of ∼3.5. The JWST data and our fiducial model are consistent within 1σ–2σ across the full redshift (1 < z < 3.5) and stellar mass (M⋆ > 10 7 M ⊙ ) range probed. We find evidence that subhalos are at least as long-lived as predicted by hydrodynamic simulations. Our framework will enable robust constraints on the tidal evolution of subhalos with future observations. This work presents the first direct comparison between cosmological models and observations of the high-redshift satellite population in this low-mass regime. These results showcase JWST’s emerging power to test structure formation in the first half of the Universe in a new domain and to constrain the physical processes driving the evolution of low-mass galaxies across cosmic time.

79 ASTRONOMY AND ASTROPHYSICS

The Algorithm Theoretical Basis Document for Tidal Corrections

This Algorithm Theoretical Basis Document deals with the tidal corrections that need to be applied to range measurements made by the Geoscience Laser Altimeter System (GLAS). These corrections result from the action of ocean tides and Earth tides which lead to deviations from an equilibrium surface. Since the effect of tides is dependent of the time of measurement, it is necessary to remove the instantaneous tide components when processing altimeter data, so that all measurements are made to the equilibrium surface. The three main tide components to consider are the ocean tide, the solid-earth tide and the ocean loading tide. There are also long period ocean tides and the pole tide. The approximate magnitudes of these components are illustrated in Table 1, together with estimates of their uncertainties (i.e. the residual error after correction). All of these components are important for GLAS measurements over the ice sheets since centimeter-level accuracy for surface elevation change detection is required. The effect of each tidal component is to be removed by approximating their magnitude using tidal prediction models. Conversely, assimilation of GLAS measurements into tidal models will help to improve them, especially at high latitudes.

Fricker, Helen A.

Tidal energy resource characterization measurements at Cook Inlet’s East Foreland: Velocity and turbulence

To characterize tidal current and turbulence at a top tidal energy site off the East Foreland in Cook Inlet, Alaska, United States, three moorings were deployed for two months between July and August 2021, and a transect survey was conducted over the course of two tidal cycles at the end of the deployment period. Measurements of velocity and turbulence were then analyzed to better understand the site's hydrodynamics and power potential. Analysis reveals that swift, north-flowing flood currents peak at 4~m/s, while south-flowing ebb currents reach just over 3~m/s. Turbulence intensity ranges from 23\% at the seafloor to 8\% near the surface, and the presence of the foreland creates more intense turbulence near-shore during ebb tide than flood. Power availability at the site could be as high as 720~MW, or 13~kW/m$^2$, though the energy available to a marine energy device will be smaller than this estimate because of water-to-wire efficiency and wake losses. The results from this measurement campaign will inform the validation of a high-resolution tidal hydrodynamic model, as well as early tidal energy projects that are beginning to move beyond the prototyping and demonstration stages to full-scale deployments.

McVey, James R.

Biosignature Anisotropy Modeled on Temperate Tidally Locked M-Dwarf Planets

A planet’s atmospheric constituents (e.g., O2, O3, H2Ov, CO2, CH4, and N2O) can provide clues to its surface habitability, and may offer biosignature targets for remote life detection efforts. The plethora of rocky exoplanets found by recent transit surveys (e.g., the Kepler mission) indicates that potentially habitable systems orbiting K- and M-dwarf stars may have very different orbital and atmospheric characteristics than Earth. To assess the physical distribution and observational prospects of various biosignatures and habitability indicators, it is important to understand how they may change under different astrophysical and geophysical configurations, and to simulate these changes with models that include feedbacks between different subsystems of a planet’s climate. Here we use a three-dimensional (3D) Chemistry–Climate model (CCM) to study the effects of changes in stellar spectral energy distribution (SED), stellar activity, and planetary rotation on Earth analogs and tidally locked planets. Our simulations show that, apart from shifts in stellar SEDs and UV radiation, changes in illumination geometry and rotation-induced circulation can influence the global distribution of atmospheric biosignatures. We find that the stratospheric day-to-nightside mixing ratio differences on tidally locked planets remain low (<20%) across the majority of the canonical biosignatures. Interestingly, however, secondary photosynthetic biosignatures (e.g., C2H6S) show much greater (∼67%) day-to-nightside differences, and point to regimes in which tidal locking could have observationally distinguishable effects on phase curve, transit, and secondary eclipse measurements. Overall, this work highlights the potential and promise for 3D CCMs to study the atmospheric properties and habitability of terrestrial worlds.

