Assimilation of altimetry data for nonlinear shallow-water tides: Quarter-diurnal tides of the Northwest European Shelf     

Gary D. Egbert  Svetlana Y. Erofeeva  Richard D. Ray 《Continental Shelf Research》2010

Non-linear tidal constituents, such as the overtide M₄ or the compound tide MS₄, are generated by interaction in shallow seas of the much larger astronomically forced “primary” tidal constituents (e.g., M₂, S₂). As such, errors in modeling these “secondary” shallow-water tides might be expected to be caused first of all by errors in modeling the primary constituents. Thus, in the context of data assimilation, observations of primary-constituent harmonic constants can indirectly constrain shallow-water constituents. Here we consider variational data assimilation for primary and secondary tidal constituents as a coupled problem, using a simple linearized perturbation theory for weak interactions of the dominant primary constituents. Variation of the resulting penalty functional leads to weakly non-linear Euler–Lagrange equations, which we show can be solved approximately with a simple two-stage scheme. In the first stage, data for the primary constituents are assimilated into the linear shallow water equations (SWE), and the resulting inverse solutions are used to compute the quadratic interactions in the non-linear SWE that constitute the forcing for the secondary constituents. In the second stage, data for the compound or overtide constituent are assimilated into the linear SWE, using a prior forced by the results of the first stage. We apply this scheme to assimilation of TOPEX/Poseidon and Jason altimetry data on the Northwest European Shelf, comparing results to a large set of shelf and coastal tide gauges. Prior solutions for M₄, MS₄ and MN₄ computed using inverse solutions for M₂, S₂, and N₂ dramatically improve fits to validation tide gauges relative to unconstrained forward solutions. Further assimilation of along-track harmonic constants for these shallow-water constituents reduces RMS differences to below 1 cm on the shelf, approaching the accuracy of the validation tide gauge harmonic constants.  相似文献   

Cycloid crack sequences on Europa: Relationship to stress history and constraints on growth mechanics based on cusp angles     

Julie M. Groenleer 《Icarus》2008,193(1):158-181

The original model developed to explain cycloidal cracks on Europa interprets cycloids as tensile fractures that grow in a curved path in response to the constantly rotating diurnal tidal stress field. Cusps form when a new cycloid crack segment propagates at an angle to the first in response to a rotation of the principal tidal stress orientation during a period of no crack growth. A recent revised model states that a cycloid cusp forms through the creation of a secondary fracture called a tailcrack at the tip of an existing cycloid segment during shearing motion induced by the rotating tidal stress field. As the tailcrack propagates away from the cusp, it becomes the next cycloid segment in the chain. The qualitative tailcrack model uniquely accounts for the normal and shear stresses that mechanically must resolve onto the tip of an existing cycloid segment at the instant of cusp formation. In this work, we provide a quantitative framework and test of the hitherto purely conceptual tailcrack model. We first present a relative age sequence inferred from geologic mapping of multiply cross-cutting cycloids in Europa's trailing hemisphere and place this into the context of the global stress history. The age sequence requires a cumulative minimum of 630° of shell reorientation due to nonsynchronous rotation to account for the observed range of orientations of cycloids of different ages. We determined the back-rotated longitudes of formation of two cycloid chain examples and used mathematical modeling of europan tidal stresses to show that the tailcrack model for cusp formation is not only viable, but places constraints on the overall development of a cycloid chain by controlling the timing of cusp development within Europa's orbit. For all cusps analyzed, the exact ratio of resolved shear to normal stress required to form the cusp angles by a process of tailcracking, as governed by the principles of linear elastic fracture mechanics, is produced at the tip of a shearing cycloid segment during Europa's orbit. Cusp formation occurs after the point in the orbit at which the maximum tensile principal tidal stress occurs, implying that tensile tidal stresses are not directly responsible for cusp development. Instead, cusps develop when a tailcrack forms at the tip of a cycloid segment in response to the highly perturbed stress field induced during concomitant opening and shearing at the tip of the cycloid segment.  相似文献   

Tidal dissipation at arbitrary eccentricity and obliquity     

Jack Wisdom 《Icarus》2008,193(2):637-640

Expressions for tidal dissipation in a body in synchronous rotation at arbitrary orbital eccentricity and obliquity are derived. The rate of tidal dissipation for a synchronously rotating body is compared to that in a body in asymptotic nonsynchronous rotation.  相似文献   

Ground-based observations of noctilucent clouds with a northern hemisphere network of automatic digital cameras     

P. Dalin  N. Pertsev  A. Zadorozhny  M. Connors  I. Schofield  I. Shelton  M. Zalcik  T. McEwan  I. McEachran  S. Frandsen  O. Hansen  H. Andersen  V. Sukhodoev  V. Perminov  V. Romejko 《Journal of Atmospheric and Solar》2008,70(11-12):1460-1472

