Jürgen Sündermann

Tidal friction and the earth's rotation

Historical Background and Introduction.- References.- Pre-Telescopic Astronomical Observations.- 1. Introduction.- 2. Historical Development.- 3. Inter-Relation of Parameters.- 4. Recent Investigations.- 5. Remarks on the Selection of Suitable Observations.- 6. Observations of Total and Near-Total Solar Eclipses.- 7. Method of Analysis.- 8. Geophysical Discussion.- 9. Conclusions.- References.- Tidal Deceleration of the Earths Rotation Deduced from Astronomical bservations in the Period A.D. 1600 to the Present.- 1. Introduction and Principle of Method.- 2. Moons Orbital Angular Deceleration.- 2.1 Deceleration with Respect to Dynamical Time.- 2.2 Deceleration with Respect to Atomic Time.- 3. Tidal Deceleration of Earths Rotation.- 4. Conclusions.- References.- Determination of the Rotation of the Earth (at Present).- 1. Introduction.- 1.1 Preview.- 2. General Features of the Rotation of the Earth.- 2.1 Variation in the Earths Rate of Rotation.- 2.2 Polar Motion.- 3. Equatorial System.- 4. Astronomic Longitude and Latitude.- 5. Time Scales.- 5.1 Astronomic Time.- 5.2 Atomic Time.- 6. Methods and Instruments of Observation.- 6.1 Optical Instruments.- 6.2 Doppler Satellite Measurements.- 7. Data Analysis Centers.- 8. Results on the Rotation of the Earth.- References.- Effect of Tidal Friction on the Lunar Orbit and the Rotation of Earth and Its Determination by Laser Ranging.- 1. Introduction.- 2. The Physical Problem.- 3. The Laser Technique and Its Application.- 4. Determination of the Lunar Acceleration.- 5. Comparisons and Difficulties of Interpretation.- References.- Appendix A: Comments on the Perturbed Mean Motion 52 ppendix B: Reality of the Venus Effect 53 ides of the Solid Earth from Gravimetric Measurements.- 1. Introduction.- 2. Basic Concepts.- 3. The Tidal Potential.- 4. Determination of LOVE numbers from Gravimetric Data.- 5. Instrumentation.- 6. Actual Problems.- 7. Recent Results.- 8. Future Activities.- References.- Tidal Friction in the Solid Earth: Loading Tides Versus Body Tides.- 1. Introduction.- 2. Dissipated Tidal Energy in the Solid Earth.- 2.1 Theory of Dissipation in a Heterogeneous Incompressible Earth.- 2.2 Dissipation of Body Tide Energy.- 2.3 Dissipation of Loading Tide Energy.- 3. Global Tidal Q and Tidal Phase Shifts.- 3.1 Loading Tide Q Versus Body Tide Q.- 3.2 Numerical Results for the Body Tide.- 3.3 Theoretical Relationship between Tidal Bulge Angles, Body Tide Phase Shifts, and the Global Body Tide Q.- 3.4 Some More Numerical Examples.- 3.5 Numerical Results for the Loading Tides.- 4. Conclusions.- References.- Tidal Dissipation in the Oceans.- References.- The Influence of Solid Earth Deformations on Semidiurnal and iurnal Oceanic Tides.- 1. Introduction.- 2. Considering Tidal Loading and Ocean Self-Attraction in.- Ocean-Tide Models.- 2.1 Tidal Integrodifferential Equations and the Energy-Equation Belonging to Them.- 2.2 Properties of Different Ocean-Tide Models.- 3. Generalization of the 4 -Primitive-Equations Model.- 3.1 The Finite-Difference Scheme.- 3.2 Oceanic Tides on a Nonrotating Earth.- 4. The Computed Global M2-Tide.- 5. The Computed Global K1-Tide.- 6. Conclusions.- Glossary of Symbols.- References.- The Numerical Computation of Tidal Friction for Present and ncient Oceans.- 1. Introduction.- 2. Computation of Tidal Friction by Hydrodynamic-Numerical.- Models.- 2.1 Basic Equations.- 2.2 Analytic Considerations.- 2.3 Hydrodynamic-Numerical Models.- 3. A Numerical Model for the Present Ocean.- 3.1 Requirements.- 3.2 Balance of Angular Momentum.- 4. Numerical Model for Ancient Oceans.- 4.1 Necessity of Such a Model.- 4.2 Bathymetry.- 4.3 Application to the Permian Ocean.- 4.4 Verification.- 5. Further Activities.- References.- The Earths Palaeorotation.- 1. The Coral Data.- 2. The Bivalve Data.- 3. Stromatolite Data.- 4. Combined Data 1.- References.- Periodic Growth Features in Fossil Organisms and the Lenght of the ay and Month.- 1. Introduction.- 2. Biological Considerations.- 2.1 Growth Increments in Corals.- 2.2 Growth Increments in Bivalves.- 2.3 Growth Increments in Stromatolites.- 2.4 Biological Clocks.- 3. The Data.- 3.1 Recording the Data.- 3.2 The Published Data.- 4. Implications of the Growth Increment Data.- 5. Conclusions.- References.- Geological and Geophysical Evidence Relating to Continental rowth and Dynamics and the Hydrosphere in Precambrian Times: Review and Analysis.- 1. Introduction.- 2. The Hydrosphere.- 3. The Continental Crust.- 4. Precambrian Dynamics of the Continental Crust.- 5. Palaeomagnetic Analysis of Precambrian Crustal Movements.- 5.1 Gondwanaland-Late Precambrian and Lower Palaeozoic.- 5.2 Laurentian Shield-Upper Proterozoic.- 5.3 African Shield-Upper Proterozoic.- 5.4 Laurentian Shield-Middle-Lower Proterozoic.- 5.5 Africa-Middle-Lower Proterozoic.- 5.6 Australia-2600-1100 my.- 5.7 Baltic-Ukrainian Shield-2000-1200 my.- 6. Palaeomagnetic Correlations Between the Proterozoic Shields.- 7. Proterozoic Supercontinent.- 8. Age of the Earth-Moon System.- 9. Stromatolite Evidence for Precambrian Tidal Parameters.- 10. Sedimentologic Evidence for Precambrian Tidal Parameters.- 11. The Tidal Couple and Changes in the Earths Rotation in Precambrian Times.- References.- Concluding Remarks.