Chen, Howard

A model of the galactic tidal interaction with the Oort comet cloud

A model of the in situ Oort cloud which is isotropic with a random distribution of perihelia directions and angular momenta is considered. The energy distribution adopted has a continuous range of values appropriate for long-period (greater than 200 yr) comets. The evolution of 1,000,000 comets are tracked as they are made observable by the galactic tidal torque. Detailed results are obtained for the predicted distribution of new comets. Predictions of observed distributions are presented and compared with the random in situ results as well as with the actual observed distributions of class I comets. The predictions are in reasonable agreement with actual observations and, in many cases, are significantly different from random when perihelia directions are separated into galactic northern and southern hemispheres.

Matese, John J.

Tidal disruption of inviscid protoplanets

Roche showed that equilibrium is impossible for a small fluid body synchronously orbiting a primary within a critical radius now termed the Roche limit. Tidal disruption of orbitally unbound bodies is a potentially important process for planetary formation through collisional accumulation, because the area of the Roche limit is considerably larger then the physical cross section of a protoplanet. Several previous studies were made of dynamical tidal disruption and different models of disruption were proposed. Because of the limitation of these analytical models, we have used a smoothed particle hydrodynamics (SPH) code to model the tidal disruption process. The code is basically the same as the one used to model giant impacts; we simply choose impact parameters large enough to avoid collisions. The primary and secondary both have iron cores and silicate mantles, and are initially isothermal at a molten temperature. The conclusions based on the analytical and numerical models are summarized.

Boss, Alan P.

Observing and Modeling Long-Period Tidal Variations in Polar Motion

By exchanging angular momentum with the solid Earth, ocean tides cause the Earth's rotation to change. While hydrodynamic tide models have been used to study the effect of ocean tides on polar motion, it is shown here that none of the published models can fully account for the observed variations. An empirical ocean tide model is therefore determined by fitting periodic terms at the tidal frequencies to polar motion excitation observations, from which atmospheric and non-tidal oceanic effects were removed. While the empirical ocean tide model does fully account for allof the observed tidal power, tests indicate that the model may not have completely converged. So better models of the effects of ocean tides on polar motion are still needed, both dynamical and empirical.

tides

High-Accuracy Tidal Flat Digital Elevation Model Construction Using TanDEM-X Science Phase Data

This study explored the feasibility of using TanDEM-X (TDX) interferometric observations of tidal flats for digital elevation model (DEM) construction. Our goal was to generate high-precision DEMs in tidal flat areas, because accurate intertidal zone data are essential for monitoring coastal environment sand erosion processes. To monitor dynamic coastal changes caused by waves, currents, and tides, very accurate DEMs with high spatial resolution are required. The bi- and monostatic modes of the TDX interferometer employed during the TDX science phase provided a great opportunity for highly accurate intertidal DEM construction using radar interferometry with no time lag (bistatic mode) or an approximately 10-s temporal baseline (monostatic mode) between the master and slave synthetic aperture radar image acquisitions. In this study, DEM construction in tidal flat areas was first optimized based on the TDX system parameters used in various TDX modes. We successfully generated intertidal zone DEMs with 57-m spatial resolutions and interferometric height accuracies better than 0.15 m for three representative tidal flats on the west coast of the Korean Peninsula. Finally, we validated these TDX DEMs against real-time kinematic-GPS measurements acquired in two tidal flat areas; the correlation coefficient was 0.97 with a root mean square error of 0.20 m.

