John B. Swenson

Fluvio-deltaic sedimentation: A generalized Stefan problem

We present a model of sedimentation in a subsiding fluvio-deltaic basin with steady sediment supply and unsteady base level. We demonstrate that mass transfer in a fluvio-deltaic basin is analogous to heat transfer in a generalized Stefan problem, where the basin’s shoreline represents the phase front. We obtain a numerical solution to the governing equations for sediment transport and deposition in this system via an extension of a deforminggrid technique from the phase-change literature. Through modication of the heat-balance integral method, we also develop a semi-analytical solution, which agrees well with the numerical solution. We construct a space of dimensionless groups for the basin and perform a systematic exploration of this space to illustrate the influence of each group on the shoreline trajectory. Our model results suggest that all subsiding fluvio-deltaic basins exhibit a standard autoretreat shoreline trajectory in which a brief period of shoreline advance is followed by an extended period of shoreline retreat. Base-level cycling produces a shoreline response that varies relative to the autoretreat signal. Contrary to previous studies, we fail to observe either a strong phase shift between shoreline and base level or a pronounced attenuation of the amplitude of shoreline response as the frequency of base-level cycling decreases. However, the amplitude of shoreline response to base-level cycling is a function of the basin’s age.

Pleistocene hydrogeology of the Atlantic continental shelf, New England

Salinity data from the Atlantic continental shelf off New England indicate that the freshwater/saltwater interface is far out of equilibrium with modern sea-level conditions. More than 150 km offshore of Long Island, New York. aquifer salinity levels are less than 5 parts per thousand (5 ppt). Salinity levels within confining units beneath Nantucket Island, Massachusetts, are 30%. 70% of seawater levels and exhibit a par abolic profile consistent with ongoing vertical diffusion. Here, we evaluate two fluid-flow-inducing mechanisms that could explain the apparent flushing of these coastal-plain aquifers: (1) meteoric recharge during Pleistocene sea-level low stands, and (2) subglacial recharge from the Laurentide Ice Sheet. Analytical models of vertical solute diffusion for the Nantucket confining units suggest that flushing of aquifers beneath Nantucket began in the late Pleistocene between ca. 195 and 21 ka; the models assume a diffusion coefficient of 3.0 × 10 - 1 1 m 2 /s. Cross-sectional numerical models of variable-density groundwater flow, heat, and solute transport could not reproduce the relatively low-salinity groundwaters observed off Long Island by applying boundary conditions consistent with Pleistocene seal-level fluctuations. Observed salinity conditions were most closely matched in the models by also including the effects of sub-glacial recharge from the Laurentide Ice Sheet and allowing groundwater to discharge from Miocene aquifers along submarine canyons near the continental slope. Simulated recharge induced by Laurentide Ice Sheet meltwater was probably short lived hut, on average, about two to ten times greater than modern subaerial levels. A sensitivity analysis performed using our cross-sectional model suggests that a narrow range of hydrologic conditions can drive fresh water long distances offshore across the continental shelf.

Autogenic attainment of large-scale alluvial grade with steady sea-level fall: An analog tank-flume experiment

A graded river conveys its sediment load without net deposition or erosion. The graded state is thought to represent the long-term response of alluvial rivers to steady external forcing. We show here that alluvial rivers building deltas can be in grade as an autogenic response to steady sea-level fall. Consider an antecedent graded river profile, the upstream end of which consists of an alluvial-bedrock transition, and the downstream end of which is a fixed overfall where constant sea level is maintained. The antecedent graded profile is then drowned by a jump in sea level, after which sea level drops. The result is a new river profile ending in a prograding delta that deposits on top of the antecedent profile. If the rate of sea-level fall is constant and the length of the antecedent reach is sufficient, the new profile eventually becomes parallel or quasi-parallel to the antecedent profile, maintaining grade as it progrades. In the experiments reported here, series of graded river profiles with prograding deltas are created by stacking fluviodeltaic systems; each graded profile and its associated delta is stacked on its immediate predecessor. For each fluviodeltaic system, a graded alluvial profile is attained with any constant rate of sea-level fall, provided that the antecedent profile is of sufficient length. Experiments suggest that this autogenic approach to grade is more rapid for higher rates of sea-level fall, lower rates of sediment supply, and higher water discharges.

An enthalpy method for moving boundary problems on the earth's surface

Purpose – To present a novel moving boundary problem related to the shoreline movement in a sedimentary basin and demonstrate that numerical techniques from heat transfer, in particular enthalpy methods, can be adapted to solve this problem.Design/methodology/approach – The problem of interest involves tracking the movement (on a geological time scale) of the shoreline of a sedimentary ocean basin in response to sediment input, sediment transport (via diffusion), variable ocean base topography, and changing sea level. An analysis of this problem shows that it is a generalized Stefan melting problem; the distinctive feature, a latent heat term that can be a function of both space and time. In this light, the approach used in this work is to explore how previous analytical solutions and numerical tools developed for the classical Stefan melting problem (in particular fixed grid enthalpy methods) can be adapted to resolve the shoreline moving boundary problem.Findings – For a particular one‐dimensional case,...

A similarity solution for a dual moving boundary problem associated with a coastal-plain depositional system

Assuming that the sediment flux in the Exner equation can be linearly related to the local bed slope, we establish a one-dimensional model for the bed-load transport of sediment in a coastal-plain depositional system, such as a delta and a continental margin. The domain of this model is defined by two moving boundaries: the shoreline and the alluvial–bedrock transition. These boundaries represent fundamental transitions in surface morphology and sediment transport regime, and their trajectories in time and space define the evolution of the shape of the sedimentary prism. Under the assumptions of fixed bedrock slope and sea level the model admits a closed-form similarity solution for the movements of these boundaries. A mapping of the solution space, relevant to field scales, shows two domains controlled by the relative slopes of the bedrock and fluvial surface: one in which changes in environmental parameters are mainly recorded in the upstream boundary and another in which these changes are mainly recorded in the shoreline. We also find good agreement between the analytical solution and laboratory flume experiments for the movements of the alluvial–bedrock transition and the shoreline.

Groundwater flow and geochemistry in the Southeastern San Juan Basin: Implications for microbial transport and activity

Recent confirmation of widespread microbial activity in the deep subsurface has raised the question whether microbes were transported to their current residence from the surface or whether they have survived in situ since sediment deposition. As a part of a larger study addressing these and related questions, we have characterized the microbiology and hydrogeology of a Late Cretaceous sandstone and shale sequence in the southeastern San Juan Basin New Mexico, near a 3.39 Ma volcanic intrusion. Deep core samples were analyzed for microbial activity to assess recolonization of the previously sterilized zone around the intrusion. Groundwater geochemistry and isotopic data were used to improve the understanding of the flow regime. We modeled the geochemical evolution of the groundwater from the recharge area to each sample location and used the resultant mass transfers to correct measured 14C activities. The 14C ages provided the basis for calibrating a cross-sectional flow model that intersects the intrusion. Based on microbial activity data, hydrogeologic modeling results supported the inference that groundwater velocities were adequate to transport microbes into the previously sterilized region in the time since the volcanic intrusion. Evidence of upward groundwater flow near the intrusion and high vertical hydraulic conductivities for shale suggest considerable hydraulic connection between lithologie units, which may influence the nutrient distribution and promote enhanced microbial activity near lithologic interfaces.