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1.
Summary. A model of the tides in a hemispherical ocean is used to investigate the effect of changes in the Earth's rotation rate on the power dissipated by the ocean tides. The results obtained are then used in an idealized astronomical model to investigate how they affect the history of the Earth—Moon system.
Using the tidal model it is found that at rotation rates higher than that of the present Earth, the power dissipated by the semi-diurnal tides in the ocean drops off rapidly as a result of the increased tidal frequency. Thus if the Earth's rotation rate is doubled from its present value, then the rate of energy dissipation in the ocean is reduced to approximately one-third of its present value and the tidal torque is reduced by a factor of about 6.
The present value for secular acceleration of the Moon, calculated from the results of the tidal model is -30.5 arcsec century-2. Using this value in the astronomical model, which has the Moon and Sun in circular orbits above the equator, and assuming that the tidal torque is independent of the tidal frequency, the Gerstenkorn event is predicted to have occurred 1.3 × 109 yr ago.
When the astronomical model is run with a torque determined at all times from the tidal model, the reduction in the energy dissipated early in the history of the system, leads to a Gerstenkorn date of 5.3 × 109 yr ago. However, dissipation within the solid earth is found to be important early in the history of the system and when this effect is included it gives a date for the Gerstenkorn event of 3.9 × 109 yr ago.  相似文献   

2.
Summary. The luni-solar forced nutations and body tide are believed to be resonant at frequencies near (1 + 1/460) cycle sidereal day−1 as seen from the rotating Earth. This resonance is due to the Earth's rotating, elliptical fluid core. We show here that tides in the open ocean and the Earth's response to those tides must also be resonant at (1 + 1/460) cycle day−1. We examine these resonant oceanic effects on the Earth's nutational motion and on the body tide. Effects on the forced nutations might be as large as 0.002 arcsec at 18.6 yr. The effects on the observed resonance in the body tide are more important. For tidal gravity, for example, the difference between K 1 and 0 1 which is usually used to determine the resonance, can be perturbed by 30 per cent or more due to the oceanic resonance effects.  相似文献   

3.
b
The results are presented from tidal gravity measurements at five sites in Europe using LaCoste and Romberg ET gravimeters. Improvements that we have made to the accuracies of these gravimeters are discussed. It is shown that the 'standard' calibration of the International Center for Earth Tides, used for worldwide tidal gravity profiles, is 1.2 per cent too high. The M2 and O1 observations are compared with model calculations of the Earth's body tide and ocean tide loading and it is shown that there is a very significant improvement in the agreement between observations and models compared to that obtained with previous tidal gravity measurements. For O1, where the ocean tide loading and attraction in central Europe is only 0.4 per cent of the body tide, our measurements verify that the Dehant-Wahr anelastic body tide model gravimetric factor is accurate to 0.2 per cent. It is also shown that the effects of lateral heterogeneities in Earth structure on tidal gravity are too small to explain the large anomalies in previously published tidal gravity amplitudes. The observations clearly show the importance of conserving tidal mass in the Schwiderski ocean tide model. For sites in central Europe, the M2 and O1 observations and the models are in agreement at the 0.1 μgal (10−9 m s−2) level and tidal corrections to this accuracy can now be made to absolute gravity measurements.  相似文献   

4.
Summary. Tidal gravity measurements have been made at six sites in Britain with two nulled LaCoste and Romberg Earth tide gravitymeters. The M 2 observations from these and two further sites are compared with calculations of the tidal loading from the seas around the British Isles and the major oceans. Models of the M 2 marine tides are convolved with Green's functions for appropriate radially stratified Earth models. The differences between the M 2 observations and the theoretical calculations are less than 0.6 μ gals and it is shown that these differences contain further information concerning the errors in the marine tide models. The M 2 marine tides on the north-west European continental shelf are reasonably well known and this allows a useful test of the feasibility of using tidal gravity measurements for the inverse ocean tide problem in areas where the ocean tides are less well known. The differential gravity loading signal between pairs of gravity stations is shown to be important for considerations of the uniqueness and accuracy of the inverse problem. M 2 tidal gravity loading maps for the British Isles and Europe have been produced which are of use in making corrections to various geodetic measurements.  相似文献   

