Tidal Symmetry Research Articles

Breaking the symmetry by breaking the ice shell: An impact origin for the south polar terrain of Enceladus

The origin of the unique south polar terrain on Enceladus is not well understood. Gravity measurements made by Cassini suggest that the ice shell is thinner at the south pole than in the north. Tides are recognized to be the ultimate energy source for the observed thermal anomaly, and are believed to regulate the activity of jets, and movement along the tiger-stripes. However, tides alone are insufficient to explain the observed pattern of heat flow and activity, because the tidal potential is symmetric about the equator and no corresponding thermal anomaly or activity is observed in the north.Tidal heating is highly sensitive to the thickness and the mechanical properties of the ice shell, and the presence of significant lateral variations in the mechanical properties of the ice shell, and in general is stronger when the ice is thinner and weaker. Although the tidal heating might be able to sustain these variations once in place, a non-tidal, physical mechanism is therefore needed to break the tidal symmetry. Here we explore the possibility that a large impact into what is now the SPT could break through the ice shell of Enceladus, and break the hemispheric symmetry as well. We have performed hydrocode simulations of the impacts of icy projectiles into the ice shell of Enceladus, and have modeled the thermal evolution of the ice shell post-impact.We find that an impact capable of forming a crater the size of the present-day south polar terrain could have completely penetrated a 20-km thick ice shell, and would have excavated a cavity extending ~30 km deep in a thicker ice shell. Although the impact does not completely punch through a thicker ice shell, the floor of the crater is extensively fractured, exposing the ocean to space. We find that the impact shock heating will be retained for a few Myr, and that it locally softens the ice to permit more tidal dissipation. The ice shell beneath the impact site thickens over time, but a 1–2 km reduction in topography is retained at the surface.

The Influence of Storms on Sand Wave Evolution: A Nonlinear Idealized Modeling Approach

We present a new 2DV nonlinear process‐based morphodynamic model to investigate the effects of storms, specifically wind‐driven flow and wind waves, on finite amplitude tidal sand wave evolution. Simulations are performed on periodic domains of two lengths: (i) on a 350‐m domain, comparable to the wavelength of observed sand waves, we study the evolution toward equilibrium shapes, and (ii) on a 4‐km domain, we study the evolution from a randomly perturbed seabed. Our model results demonstrate that both wind‐driven flow and wind waves reduce sand wave height and tend to increase wavelength. Wind‐driven flow breaks the tidal symmetry, resulting in horizontal sand wave asymmetry and migration. Waves alone do not induce migration but can enhance migration induced by, for example, tidal asymmetry and wind‐driven flow. On the 350‐m domain, we further find that migration rates decrease with increasing sand wave height. However, in an irregular sand wave field, large sand waves tend to overtake the smaller ones, suggesting a complicated interaction among neighboring bed forms. The above results concern steady state storm conditions. However, since storms occur on an intermittent basis, we also simulated a synthetic storm climate consisting of alternating short periods of storm conditions and long periods of fair‐weather conditions. Simulations reveal a dynamic equilibrium with sand wave heights significantly below those obtained for tide‐only conditions, also for relatively short storm duration. Our work identifies mechanisms that explain why sand wave heights are generally overpredicted by numerical models that do not include storm processes.

The impact of tidal stream turbines on large-scale sediment dynamics

Tidal stream turbines are exploited in regions of high tidal currents. Such energy extraction will alter the hydrodynamics of a tidal region, analogous to increasing the bed friction in the region of extraction. In addition, this study demonstrates that energy extracted with respect to tidal asymmetries due to interactions between quarter ( M 4) and semi-diurnal ( M 2) currents will have important implications for large-scale sediment dynamics. Model simulations show that energy extracted from regions of strong tidal asymmetry will have a much more pronounced effect on sediment dynamics than energy extracted from regions of tidal symmetry. The results show that energy extracted from regions of strong tidal asymmetry led to a 20% increase in the magnitude of bed level change averaged over the length of a large estuarine system, compared with energy extracted from regions of tidal symmetry. However, regardless of the location of a tidal stream farm within a tidal system, energy extraction reduces the overall magnitude of bed level change in comparison with non-extraction cases. This has practical application to many areas surrounding the UK, including the Irish Sea and the Bristol Channel, that exhibit strong tidal currents suitable for exploitation of the tidal stream resource, but where large variations in tidal asymmetry occur.