Consideration of ocean tides in an OGCM and impacts on subseasonal to decadal polar motion excitation

Ocean induced changes of Earths rotation are attributed either to tides or to variations of the general circulation. Analogously, numerical world ocean models can still be divided into Ocean General Circulation and tidal models, although a neglect of nonlinear interactions in favor of a linear superimposition of both components of motion is questionable. By means of a simultaneous simulation of the oceans circulation and tides we estimate the importance of two oceanic effects with respect to excitation of polar motion: nonlinearities between circulation and long-period tides and the circulation induced potential due to loading and self-attraction of a baroclinic ocean. Comparing the linear superimposition of separate model simulations with the simultaneous calculation of circulation and tides it turns out that these second-order effects contribute about 8% to ocean induced changes in Earths orientation.

Microstructure of turbulence in the northern North Sea: a comparative study of observations and model simulations

Dissipation rate measurements in the northern North Sea from two independent observations are compared with various numerical models. The turbulence was characterised by tidal forcing in the bottom boundary layer and atmospheric forcing in the surface boundary layer. The observations were carried out by using free-falling profilers equipped with shear probes and fast CTD sensors. The models are based on Reynolds averaging and range from simple one-equation models to two-equation models with algebraic second-moment closures. Several error measures are applied for comparison of observations and model results. It is shown that the differences between the two observations are significantly larger than the equivalent measures between the model results. This is caused by the stochastic character of turbulent microstructure in connection with under-sampling, but also by the distance between the two observational sites, the movements of the vessels, instrument errors and so forth. The models on the other hand, although closed on different levels, are all based on the same assumptions and driven by the same external forcing, thus showing only relatively small differences between each other.

A modelling study of SPM transport in the Bohai Sea

Abstract A 3-D SPM transport model is applied to the Bohai Sea in China. The model includes: (1) the movement of the SPM in the water body, (2) the movement of the sediment fine fraction in the sea bottom and (3) the deposition and erosion processes at the seabed. The model is of Lagrangian type, i.e., the tracer method is used. The influence of the SPM on the hydrodynamic condition is studied here because the Yellow River releases huge amount of SPM into the Bohai Sea. Thus, the usual model configuration is modified by taking into account the density change due to the SPM. The results show that the effect of the SPM can not be neglected near the river mouth area where the SPM concentration gradient is very high. With the SPM considered the SPM is disposed over a wider area. Based on the modified model a one-year simulation is performed for the year 1982. The results are compared with the CZCS satellite data at the same time. The results of the monthly averaged SPM concentrations in the Bohai Sea are compared between the seasons. They agree reasonably with observations. The exchange of SPM and water through the Bohai Strait is also studied. The results show that most of SPM from the Yellow River stays in the Bohai Sea.

Tides and tidal torques of the world ocean since the last glacial maximum

Peltiers [1994] paleobathymetries are used to investigate tides and corresponding balances of torques of the world ocean since the last glacial maximum 21,000 years before present. Simulations with a numerical tidal model point out that variable ice loads at the Earths surface and rearrangements in the interior led to considerable modifications of the resonance behavior of the oceans. Associated evident changes of the tidal range were not confined to the vicinity of formerly ice-covered areas. In contrast to the tidal oscillation system that was subject to almost uniform changes since the beginning of ice retreat, the dissipation rate of the M2 tide increased distinctly during the principal melting time from 15 to 8 kyr B. P. and reached a local extreme eight thousand years ago though surface and volume of the world ocean were already very similar to present conditions. Postglacial deformations during the following two thousand years caused the decrease of tidal dissipation from the maximum value to the present-day level, indicating the sensibility of tidal torques and dissipation rates to comparatively small variations of oceans geometry. Since the vicinity of the tidal oscillation system to a resonance situation is more decisive with respect to total dissipation than the extension of shelves where most of the tidal dissipation is expected to take place, states of extreme dissipation rates do not necessarily coincide with extreme bathymetric conditions.