5.
The tidal dynamics of the Irish and Celtic Seas   总被引：1，自引：0，他引：1  
Summary. Current meter data collected over periods of more than 14 day from the Irish and Celtic Seas are harmonically analysed and presented in maps of tidal stream information. Making use of the analysed current data, and by constructing time series of frictional and inertial stresses which are also harmonically analysed, harmonic constituents of the surface tidal slopes at current meter stations are obtained. Using these with data collected from offshore tide gauges, and in conjunction with coastal tide data, cotidal maps are drawn with some confidence for M 2, S 2, O 1 and K 1, the M 2 chart resolving the discrepancy which exists between the different charts of the Celtic Sea already produced. Cotidal maps for M 3 and M 4 are also presented.
The mean over a tidal cycle of the energy flux for M 2, S 2 and O 1 is also presented in the form of the total energy flux in these constituents which crosses different sectional lines. A flux of 44 × 106 kW is observed to enter the Celtic Sea from the Atlantic and this is compared with previous estimates. An energy budget is also performed for M 2, including all the effects of astronomical forcing and Earth tides to enable comparison to be made between the true energy inflow and the estimated frictional dissipation. Finally, comparison is made between the mean of the instantaneous energy flux and the sum of the energy fluxes associated with the major harmonics.  相似文献   

6.
Summary. Long-period tidal records from eight ports on the west coast of Great Britain are analysed, using both the harmonic method and the response function. Time series up to 9.5 yr were used so that fine structure of certain regions of high energy in the tidal residual spectrum may be examined. This also assisted in accurate separation of tides from surges. According to the currently accepted formulation of M1, its composition is not compatible with its actual composition in the real tide and, as such, has no useful purpose to serve in computation of predictions. Constituents Sa, Ssa, MA, and MB, are adversly affected by weather and long records are essential for their accurate separation. It has been observed that annual perturbations of S2, similar to those confirmed in recent years for M2, also exist but these are not readily recognisable because their speeds are the same as those of constituents T2 and R2. These perturbations, being highly sensitive to meteorological forces, are mainly responsible for cusps or humps in the vicinity of major tidal constituents in tidal residual spectra. The relationship of radiational and gravitational tides is found to be in very good agreement with theoretical results. In summer months non-predictable variance reduces to about half of the annual variance, reflecting the regional weather conditions of summer and winter.  相似文献   

7.
Summary. A reduced equation of motion is used to compute the residual velocity and the residual transport through the West Solent from the water levels recorded over an eight-month period at tide gauges at either end of the channel. A coefficient of bottom friction of 5·0 × 10−3 is assumed. There was a spring-neap variation and a significant correlation of fluctuations in the residual velocity with meteorological conditions. Westward residual velocities occurred at spring tides with low barometric pressure and south-westerly winds. Eastward residual velocities occurred at neap tides with high pressure and north-easterly winds. Because of the progressive nature of the tidal wave the long term residual transport appeared to be towards the west and the flushing time for the Solent system was long for considerable periods. The maximum velocities experienced during a tidal cycle half way along the channel are towards the west with a probability of values exceeding 160 cm s−1 for 10 min in 5·4 days.  相似文献   

8.
Summary. An existing experimentally verified model for energy dissipation in a processing spherical cavity filled with liquid assumed to be in a semirigidized state except for a viscous Ekman boundary layer is applied to the Earth's liquid core to assess energy dissipation magnitudes. Application of the model to the best available Earth data occurs at the derived energy dissipation maximum for the model. Other existing research showing that the Earth's atmosphere appears to adjust to a state of maximum dissipation led to generic models for systems of maximum dissipation. The maximum dissipation mantle—core model with core motion driven by Earth precession alone, coupled to the mantle only by viscous shear stresses, and with a spherical mantle—core boundary leads to energy dissipation rates on the order of 104 times those necessary for an Earth dynamo. The maximum dissipation model also leads to excessive magnetic field drift rates and to excessive retardation of the Earth's rotation rate. Effects of the mantle—core ellipticity and of magnetic field coupling are briefly discussed and are used to help develop a less than maximum dissipation model also driven by precession alone but using the additional coupling to yield a model more consistent with observed phenomena.  相似文献   

9.
Summary. The results of previous work by the authors is used to remove most of the effects of ocean and atmospheric loading from an 18-month Earth gravity-tide record. The remaining signal is examined for additional influence of ocean and atmosphere and for evidence of the frequency-dependence of the response of the solid earth. Variations in time of the measured tides are shown to result from the atmospheric tide at S 2 and appear to result from variations in ocean tides at other frequencies. The frequency-dependence of the solid earth response near 1 cycle per siderial day is found to be consistent with the nearly diurnal free wobble. However, the influence of the ocean on the small but crucial Ψ1 tide is uncertain. Anomalous responses are observed at several other frequencies but except for the case of ρ1 it is argued that anomalous ocean tides are plausible and could therefore explain the observations.  相似文献   