Lee, Seung-Kuk

Strike-Slip Fault Patterns on Europa: Obliquity or Polar Wander?

Variations in diurnal tidal stress due to Europa's eccentric orbit have been considered as the driver of strike-slip motion along pre-existing faults, but obliquity and physical libration have not been taken into account. The first objective of this work is to examine the effects of obliquity on the predicted global pattern of fault slip directions based on a tidal-tectonic formation model. Our second objective is to test the hypothesis that incorporating obliquity can reconcile theory and observations without requiring polar wander, which was previously invoked to explain the mismatch found between the slip directions of 192 faults on Europa and the global pattern predicted using the eccentricity-only model. We compute predictions for individual, observed faults at their current latitude, longitude, and azimuth with four different tidal models: eccentricity only, eccentricity plus obliquity, eccentricity plus physical libration, and a combination of all three effects. We then determine whether longitude migration, presumably due to non-synchronous rotation, is indicated in observed faults by repeating the comparisons with and without obliquity, this time also allowing longitude translation. We find that a tidal model including an obliquity of 1.2?, along with longitude migration, can predict the slip directions of all observed features in the survey. However, all but four faults can be fit with only 1? of obliquity so the value we find may represent the maximum departure from a lower time-averaged obliquity value. Adding physical libration to the obliquity model improves the accuracy of predictions at the current locations of the faults, but fails to predict the slip directions of six faults and requires additional degrees of freedom. The obliquity model with longitude migration is therefore our preferred model. Although the polar wander interpretation cannot be ruled out from these results alone, the obliquity model accounts for all observations with a value consistent with theoretical expectations and cycloid modeling.

Rhoden, Alyssa Rose

Barotropic Tidal Predictions and Validation in a Relocatable Modeling Environment

Under funding from the Office of Naval Research (ONR), and the Naval Oceanographic Office (NAVOCEANO), the Mississippi State University Center for Air Sea Technology (CAST) has been working on developing a Relocatable Modeling Environment(RME) to provide a uniform and unbiased infrastructure for efficiently configuring numerical models in any geographic/oceanic region. Under Naval Oceanographic Office (NAVO-CEANO) funding, the model was implemented and tested for NAVOCEANO use. With our current emphasis on ocean tidal modeling, CAST has adopted the Colorado University's numerical ocean model, known as CURReNTSS (Colorado University Rapidly Relocatable Nestable Storm Surge) Model, as the model of choice. During the RME development process, CURReNTSS has been relocated to several coastal oceanic regions, providing excellent results that demonstrate its veracity. This report documents the model validation results and provides a brief description of the Graphic user Interface (GUI).

Mehra, Avichal

Barotropic Tidal Predictions and Validation in a Relocatable Modeling Environment

Under funding from the Office of Naval Research (ONR), the Mississippi State University Center for Air Sea Technology (CAST) has been working on developing a Relocatable Modeling Environment (RME) to provide a uniform and unbiased infrastructure for efficiently configuring numerical models in any geographic or oceanic region. Under Naval Oceanographic Office (NAVOCEANO) funding, the model was implemented and tested for NAVOCEANO use. With our current emphasis on ocean tidal modeling, CAST has adopted the Colorado University's numerical ocean model, known as CURReNTSS (Colorado University Rapidly Relocatable Nestable Storm Surge) Model, as the model of choice. During the RME development process, CURReNTSS has been relocated to several coastal oceanic regions, providing excellent results that demonstrate its veracity. This report documents the model validation results and provides a brief description of the Graphic user Interface.