Modelling sand wave migration in shallow shelf seas

Sand waves form a prominent regular pattern in the offshore seabed of sandy shallow seas. The positions of sand-wave crests and troughs slowly change in time. Sand waves are usually assumed to migrate in the direction of the residual current. This paper considers the physical mechanisms that may cause sand waves to migrate and methods to quantify the associated migration rates. We carried out a theoretical study based on the assumption that sand waves evolve as free instabilities of the system. A linear stability analysis was then performed on a 2DV morphological model describing the interaction between the vertically varying water motion and an erodible bed in a shallow sea. Here, we disrupted the basic tidal symmetry by choosing a combination of a steady current ( M 0) and a sinusoidal tidal motion ( M 2) as the basic flow. We allowed for two different physical mechanisms to generate the steady current: a sea surface wind stress and a pressure gradient. The results show that similar sand waves develop for both flow conditions and that these sand waves migrate slowly in the direction of the residual flow. The rates of migration and wavelengths found in this work agree with theoretical and empirical values reported in the literature.

Deviation from tidal symmetry for scattering ofpolarized23Nafrom the deformed nucleus27Al

The second-rank analyzing powers ${T}_{20}$ and ${}^{T}{T}_{20}$ were measured using a tensor-polarized beam of ${}^{23}\mathrm{Na}$ scattered from ${}^{27}\mathrm{Al}$ at an incident energy of 150 MeV. The concept of tidal symmetry in scattering systems leads directly to a shape-effect relationship between the two sets of analyzing powers which should hold good at low values of the isocentrifugal parameter and this has been confirmed in other scattering systems. $\mathrm{For}{ }^{23}\mathrm{Na}{+}^{27}\mathrm{Al}$ at 150 MeV the isocentrifugal parameter has the low value of 0.04, yet the shape effect relations do not hold true for the data forward of $12\ifmmode^\circ\else\textdegree\fi{} \mathrm{c}.\mathrm{m}.$ It is suggested that this may be evidence for an effect of the deformation of the target nucleus and this is supported by coupled-channel calculations which agree well with the data.

Mechanism of the elastic and inelastic scattering of polarised 7Li by 54Fe at 70 and 50 MeV

Differential cross sections and the analysing powers iT 11, TT 20, T 20 and T 21 were measured for both the elastic scattering of 70 and 50 MeV polarised 7Li from 54Fe and the inelastic scattering to the first excited states of the projectile and target. In both the elastic scattering and target excitation, the second-rank analysing powers follow the shape effect relations while the analogous projectile excitation data do not. Two-channel adiabatic tidal symmetry calculations reproduce only the elastic scattering data, A coupled-channels analysis including unbound states of 7Li and a cluster folding-model spin-orbit potential accounts for the main features of all the observables.

Reorientation and coupling effects in polarized heavy ion fusion

A simple model to understand the reaction mechanisms in the fusion of polarized heavy ions based on tidal symmetry, the sudden approximation and barrier penetration is presented. The model is applied to 23Na+ 208Pb. The effect of the ground state reorientation and the coupling to rotational states is studied. Enhancement of the sub-barrier fusion cross sections and the fusion J-moments just above the barrier are found. The polarization of the projectile affects strongly the fusion around and below the Coulomb barrier.

Deviations from tidal symmetry in polarized 7Li excitation

A simple model that describes the excitation of polarized projectiles is proposed. The disagreement between the experimental analysing power data for 7Li on 120Sn at 44 MeV and the shape effect relations, and the value of the vector analysing power are explained as a consequence of deviations from the tidal symmetry.