For the first time we present an analysis of observations of noctilucent clouds obtained with a network of automatic digital cameras located at opposite sides of the northern hemisphere. The advantage of this network is that the cameras are located along the same latitude circle producing comparable measurements. We find that there is an indication of the 2-day planetary wave propagation influencing the occurrence frequency, geographical distribution and brightness variations of noctilucent clouds. The 5-day planetary wave has much less effect on noctilucent clouds than that of the 2-day wave, at least for the summers of 2006 and 2007. At the same time, bright noctilucent clouds tend to occur every successive night during short periods of 3–5 nights.  相似文献   

Suspended sediment fluxes at an intertidal flat: The shifting influence of wave,wind, tidal,and freshwater forcing   总被引：1，自引：0，他引：1  

Stefan A. Talke  Mark T. Stacey 《Continental Shelf Research》2008

Using in situ, continuous, high frequency (8–16 Hz) measurements of velocity, suspended sediment concentration (SSC), and salinity, we investigate the factors affecting near-bed sediment flux during and after a meteorological event (cold front) on an intertidal flat in central San Francisco Bay. Hydrodynamic forcing occurs over many frequency bands including wind wave, ocean swell, seiching (500–1000 s), tidal, and infra-tidal frequencies, and varies greatly over the time scale of hours and days. Sediment fluxes occur primarily due to variations in flow and SSC at three different scales: residual (tidally averaged), tidal, and seiching. During the meteorological event, sediment fluxes are dominated by increases in tidally averaged SSC and flow. Runoff and wind-induced circulation contribute to an order of magnitude increase in tidally averaged offshore flow, while waves and seiching motions from wind forcing cause an order of magnitude increase in tidally averaged SSC. Sediment fluxes during calm periods are dominated by asymmetries in SSC over a tidal cycle. Freshwater forcing produces sharp salinity fronts which trap sediment and sweep by the sensors over short (∼30 min) time scales, and occur primarily during the flood. The resulting flood dominance in SSC is magnified or reversed by variations in wind forcing between the flood and ebb. Long-term records show that more than half of wind events (sustained speeds of greater than 5 m/s) occur for 3 h or less, suggesting that asymmetric wind forcing over a tidal cycle commonly occurs. Seiching associated with wind and its variation produces onshore sediment transport. Overall, the changing hydrodynamic and meteorological forcing influence sediment flux at both short (minutes) and long (days) time scales.  相似文献   

Effects of low-viscous layers and a non-zero obliquity on surface stresses induced by diurnal tides and non-synchronous rotation: The case of Europa     

Hermes M. Jara-Orué  Bert L.A. Vermeersen 《Icarus》2011,215(1):417-438

In this study we present a semi-analytical Maxwell-viscoelastic model of the variable tidal stress field acting on Europa’s surface. In our analysis, we take into account surface stresses induced by the small eccentricity of Europa’s orbit, the non-zero obliquity of Europa’s spin axis - both acting on a diurnal 3.55-days timescale - and the reorientation of the ice shell as a result of non-synchronous rotation (NSR). We assume that Europa’s putative ocean is covered by an ice shell, which we subdivide in a low-viscous and warm lower ice layer (asthenosphere, viscosity 10¹²-10¹⁷ Pa s), and a high-viscous and cold upper ice layer (lithosphere, viscosity 10²¹ Pa s).Viscoelastic relaxation influences surface stresses in two ways: (1) through viscoelastic relaxation in the lithosphere and (2) through the viscoelastic tidal response of Europa’s interior. The amount of relaxation in the lithosphere is proportional to the ratio between the period of the forcing mechanism and the Maxwell time of the high-viscous lithosphere. As a result, this effect is only relevant to surface stresses caused by the slow NSR mechanism. On the other hand, the importance of the viscoelastic response on surface stresses is proportional to the ratio between the relaxation time (τ_j) of a given viscoelastic mode j and the period of the forcing function. On a diurnal timescale the fast relaxation of transient modes related to the low viscosity of the asthenosphere can alter the magnitude and phase shift of the diurnal stress field at Europa’s surface. The effects are largest, up to 20% in magnitude and 7° in phase for ice rigidities lower than 3.487 GPa, when the relaxation time of the aforementioned transient modes approaches the inverse of the average angular rate of Europa’s orbit. On timescales relevant for NSR (>10⁴ years) the magnitude and phase shift of NSR surface stresses can be affected by viscoelastic relaxation of the ocean-ice boundary. This effect, however, becomes only important when the behavior of the lithosphere w.r.t. NSR approaches the fluid limit, i.e. for strong relaxation in the lithosphere. The combination of NSR and diurnal stresses for different amounts of viscoelastic relaxation of NSR stresses in the lithosphere leads to a large variety of global stress fields that can explain the formation of the large diversity of lineament morphologies observed on Europa’s surface. Variation of the amount of relaxation in the lithosphere is likely due to changes in the spin rate of Europa and/or the rheological properties of the surface.In addition, we show that a small obliquity(<1°) can have a considerable effect on Europa’s diurnal stress field. A non-zero obliquity breaks the symmetric distribution of stress patterns with respect to the equator, thereby affecting the magnitude and orientation of the principal stresses at the surface. As expected, increasing the value of Europa’s obliquity leads to larger diurnal stresses at the surface, especially when Europa is located 90° away from the nodes formed by the intersection of its orbital and equatorial planes.  相似文献   