Mehra, Avichal

Observed tidal braking in the earth/moon/sun system

The low degree and order terms in the spherical harmonic model of the tidal potential were observed through the perturbations which are induced on near-earth satellite orbital motions. Evaluations of tracking observations from 17 satellites and a GEM-T1 geopotential model were used in the tidal recovery which was made in the presence of over 600 long-wavelength coefficients from 32 major and minor tides. Wahr's earth tidal model was used as a basis for the recovery of the ocean tidal terms. Using this tidal model, the secular change in the moon's mean motion due to tidal dissipation was found to be -25.27 + or - 0.61 arcsec/century-squared. The estimation of lunar acceleration agreed with that observed from lunar laser ranging techniques (-24.9 + or - 1.0 arcsec/century-squared), with the corresponding tidal braking of earth's rotation being -5.98 + or - 0.22 X 10 to the -22 rad/second-squared. If the nontidal braking of the earth due to the observed secular change in the earth's second zonal harmonic is considered, satellite techniques yield a total value of the secular change in the earth's rotation rate of -4.69 + or - 0.36 X 10 to the -22 rad/second-squared.

Christodoulidis, D. C.

Observed tidal braking in the earth/moon/sun system

The low degree and order terms in the spherical harmonic model of the tidal potential were observed through the perturbations which are induced on near-earth satellite orbital motions. Evaluations of tracking observations from 17 satellites and a GEM-T1 geopotential model were used in the tidal recovery which was made in the presence of over 600 long-wavelength coefficients from 32 major and minor tides. Wahr's earth tidal model was used as a basis for the recovery of the ocean tidal terms. Using this tidal model, the secular change in the moon's mean motion due to tidal dissipation was found to be -25.27 + or - 0.61 arcsec/century squared. The estimation of lunar acceleration agreed with that observed from lunar laser ranging techniques (-24.9 + or - 1.0 arcsec/century squared), with the corresponding tidal braking of earth's rotation being -5.98 + or - 0.22 x 10 to the minus 22 rad/second squared. If the nontidal braking of the earth due to the observed secular change in the earth's second zonal harmonic is considered, satellite techniques yield a total value of the secular change of the earth's rotation rate of -4.69 + or - 0.36 x 10 to the minus 22 rad/second squared.

Christodoulidis, D. C.

Detection and Modeling of Non-Tidal Oceanic Effects on the Earth's Rotation Rate

Sub-decadal changes in the Earth's rotation rate, and hence in the length-of-day (LOD), are largely controlled by variations in atmospheric angular momentum. Results from two oceanic general circulation models (OGCMs), forced by observed wind stress and heat flux for the years 1992-1994, show that ocean current and mass distribution changes also induce detectable LOD variations.

Earth's rotation rate length-of-day LOD atmospheri

Evolution of the Earth-Moon system

The tidal evolution of the Earth-Moon system is reexamined. Several models of tidal friction are first compared in an averaged Hamiltonian formulation of the dynamics. With one of these models, full integrations of the tidally evolving Earth-Moon system are carried out in the complete, fully interacting, and chaotically evolving planetary system. Classic results on the history of the lunar orbit are confirmed by our more general model. A detailed history of the obliquity of the Earth which takes into account the evolving lunar orbit is presented.

Touma, Jihad

Tidal disruption of open clusters in their parent molecular clouds

A simple model of tidal encounters has been applied to the problem of an open cluster in a clumpy molecular cloud. The parameters of the clumps are taken from the Blitz, Stark, and Long (1988) catalog of clumps in the Rosette molecular cloud. Encounters are modeled as impulsive, rectilinear collisions between Plummer spheres, but the tidal approximation is not invoked. Mass and binding energy changes during an encounter are computed by considering the velocity impulses given to individual stars in a random realization of a Plummer sphere. Mean rates of mass and binding energy loss are then computed by integrating over many encounters. Self-similar evolutionary calculations using these rates indicate that the disruption process is most sensitive to the cluster radius and relatively insensitive to cluster mass. The calculations indicate that clusters which are born in a cloud similar to the Rosette with a cluster radius greater than about 2.5 pc will not survive long enough to leave the cloud. The majority of clusters, however, have smaller radii and will survive the passage through their parent cloud.

Long, Kevin