10.
Sagitta elegans var. arctica , the dominant and locally abundant chaetognath in the Barents sea, was collected from the upper 50 m in Arctic water masses during an ice edge bloom in early summer 1983. In situ sampling was made along a transect at discrete depths with a 375 μm mesh net mounted on a plankton pump. Prey composition and feeding rate were estimated from gut content analyses on preserved specimens combined with data on digestion times from previous studies. No diel variations were found in feeding activity. The diet reflected the composition of available prey in the zooplankton and consisted mainly of nauplii, small copepods (early stages of Calanus, Pseudocalanus, Oithona ) and appendicularians. Prey usually occurred as a single item in the gut.
Mean prey body width related to chaetognath head width yielded a power curve, with a large amount of scatter, showing that chaetognaths in the Barents Sea can use a wide spectrum of prey sizes. Similarly, maximum prey body width was related to chaetognath head width as a power curve, reflecting the existence of an upper prey size limitation due to the chaetognath mouth size. The highest abundance of S. elegans (5 specimens m−3), and the most intense feeding activity, were found within or beneath the maximum zooplankton biomass. Further, distribution and feeding were affected by light intensity, salinity, and the population structure of 5. elegans var. arctica.
Estimated feeding rates ranged between 0.30 and 1.05 prey items per chaetognath day−1. This corresponds to an ingestion of 8-54 μg AFDW day−1, and a consumption of 0.08–0.22% of the zooplankton standing stock day−1. From these rates, the calculated yearly ingestion by S. elegans var. arctica was 3% of the annually secondary production.  相似文献   

11.
An excitation mechanism for the free 'core nutation'   总被引：2，自引：0，他引：2  
Summary. The Earth is believed to possess a free nutational mode due to its rotating, elliptical, fluid core, with an eigenfrequency of approximately (1 + 1/460) cycle sidereal day−1 as seen from the sidereally rotating Earth. This free 'core nutation' has not yet been undisputably observed. Furthermore, there has been considerable doubt that any known mechanism could excite this mode to an observable level. We show here that diurnal atmospheric and oceanic loading of the Earth's surface provide an efficient excitation mechanism which depends critically on the physical damping of the mode. Possible effects of the mode on geodetic measurements are discussed. We also consider the effects of 'wobble' and 'nutation' on astrometric observations.  相似文献   

12.
Summary. The viscoelastic response of the Earth to the mass displacements caused by late Pleistocene deglaciation and concomitant sea level changes is shown to be capable of producing the secular motion of the Earth's rotation pole as deduced from astronomical observations. The calculations for a viscoelastic Earth yield a secular motion in the direction of 72° W meridian which is in excellent agreement with observed values. The average Newtonian viscosity and the relaxation time obtained from polar motion data are about (1.1 ± 0.6)1023 poise (P) and 104 (1 ± 0.5) yr. The non-tidal secular acceleration of the Earth can also be attributed to the viscoelastic response to deglaciation and results in an independent viscosity estimate of 1.6 × 1023 P with upper and lower limits of 1.1 × 1023 and 2.8 × 1023 P. These values are in agreement with those based on the polar drift analysis and indicate an average mantle viscosity of 1–2 × 1023 P.  相似文献   

13.
Dissipative core–mantle coupling is evident in observations of the Earth's nutations, although the source of this coupling is uncertain. Magnetic coupling occurs when conducting materials on either side of the boundary move through a magnetic field. In order to explain the nutation observations with magnetic coupling, we must assume a high (metallic) conductivity on the mantle side of the boundary and a rms radial field of 0.69 mT. Much of this field occurs at short wavelengths, which cannot be observed directly at the surface. High levels of short-wavelength field impose demands on the power needed to regenerate the field through dynamo action in the core. We use a numerical dynamo model from the study of Christensen & Aubert (2006) to assess whether the required short-wavelength field is physically plausible. By scaling the numerical solution to a model with sufficient short-wavelength field, we obtain a total ohmic dissipation of 0.7–1 TW, which is within current uncertainties. Viscous coupling is another possible explanation for the nutation observations, although the effective viscosity required for this is 0.03 m2 s−1 or higher. Such high viscosities are commonly interpreted as an eddy viscosity. However, physical considerations and laboratory experiments limit the eddy viscosity to 10−4 m2 s−1, which suggests that viscous coupling can only explain a few percent of the dissipative torque between the core and the mantle.  相似文献   

14.
Summary. The power spectrum of the Earth's spin has important components with periods ranging from a few days to at least a few thousand years, and probably to the age of the Earth. The secular acceleration, as the term is used here, refers to the components with periods longer than three centuries. In the year 600, the secular acceleration was —19.9 ± 0.8 parts in 109 per century, while the value at the present time is less than half this size. The spin acceleration has important contributions from tidal friction and from an effect that is proportional to the square of the magnetic dipole moment. When these contributions are subtracted from the observed acceleration, we are left with a contribution that amounts to +41 parts in 109 per century. This amount probably results from an unknown combination of changes in the size of the core, in the amount of glaciation, and in the size of the gravitational constant.  相似文献   

