Complex Bed Topography Research Articles

An efficient semi-implicit friction source term treatment for modeling overland flow

In this study, a new numerical treatment of the friction source term is proposed for modeling shallow water flows over complex bed topography. We design a novel semi-implicit temporal discretization technique based on Taylor series expansion of friction source terms. A well-balanced positivity-preserving finite volume scheme on unstructured triangular grids is used to solve the shallow water model. We present a series of numerical tests to demonstrate the robustness and effectiveness of the proposed numerical model where we used rapidly varying flows over complex topography as well as flows involving small values of water depth and wet/dry zones. The simulation results of the numerical model based on the proposed approach for friction source terms are compared to experimental data and to those obtained by using other existing techniques. The proposed numerical model is stable and second-order accurate and our predictions are in good agreement with experimental observations.

Regional-scale abrupt Mid-Holocene ice sheet thinning in the western Ross Sea, Antarctica

Abstract Outlet glaciers drain the majority of ice flow in the Antarctic ice sheet. Theory and numerical models indicate that local bed topography can play a key role in modulating outlet glacier response to climate warming, potentially resulting in delayed, asynchronous, or enhanced retreat. However, the period of modern observations is too short to assess whether local or regional controls dominate ice sheet response on time scales that are critical for understanding ice sheet mass loss over this century and beyond. The recent geological past allows for insight into such centennial-scale ice sheet behavior. We present a cosmogenic surface-exposure chronology from Mawson Glacier, adjacent to a region of the Ross Sea that underwent dynamic marine-based ice sheet retreat following the Last Glacial Maximum. Our data record at least 220 m of abrupt ice thinning between 7.5 and 4.5 ka, followed by more gradual thinning until the last millennium. The timing, rates, and magnitudes of thinning at Mawson Glacier are remarkably similar to that documented 100 km to the south at Mackay Glacier. Together, both outlet glaciers demonstrate that abrupt deglaciation occurred across a broad region in the Mid-Holocene. This happened despite the complex bed topography of the western Ross Sea and implies an overarching external driver of retreat. When compared to regional sea-level and ocean-temperature changes, our data indicate that ocean warming most likely drove grounding-line retreat and ice drawdown, which then accelerated as a result of marine ice sheet instability.

A robust two-dimensional model for highly sediment-laden unsteady flows of variable density over movable beds

AbstractIn this work, a novel 2D depth-integrated numerical model for highly sediment-laden shallow flows over non-uniform erodible beds is presented, including variable density and exchange between the bed layer and the water–sediment mixture flow. The system of equations is formed by the 2D conservation equations for the mass and momentum of the mixture, the mass conservation equation for the different sediment size-classes transported in the flow and the bed evolution equation. The depth-averaged mixture density varies according to the volumetric concentration of the different sediment size-classes that can be incorporated from the bed to the flow and transported as suspended materials. The rheological behaviour of the flow is directly controlled by the properties of the mixture. A new x-split augmented Roe (xA-Roe) scheme is derived to solve the coupled flow and suspended solid-phase equations in both structured and unstructured meshes. The numerical scheme is defined to properly include density variations and momentum source terms, retaining a well-balanced flux formulation in steady states and the correct treatment of the wet–dry fronts. The numerical scheme is assessed with steady and transient cases involving highly sediment-laden flows, demonstrating its accuracy, stability and robustness in the presence of complex bed topography, wetting–drying fronts and rapid morphological changes.

Validation of a Novel, Shear Reynolds Number Based Bed Load Transport Calculation Method for Mixed Sediments against Field Measurements

In this study, the field measurement-based validation of a novel sediment transport calculation method is presented. River sections with complex bed topography and inhomogeneous bed material composition highlight the need for an improved sediment transport calculation method. The complexity of the morphodynamic features (spatially and temporally varied bed material) can result in the simultaneous appearance of the gravel and finer sand dominated sediment transport (e.g., parallel bed armoring and siltation) at different regions within a shorter river reach. For the improvement purpose of sediment transport calculation in such complex river beds, a novel sediment transport method was elaborated. The base concept of it was the combined use of two already existing empirical sediment transport models. The method was already validated against laboratory measurements. The major goal of this study was the verification of the novel method with a real river case study. The combining of the two sediment transport models was based on the implementation of a recently presented classification method of the locally dominant sediment transport nature (gravel or sand transport dominates). The results were compared with measured bed change maps. The verification clearly referred to the meaningful improvement in the sediment transport calculation by the novel manner in the case of spatially varying bed content.