Subsurface oceans and deep interiors of medium-sized outer planet satellites and large trans-neptunian objects   总被引：1，自引：0，他引：1  

Hauke Hussmann  Frank Sohl 《Icarus》2006,185(1):258-273

The detection of induced magnetic fields in the vicinity of the jovian satellites Europa, Ganymede, and Callisto is one of the most surprising findings of the Galileo mission to Jupiter. The observed magnetic signature cannot be generated in solid ice or in silicate rock. It rather suggests the existence of electrically conducting reservoirs of liquid water beneath the satellites' outermost icy shells that may contain even more water than all terrestrial oceans combined. The maintenance of liquid water layers is closely related to the internal structure, composition, and thermal state of the corresponding satellite interior. In this study we investigate the possibility of subsurface oceans in the medium-sized icy satellites and the largest trans-neptunian objects (TNO's). Controlling parameters for subsurface ocean formation are the radiogenic heating rate of the silicate component and the effectiveness of the heat transfer to the surface. Furthermore, the melting temperature of ice will be significantly reduced by small amounts of salts and/or incorporated volatiles such as methane and ammonia that are highly abundant in the outer Solar System. Based on the assumption that the satellites are differentiated and using an equilibrium condition between the heat production rate in the rocky cores and the heat loss through the ice shell, we find that subsurface oceans are possible on Rhea, Titania, Oberon, Triton, and Pluto and on the largest TNO's 2003 UB₃₁₃, Sedna, and 2004 DW. Subsurface oceans can even exist if only small amounts of ammonia are available. The liquid subsurface reservoirs are located deeply underneath an ice-I shell of more than 100 km thickness. However, they may be indirectly detectable by their interaction with the surrounding magnetic fields and charged particles and by the magnitude of a satellite's response to tides exerted by the primary. The latter is strongly dependent on the occurrence of a subsurface ocean which provides greater flexibility to a satellite's rigid outer ice shell.  相似文献   

Ridges and tidal stress on Io     

Gwendolyn D. Bart  Elizabeth P. Turtle  Laszlo P. Keszthelyi 《Icarus》2004,169(1):111-126

Sets of ridges of uncertain origin are seen in twenty-nine high-resolution Galileo images, which sample seven locales on Io. These ridges are on the order of a few kilometers in length with a spacing of about a kilometer. Within each locale, the ridges have a consistent orientation, but the orientations vary from place to place. We investigate whether these ridges could be a result of tidal flexing of Io by comparing their orientations with the peak tidal stress orientations at the same locations. We find that ridges grouped near the equator are aligned either north-south or east-west, as are the predicted principal stress orientations there. It is not clear why particular groups run north-south and others east-west. The one set of ridges observed far from the equator (52° S) has an oblique azimuth, as do the tidal stresses at those latitudes. Therefore, all observed ridges have similar orientations to the tidal stress in their region. This correlation is consistent with the hypothesis that tidal flexing of Io plays an important role in ridge formation.  相似文献   

Binary near-Earth asteroid formation: Rubble pile model of tidal disruptions     

Kevin J. Walsh  Derek C. Richardson 《Icarus》2006,180(1):201-216

We present numerical simulations of near-Earth asteroid (NEA) tidal disruption resulting in bound, mutually orbiting systems. Using a rubble pile model we have constrained the relative likelihoods for possible physical and dynamical properties of the binaries created. Overall 110,500 simulations were run, with each body consisting of ∼1000 particles. The encounter parameters of close approach distance and velocity were varied, as were the bodies' spin, elongation and spin axis direction. The binary production rate increases for closer encounters, at lower speeds, for more elongated bodies, and for bodies with greater spin. The semimajor axes for resultant binaries are peaked between 5 to 20 primary radii, and there is an overall trend for high eccentricity, with 97% of binaries having e > 0.1. The secondary-to-primary size ratios of the simulated binaries are peaked between 0.1 and 0.2, similar to trends among observed asteroid binaries. The spin rates of the primary bodies are narrowly distributed between 3.5- and 6-h periods, whereas the secondaries' periods are more evenly distributed and can exceed 15-h periods. The spin axes of the primary bodies are very closely aligned with the angular momenta of the binary orbits, whereas the secondary spin axes are nearly random. The shapes of the primaries show a large distribution of axis ratios, where those with low elongation (ratio of long and short axis) are both oblate and prolate, and nearly all with large elongation are prolate. This work presents results that suggest tidal disruption of gravitational aggregates can make binaries physically similar to those currently observed in the NEA population. As well, tidal disruption may create an equal number of binaries with qualities different from those observed, mostly binaries with large separation and with elongated primaries.  相似文献   

Tidal heating in Enceladus   总被引：1，自引：0，他引：1  

Jennifer Meyer  Jack Wisdom 《Icarus》2007,188(2):535-539

The heating in Enceladus in an equilibrium resonant configuration with other saturnian satellites can be estimated independently of the physical properties of Enceladus. We find that equilibrium tidal heating cannot account for the heat that is observed to be coming from Enceladus. Equilibrium heating in possible past resonances likewise cannot explain prior resurfacing events.  相似文献