A numerical sandbox: high-resolution distinct element models of halfgraben formation

Basin-scale tectonics and sedimentation are studied using particle flow code (PFC), a special implementation of the distinct-element method (DEM) using circular elements. Special focus is on the development and application of new techniques, which allow for strain weakening and localisation effects and, thus, the formation of discrete fault patterns in high-resolution DE models.Fundamental modelling assumptions and the procedures necessary to define the microproperties of a DE material from given rock mechanical data are first explained. Recent methodical enhancements, consisting of automatic fault detection (AFD) and intelligent crack management (ICM) algorithms are also discussed. Refined DE modelling techniques are then applied to three scenarios of extensional basin formation, i.e. the evolution of halfgrabens above detachments with simple listric and ramp–flat–ramp geometries, respectively. Numerical modelling results compare favourably with the analogue (‘sandbox’) models widely used in this kind of basin studies. Not only do they reproduce the general basin architecture (e.g. roll-over anticlines and crestal collapse grabens), but also detailed fault structure and the sequence of faulting. In addition, numerical models can describe temporal changes in mechanical material properties to model compaction and diagenesis of syntectonic sediments.     

Modelling the influence of spatially varying hydrodynamics on the cross-sectional stability of double inlet systems

The cross-sectional stability of double inlet systems is investigated using an exploratory model that combines Escoffier’s stability concept for the evolution of the inlet’s cross-sectional area with a two-dimensional, depth-averaged (2DH) hydrodynamic model for tidal flow. The model geometry consists of four rectangular compartments, each with a uniform depth, associated with the ocean, tidal inlets and basin. The water motion, forced by an incoming Kelvin wave at the ocean’s open boundary and satisfying the linear shallow water equations on the f -plane with linearised bottom friction, is in each compartment written as a superposition of eigenmodes, i.e. Kelvin and Poincaré waves. A collocation method is employed to satisfy boundary and matching conditions. The analysis of resulting equilibrium configurations is done using flow diagrams.

Model results show that internally generated spatial variations in the water motion are essential for the existence of stable equilibria with two inlets open. In the hydrodynamic model used in the paper, both radiation damping into the ocean and basin depth effects result in these necessary spatial variations. Coriolis effects trigger an asymmetry in the stable equilibrium cross-sectional areas of the inlets. Furthermore, square basin geometries generally correspond to significantly larger equilibrium values of the inlet cross-sections. These model outcomes result from a competition between a destabilising (caused by inlet bottom friction) and a stabilising mechanism (caused by spatially varying local pressure gradients over the inlets).

     

The effect of tidal asymmetry and temporal settling lag on sediment trapping in tidal estuaries

Over decades and centuries, the mean depth of estuaries changes due to sea-level rise, land subsidence, infilling, and dredging projects. These processes produce changes in relative roughness (friction) and mixing, resulting in fundamental changes in the characteristics of the horizontal (velocity) and vertical tides (sea surface elevation) and the dynamics of sediment trapping. To investigate such changes, a 2DV model is developed. The model equations consist of the width-averaged shallow water equations and a sediment balance equation. Together with the condition of morphodynamic equilibrium, these equations are solved analytically by making a regular expansion of the various physical variables in a small parameter. Using these analytic solutions, we are able to gain insight into the fundamental physical processes resulting in sediment trapping in an estuary by studying various forcings separately. As a case study, we consider the Ems estuary. Between 1980 and 2005, successive deepening of the Ems estuary has significantly altered the tidal and sediment dynamics. The tidal range and the surface sediment concentration has increased and the position of the turbidity zone has shifted into the freshwater zone. The model is used to determine the causes of these historical changes. It is found that the increase of the tidal amplitude toward the end of the embayment is the combined effect of the deepening of the estuary and a 37% and 50% reduction in the vertical eddy viscosity and stress parameter, respectively. The physical mechanism resulting in the trapping of sediment, the number of trapping regions, and their sensitivity to grain size are explained by careful analysis of the various contributions of the residual sediment transport. It is found that sediment is trapped in the estuary by a delicate balance between the M ₂ transport and the residual transport for fine sediment ( $\emph{w}_s=0.2$  mm s^???1) and the residual, M ₂ and M ₄ transports for coarser sediment ( $\emph{w}_s=2$  mm s^???1). The upstream movement of the estuarine turbidity maximum into the freshwater zone in 2005 is mainly the result of changes in tidal asymmetry. Moreover, the difference between the sediment distribution for different grain sizes in the same year can be attributed to changes in the temporal settling lag.     