The impact of model resolution on the simulated Holocene retreat of the southwestern Greenland ice sheet using the Ice Sheet System Model (ISSM)

Abstract. Geologic archives constraining the variability of the Greenland ice sheet (GrIS) during the Holocene provide targets for ice sheet models to test sensitivities to variations in past climate and model formulation. Even as data–model comparisons are becoming more common, many models simulating the behavior of the GrIS during the past rely on meshes with coarse horizontal resolutions (≥10 km). In this study, we explore the impact of model resolution on the simulated nature of retreat across southwestern Greenland during the Holocene. Four simulations are performed using the Ice Sheet System Model (ISSM): three that use a uniform mesh and horizontal mesh resolutions of 20, 10, and 5 km, and one that uses a nonuniform mesh with a resolution ranging from 2 to 15 km. We find that the simulated retreat can vary significantly between models with different horizontal resolutions based on how well the bed topography is resolved. In areas of low topographic relief, the horizontal resolution plays a negligible role in simulated differences in retreat, with each model instead responding similarly to retreat driven by surface mass balance (SMB). Conversely, in areas where the bed topography is complex and high in relief, such as fjords, the lower-resolution models (10 and 20 km) simulate unrealistic retreat that occurs as ice surface lowering intersects bumps in the bed topography that would otherwise be resolved as troughs using the higher-resolution grids. Our results highlight the important role that high-resolution grids play in simulating retreat in areas of complex bed topography, but also suggest that models using nonuniform grids can save computational resources through coarsening the mesh in areas of noncomplex bed topography where the SMB predominantly drives retreat. Additionally, these results emphasize that care must be taken with ice sheet models when tuning model parameters to match reconstructed margins, particularly for lower-resolution models in regions where complex bed topography is poorly resolved.

Radiostratigraphy Reflects the Present-Day, Internal Ice Flow Field in the Ablation Zone of Western Greenland

Englacial radar reflectors in the ablation zone of the Greenland Ice Sheet are derived from layering deposited in the accumulation zone over past millennia. The original layer structure is distorted by ice flow toward the margin. In a simplified case, shear and normal strain incurred between the ice divide and terminus should align depositional layers such that they closely approximate particle paths through the ablation zone where horizontal motion dominates. It is unclear, however, if this relationship holds in western Greenland where complex bed topography, three dimensional ice flow, and historical changes to ice sheet mass and geometry since layer deposition may promote a misalignment between present-day layer orientation and the modern ice flow field. We investigate this problem using a suite of analyses that leverage ice sheet models and observational datasets. Our findings suggest that across a study sector of western Greenland, the radiostratigraphy of the ablation zone is closely aligned with englacial particle paths, and is not far departed from a state of balance. The englacial radiostratigraphy thus provides insight into the modern, local, internal flow field, and may serve to further constrain ice sheet models that simulate ice dynamics in this region.

An Implicit Scheme for Shallow Water Flow with Wet Dry Interface

A finite difference implicit scheme is presented in this paper for solution of the shallow water equations in one dimensional (1D) form. The present model has many advantages like, handling of discontinuous and complex bed topography, satisfying C-property (preservation of motionless water surface over a wet or dry bed) and capability of handling large value of temporal step etc. Another very important feature of the present model is that, no special treatment of the source vector of the governing equations is required here to deal with very less water depth. To investigate the performance of the present model in diverse situations, it is used to replicate four different problems of known analytical solution, and the model is found to be quite capable for varied situations.

Direct measurements of lift and drag on shallowly submerged cobbles in steep streams: Implications for flow resistance and sediment transport

AbstractSteep mountain streams have higher resistance to flow and lower sediment transport rates than expected by comparison with low gradient rivers, and often these differences are attributed to reduced near‐bed flow velocities and stresses associated with form drag on channel forms and immobile boulders. However, few studies have directly measured drag and lift forces acting on bed sediment for shallow flows over coarse sediment, which ultimately control sediment transport rates and grain‐scale flow resistance. Here we report on particle lift and drag force measurements in flume experiments using a planar, fixed cobble bed over a wide range of channel slopes (0.004 < S < 0.3) and water discharges. Drag coefficients are similar to previous findings for submerged particles (CD ∼ 0.7) but increase significantly for partially submerged particles. In contrast, lift coefficients decrease from near unity to zero as the flow shallows and are strongly negative for partially submerged particles, indicating a downward force that pulls particles toward the bed. Fluctuating forces in lift and drag decrease with increasing relative roughness, and they scale with the depth‐averaged velocity squared rather than the bed shear stress. We find that, even in the absence of complex bed topography, shallow flows over coarse sediment are characterized by high flow resistance because of grain drag within a roughness layer that occupies a significant fraction of the total flow depth, and by heightened critical Shields numbers and reduced sediment fluxes because of reduced lift forces and reduced turbulent fluctuations.