15.
We have used tidal gravity measurements from six stations in central Europe to investigate the resonance in the diurnal tidal band, caused by inertial coupling between the mantle and outer core of the Earth. By the use of stacking it was possible to determine the eigenfrequency and quality factor of this eigenmode, commonly called the 'nearly diurnal free-wobble'. We assessed the effect of systematic errors from the ocean correction to the tidal measurements employing a Monte-Carlo method. The observed eigenfrequency is 1 + 1/(434 ± 7) cycles per sidereal day, and is significantly higher than predicted by theories. The observed quality factor is (2.8 ± 0.5) × 103.  相似文献   

16.
Summary. Recent results from the analysis of postglacial rebound data suggest that the viscosity of the Earth's mantle increases through the transition region. Models which fit both relative sea-level and free air gravity data have viscosities which increase from a value near 1022 poise in the upper mantle beneath the lithosphere to a value of about 1023 poise in the lower mantle. In this paper we analyse the effect of deglaciation upon the Earth's rotation and thereby show that the observed secular trend (polar wander) evident in the ILS—IPMS pole path, and measurements of the non-tidal acceleration of the length of day, are both consistent with the viscosity profile deduced from postglacial rebound. The two analyses are therefore mutually reinforcing.  相似文献   

17.
Summary. The effect of attenuation on the coupling of nearly resonant multiplets in the Earth's free oscillation spectrum is investigated and numerical results are presented for several of the most strongly coupled low frequency multiplet pairs. The coupling influences considered are those of the Coriolis forces due to rotation and of the Earth's hydrostatic ellipticity of figure. It is found that the effects of attenuation (in particular the difference in Q −1 for the two multiplets) can significantly change the splitting diagrams and the degree to which coupling takes place. The Q values for the coupled singlets are, in general, all different and lie between the two Q values of the uncoupled multiplet pair. In addition it is shown that the diagonal sum rule may be readily extended to sets of coupled multiplets.  相似文献   

18.
Summary. The long period luni-solar tidal potential is known to cause periodic changes in the Earth's rotation rate. We find that the effect of a dissipationless fluid outer core is to reduce the amplitudes of these tidal perturbations by ∼ 11 per cent. When the fluid core effect is added to Agnew & Farrell's estimate of the effect of an equilibrium ocean, the result is in accord with observation.
The effects of dissipative processes within the fluid core are also examined. We find out-of-phase perturbations which could be as large as ∼ 10ms at 18.6 yr. We conclude, however, that the poorly understood decade fluctuations in the Earth's rotation rate will prohibit observation of this effect.  相似文献   

19.
Summary. The tidal deformation of a homogeneous viscoelastic sphere due to the gravitational attraction of an external body is calculated. The sphere is modelled as an incompressible Kelvin-Voigt solid. An equation for the displacement field is obtained assuming that strains are small and inertia is negligible. This equation has a series solution in terms of Legendre polynomials. The resulting expression for the displacement field reduces to that for an elastic solid and a viscous fluid in the appropriate limits of the material constants. The first term in the viscoelastic solution is used to calculate the moments induced by tidal deformation assuming a circular orbit. In the absence of obliquity and precession, these moments reduced to a torque about the spin axis. This torque is compared to that predicted by a phase lag analysis. These two approaches are formally equivalent if the tidal dissipation function Q −1 depends in a specific way on the difference of the spin and orbital angular velocities.  相似文献   

20.
Summary. A method is outlined to determine the dynamic behaviour of a phase boundary in the Earth when non-uniform time-varying pressure and temperature conditions are assumed at the Earth's surface. An integral equation describing the phase boundary motion is derived and it is solved under a linearizing assumption. The solution is obtained in the form of a double integral transform. Short and long time-expansions of the solution can be obtained from series expansion and integration of the Laplace transform along a branch cut. The method is illustrated by considering a stepwise change in surface pressure conditions.
For short times, the solution exhibits the same type of time dependence (i.e. the first-order term is in t 1/2) as the one obtained in the one-dimensional case (i.e. uniform pressure perturbation at the Earth's surface).
For long times, it is shown that the time dependence of the phase boundary motion is almost identical to the one derived for the one- dimensional case if the wavenumber k L of the surface excitation is such that κ k 2Lτ≤ 1 (where τ is the relaxation time associated with the one-dimensional phase boundary motion and κ is the thermal diffusivity). If κ k 2Lτ > 1, then the relaxation time for the phase boundary motion in two dimensions is of the order of κ−1 k −2L.
When considering parameters that would be appropriate for a basalt to eclogite phase transition at Moho depth, the latter situation is met only when the load wavelength is smaller than 35 km.  相似文献   

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