Tidal symmetry in scattering of polarized 23Na from 208Pb

The data for differential cross sections and transverse tensor analysing powers in scattering of polarized 23Na from 208Pb at 170 MeV were obtained for the ground, first and second excited states of 23Na. The measurements were performed with the QMG/2 magnetic spectrometer at Daresbury Laboratory. The extracted data were analysed on the basis of the tidal symmetry model and the adiabatic approximation. The ground-state reorientation coupling together with two-channel and three-channel coupling schemes for 23Na states have been attempted. Both nuclear and Coulomb terms were used in the reorientation and coupling potentials. The differential cross section and the transverse tensor analysing powers in the elastic channel are successfully described in the tidal symmetry model. However, the data in the inelastic channels are only approximately described by this model. Comparison of these results with exact coupled-channel calculations shows the implications of tidal symmetry breaking in the inelastic channels.

Coupled-channels calculation for the system 23Na+208Pb: a test of tidal symmetry

The results of a coupled-channels calculation for the elastic and inelastic scattering of 170 MeV 23Na by 208Pb are compared with the adiabatic model and the isocentrifugal model. It is shown that, in the absence of Coulomb excitation, the tidal spin is conserved to a very good approximation. The effect of Coulomb excitation is to cause deviations from tidal symmetry. It is shown that the extent to which tidal symmetry is satisfied becomes very transparent if the amplitudes and analysing powers are calculated in a recoil frame where the recoil direction is chosen as the z axis.

Neutron transfer reactions induced by polarized 7Li

A semiclassical model is applied to calculate the analyzing powers of neutron transfer reactions. The Q-dependence of the transfer cross sections and analyzing powers is studied. The dependence of the analyzing powers on the quantum numbers of the final state is also investigated. The applicability of tidal symmetry to transfer reactions is discussed. The results are compared to experimental data for the reaction 120Sn( 7Li, 6'Li) 121Sn at 44 MeV.

Tidal symmetry in the scattering of polarised23Na

The differential cross section, vector analysing power and three components of the second-rank tensor analysing power were measured for quasi-elastic scattering of 170 MeV 23Na from 208Pb. The data have been successfully interpreted in terms of the tidal symmetry model and the sign and magnitude of the observed polarisation effects are in good agreement with the known quadrupole moment of 23Na.

Tidal symmetry in nuclear reactions: application to the scattering of polarised projectiles

Tidal symmetry in nuclear reactions: application to the scattering of polarised projectiles

Tidal symmetry in scattering of polarised7Li projectiles

Tidal symmetry is a recently proposed concept which introduces considerable simplifications into the theoretical analysis of heavy-ion scattering and fusion. It also facilitates the understanding of features of nuclear reactions induced by polarised heavy ions. Key pointers to this symmetry are presented and compared with new experimental results and published data for 7Li elastic scattering. The discussion gives an indication of the usefulness of the tidal symmetry concept.

Tidal symmetry in nuclear reactions: application to the reaction cross sections of polarized projectiles

The calculation of reaction cross sections is greatly simplified when the difference in centrifugal barriers of the channels coupled together is ignored. This is due to the “tidal symmetry”, that is the invariance of momentum independent interactions with respect to rotations of the interacting particles about their relative coordinate.

Tidal symmetry in nuclear reactions: application to the scattering of polarised projectiles

The consequences for nucleus-nucleus collisions of the invariance (tidal symmetry) of arbitrary but momentum-independent interactions under rotations about the relative coordinate of the interacting nuclei are examined. In conjunction with an approximate treatment of the centrifugal barrier this symmetry leads to a partial diagonalisation of the coupled-channels description of the scattering of the two nuclei. This approximation is found to give an accurate description of the tensor polarisation observables in a specific heavy-ion elastic scattering case. A consequence of the treatment given here is that the so-called 'shape effect' relations can be satisfied in strong-coupling situations.