A modified lattice Boltzmann model for shallow water flows over complex topography

SummaryA modified lattice Boltzmann model is proposed to describe shallow water flows over complex topography. In the proposed model, the quadratic depth term is excluded from the equilibrium distribution functions (EDFs), and the hydrostatic pressure term is combined with the bed slope term to be treated as a part of the sourcing term in the lattice Boltzmann equation (LBE). Therefore, it is unnecessary to match the coefficients of the quadratic depth term in the EDFs with those of the bed slope term in the sourcing terms in the LBE. This would bring more flexibility to the treatment of the sourcing terms in the LBE. In order to recover the shallow water equations (SWEs), the basic constraints are redefined, and under these constraints, the coefficients of the EDFs are derived afterwards. Several benchmark problems are used to validate the proposed model, including stationary case, steady flows over a two‐dimensional bump and tidal wave flows over irregular bed elevation. The computed results are in excellent agreement with the results of the other numerical methods and the analytical solutions, indicating that the proposed model is capable of simulating shallow water flows over complex bathymetry. It also proves that the proposed model has potential to produce competitive solutions to shallow water flows over complex bed topography. Copyright © 2014 John Wiley & Sons, Ltd.

A note on acoustic measurements of turbulence, suspended sediment, and bed forms in mobile-bed experiments

Mobile-bed laboratory measurements allow observation of interactions between turbulent sediment-laden flows and irregular, non-stationary bed topography. Water in mobile-bed experiments is typically clouded by suspended particles, complicating the use of optical and laser based measurement techniques. In such conditions, acoustic techniques can be used to measure turbulence, suspended sediment transport, and bed topography; however, these procedures also have unique challenges. Here, the effect of suspended particles on acoustic Doppler turbulence measurement, the effect of particle size on acoustic measurement of suspended-sediments, and a method for statistically describing bed topography (measured acoustically or otherwise) are addressed. It is found that suspended particles have a small effect on Reynolds stresses measured with an acoustic Doppler velocimeter and that those effects could be minimized by excluding data collected with the highest and lowest acoustic amplitudes. The effect of particle size on acoustic backscatter amplitude is most strongly pronounced for particles smaller than 0.3 mm. Semivariogram analysis is shown to be a viable method for analyzing complex bed topography produced by mobile-bed experiments.

Coarse sediment transport in a bedrock channel with complex bed topography

Independent lithologic and structural controls in fluvial bedrock systems interact with coarse sediment transport processes to play a key role in bedrock incision processes such as abrasion. During a 3 year study on the Ocoee River in the Blue Ridge Province of the southern Appalachians, USA, we used painted tracer clasts to measure coarse sediment transport dynamics and address whether different scales of morphologic variability in bedrock channels lead to coarse sediment transport processes that differ from alluvial channels. At the reach scale, folded metasedimentary units are exposed in the channel bed and appear as linear bedrock ribs that vary in amplitude and orientation to flow. Under similar flow conditions for which size‐dependent transport has been observed in alluvial channels (dimensionless Shields stress within 1.5–2.0 times the dimensionless critical shear stress), transport distance was a significant function of grain size where bedrock ribs were longitudinal to flow (Reach 1 and Reach 2). However, transport distance was not size dependent where bedrock ribs were oblique to flow (Reach 3). At different intrareach scales, the variables characterizing the local bedrock topography and sediment architecture were the best predictors of transport distance in all three reaches. Therefore, bed load transport processes may be influenced by bed forms in bedrock streams (bedrock ribs) but at potentially smaller scales than bed forms in alluvial channels. The strong influence of bedrock ribs on coarse sediment transport suggested that coarse sediment transport processes are controlled by different factors in bedrock channels only when bedrock ribs cross the channel at a high angle to the flow.

Local high‐slope effects on sediment transport and fluvial bed form dynamics

We investigate the morphodynamic evolution of an arbitrarily tilted, coarse, mobile bed under the action of a free surface water flow. The analysis is based on the experimental observations of the evolution of a mobile bed from its initial, laterally tilted configuration to the final laterally flat state, due to the presence of a lateral component of bed load transport. Measurements of the bed topography at different times allow one to reconstruct the flattening process. The experimental observations are interpreted by means of a three‐dimensional numerical hydromorphodynamic model employing different relationships, linear and nonlinear, to evaluate bed load intensity and direction. The analysis shows that the inclusion of nonlinear gravitational effects in the description of the bed load leads to a more satisfactory description of the bed evolution. This finding opens important issues on how the inclusion of the nonlinear gravitational effects on the bed load can affect the morphodynamic evolution of complex bed topography occurring in natural rivers. To investigate this point, an application to the evolution of river bars is presented.