Modelling ocean climate variability

Mathematical Background and Methods of Ocean Modelling.- Simple Linear Models for Diagnostic Calculation of Ocean Climate Characteristics.- Nonlinear Models for Diagnostic, Prognostic and Adjustment Calculations of Ocean Climate Characteristics.- Synthesis of Models and Observed Data.- Modelling of Climate Variability in Selected Ocean Basins.- Modelling Climate Variability of Selected Shelf Seas.

Processes of Vertical Exchange in Shelf Seas (PROVESS)

Papers in this and a companion issue report on an interdisciplinary study of the vertical fluxes of properties throughout the water column from the sea surface to the seabed. The project was centred on measuring and modelling for two contrasting sites in the North Sea of turbulence properties and their effects on particles, zooplankton and nutrient cycling, particularly the relative importance of cycling in the water column, the seabed fluff layer and the sediments. Turbulence activity was weaker at the northern site, which stratified in summer, and where measurements were obtained during the start of the autumnal breakdown of stratification. The southern site, where measurements were taken during and after the spring bloom, was much more dynamic both in terms of turbulence and of particles. The site was close to the Dutch coast and was well mixed throughout the year, except for the intermittent influence of the Rhine plume. The study contributes towards the long-term goal of developing robust water column plankton models applicable in the full range of turbulence environments encountered in continental shelf seas.

Modelling and numerical simulation of turbulence, waves and suspended sediments for pre-operational use in coastal seas

Abstract The role of small-scale processes in models of coastal seas is reviewed, and the respective uses of vertically integrated and vertically resolving models are described. Although applied with heavily tuned empirical parameters to the Holderness coast a vertically integrated model shows the importance of surface waves for predicting suspended particulate matter (SPM) and their distributions. In formulating a generic vertically resolving module, as kernel, the k–e turbulence closure has been selected. On a uniform vertical grid this model gave reasonably accurate results for a neutrally stratified channel flow forced by an M2 tidal wave (Elbe estuary) as well as on a nonuniform grid highly refined in the high-dissipation near-bed region for short-period (8 s) surface waves in a laboratory flume. The model was completed with modules accounting for the effect of waves on the turbulent kinetic energy (TKE) influx at the surface and on the apparent roughness at the bottom. It was finally coupled with different versions of vertically high resolving SPM models. In test applications to the English Channel and to the Sylt–Romo Bight (Germany/Denmark) the generic model versions performed with sufficient accuracy. However, in both cases: (i) fine tuning of erosion and deposition terms was necessary thus underlining the need for further experimental research towards an improved data base on erodible sediments and SPM; (ii) the parameters of the submodel for the TKE injection by surface waves could not be determined consistently and indicate the existence of a further still hidden parameter; (iii) the technical basis for in situ observations of small-scale processes in the coastal zone needs further improvements and consolidation.

Suspended particulate matter in the Southern North Sea: Application of a numerical model to extend NERC North Sea project data interpretation

A numerical SPM (suspended particulate matter) transport model for the North Sea is used for supporting the interpretation of SPM data collected during the British NERC North Sea Project (NSP) in the southern North Sea. This interpretation applies to (i) the assessment of the spatial and temporal representativity of the measured data, (ii) the presentation of the SPM’s origin in the southern North Sea and (iii) the estimation of SPM fluxes.

Long-term propagation of tailings from deep-sea mining under variable conditions by means of numerical simulations

Abstract Numerical experiments that simulate the dispersion and resettling of particulate matter in a potential deep-sea mining area are used to estimate the possible long-term effects from deep-sea mining on the benthic ecosystem. The mining of manganese nodules is estimated to stir up 50,000 tonne of sediment per day, an estimated 4000 tonne of which is transported to the surface together with the nodules. The potential mining site is located in the eastern equatorial Pacific, an area where hydrographic conditions close to the surface are highly variable. In order to determine the variations of the transport of tailings, the simulations were run for El Nino and La Nina conditions. Resettlement of stirred-up sediments is determined by the grain-size distribution (and hence settling velocity) of the particulate matter and scavenging processes. Two different grain-size distributions, both derived from measurements, are applied, which are characterised by “finer” and “coarser” grains. The flux of biogenic matter obtained from a model is used to simulate the additional downflux of particles caused by scavenging. Results differ strongly depending on the properties of the released sediments. Resettling of 90–95% of the total mass of the relatively fine grain-size distribution takes 3–14 years depending on the water depth of the release, whereas it is deposited shortly after release for the coarser distribution.