Optimal nonlinear excitation of decadal variability of the North Atlantic thermohaline circulation

Nonlinear development of salinity perturbations in the Atlantic thermohaline circulation （THC） is investigated with a three-dimensional ocean circulation model, using the conditional nonlinear optimal perturbation method. The results show two types of optimal initial perturbations of sea surface salinity, one associated with freshwater and the other with salinity. Both types of perturbations excite decadal variability of the THC. Under the same amplitude of initial perturbation, the decadal variation induced by the freshwater perturbation is much stronger than that by the salinity perturbation, suggesting that the THC is more sensitive to freshwater than salinity perturbation. As the amplitude of initial perturbation increases, the decadal variations become stronger for both perturbations. For salinity perturbations, recovery time of the THC to return to steady state gradually saturates with increasing amplitude, whereas this recovery time increases remarkably for freshwater perturbations. A nonlinear （advective） feedback between density and velocity anomalies is proposed to explain these characteristics of decadal variability excitation. The results are consistent with previous ones from simple box models, and highlight the importance of nonlinear feedback in decadal THC variability.     

The effect of gateways on ocean circulation patterns in the Cenozoic

Both geological data and climate model studies indicate that substantially different patterns of the global ocean circulation have existed throughout the Cenozoic. In a climate model study of the late Oligocene [von der Heydt, A., Dijkstra, H.A. (2006). Effect of ocean gateways on the global ocean circulation in the late Oligocene and early Miocene. Paleoceanography, 21, PA1011] a “northern sinking” type of circulation was found, with (shallow) deep water formation in both the North Pacific Ocean and the North Atlantic Ocean. This is in contrast to the present-day “conveyor” circulation, where there is deep water formation in the North Atlantic but not in the North Pacific. In order to explain these differences, we use an ocean general circulation model for idealized two-basin flows and study the effect of asymmetries in the continental geometry on the circulation patterns. Two types of asymmetry are considered: (i) the relative northward extent of the Pacific and the Atlantic basin, and (ii) the existence of a circum-global gateway at low latitudes. The more northward extent of the Pacific basin in the Oligocene makes the Conveyor solution less likely and facilitates deep water formation in the North Pacific compared to the North Atlantic. The low-latitude gateway on the other hand, allows salinity and heat exchange between the two main ocean basins and therefore leads to deep water formation in both the North Atlantic and the North Pacific.     

Response of large-scale coastal basins to wind forcing: influence of topography

Because wind is one of the main forcings in storm surge, we present an idealised process-based model to study the influence of topographic variations on the frequency response of large-scale coastal basins subject to time-periodic wind forcing. Coastal basins are represented by a semi-enclosed rectangular inner region forced by wind. It is connected to an outer region (represented as an infinitely long channel) without wind forcing, which allows waves to freely propagate outward. The model solves the three-dimensional linearised shallow water equations on the f plane, forced by a spatially uniform wind field that has an arbitrary angle with respect to the along-basin direction. Turbulence is represented using a spatially uniform vertical eddy viscosity, combined with a partial slip condition at the bed. The surface elevation amplitudes, and hence the vertical profiles of the velocity, are obtained using the finite element method (FEM), extended to account for the connection to the outer region. The results are then evaluated in terms of the elevation amplitude averaged over the basin’s landward end, as a function of the wind forcing frequency. In general, the results point out that adding topographic elements in the inner region (such as a topographic step, a linearly sloping bed or a parabolic cross-basin profile), causes the resonance peaks to shift in the frequency domain, through their effect on local wave speed. The Coriolis effect causes the resonance peaks associated with cross-basin modes (which without rotation only appear in the response to cross-basin wind) to emerge also in the response to along-basin wind and vice versa.     

Energy balance closure for the LITFASS-2003 experiment

In the first part, this paper synthesises the main results from a series of previous studies on the closure of the local energy balance at low-vegetation sites during the LITFASS-2003 experiment. A residual of up to 25% of the available energy has been found which cannot be fully explained either by the measurement uncertainty of the single components of the surface energy balance or by the length of the flux-averaging period. In the second part, secondary circulations due to heterogeneities in the surface characteristics (roughness, thermal and moisture properties) are discussed as a possible cause for the observed energy balance non-closure. This hypothesis seems to be supported from the fluxes derived from area-averaging measurement techniques (scintillometers, aircraft).