A coupled lattice Boltzmann model for advection and anisotropic dispersion problem in shallow water

A coupled lattice Boltzmann model (CLBM) for 2D advection and anisotropic dispersion equation (AADE) and shallow water equations is formulated and implemented. Multi-relaxation-time (MRT) method is used for the flow field and the L-basis two-relaxation-time (TRT) method is used for the pollutant field. The relaxation time for the antisymmetric part of the pollutant deviates from a constant for flows with variable free surface water depth. Numerical tests show that this scheme strictly obeys conservation of mass and momentum. And the model has a better accuracy when τ D is closer to 1 2 and τ e is closer to ∑ τ D ∗ 9 . Excellent agreement is obtained between numerical predictions and analytical solutions in pure dispersion problem and advection–dispersion problem. Comparison with finite different method indicates that the variation of the free surface water depth does not affect the mass and momentum conservation of the model and that the model has the ability to simulate complex bed topography problem. Comparison with finite volume method in the 2D steady flow around a rectangular column with non-slip boundary shows that the LB scheme has the capacity to solve the complex advection–dispersion problems in shallow water.

Subglacial topography inferred from ice surface terrain analysis reveals a large un‐surveyed basin below sea level in East Antarctica

A terrain analysis technique relating ice‐surface plan curvature to basal topography is applied to the Antarctic Ice Sheet. The technique suggests complex bed topography and a large subglacial basin more than 1500 m below present day sea level under the Recovery Glacier and its catchment in East Antarctica. Despite the importance of accurate subglacial topography for understanding the nature of ice flow and for numerical modeling, available data in this region are sparse. The presence of a large area of ice grounded below sea level, flowing at elevated velocities could have significant implications for the potential stability of this region of East Antarctica, previously thought to contain only small areas of marine ice sheet. The catchment region alone contains an ice volume equivalent to 2.6 m of global sea level rise, therefore it is important that the nature of the basal conditions in this region are better understood.

Assessing different methods of generating a three-dimensional numerical model mesh for a complex stream bed topography

Three-dimensional numerical models of flow over complex bed geometry are becoming widely used in river and coastal engineering. Boundary-fitted coordinate grids are typically used to deal with this problem in natural channels. Recently, a regular structured grid method based on numerical porosity has been developed for high-resolution gravel-bed models. A simpler alternative approach is to use a Cartesian mesh with an interpolated 3D solid object representing the river bed. The objective of this study is to assess the impact of these three methods of mesh generation on the simulated flow field above complex bed topography around stream deflectors in a laboratory setting. Results show marked differences between the three types of simulations when running mesh sensitivity analysis. Because the bed porosity approach uses the digital elevation model (DEM) information in each cell to represent bed topography, it requires a finer mesh resolution in order to reach an accurate solution. Although there was good qualitative agreement between the simulated flow fields and Acoustic Doppler Velocity measurements, the quantitative comparison showed relatively poor agreement for all mesh design types. However, the three mesh types were in good agreement when compared to each other for velocity and pressure variables (average correlation coefficient, r, of 0.95), with the 3D object bed and bed porosity showing the best agreement (r = 0.97). Simulated turbulence variables (KE and EP), however, showed more scatter (r = 0.85) and slopes markedly different from unity.

Numerical Prediction of Dam-Break Flows in General Geometries with Complex Bed Topography

Dam-break flows in general geometries with complex bed topography are simulated numerically using a high-resolution Godunov-type cut cell method. The model is based on the shallow water equations with appropriate source terms. A vertical step in the bed is treated efficiently and accurately with the surface gradient method. For dam-break flows occurring in complicated geometries, the Cartesian cut cell method together with transmissive boundary conditions is incorporated. Verification of the method is carried out by predicting dam-break flows typical of practical situations, i.e., dam-break flows over a vertical step into bent channels and a dam-break flow over a bump in a bed with both transmissive and reflective boundary conditions at the channel end. The results are compared with experimental data showing good agreement. The method is simple, efficient, and conservative. It shows promise for handling a wide range of dam-break flows.

High‐resolution numerical modelling of three‐dimensional flows over complex river bed topography

AbstractThis paper describes preliminary results from a method for the treatment of complex bed topography for the understanding of three‐dimensional flow processes. It develops an established porosity‐based method and couples it to high‐resolution bed topographical data acquired using digital photogrammetry. The results provide quantitative data on flow processes that match and perhaps exceed current measurement capabilities, and so raise difficult questions for model validation. However, the detailed flow fields provided by the method allow us to develop current models for flow–form interactions in gravel‐bed rivers. Of most importance, the method will allow us to enhance significantly the application of computational fluid dynamics to complex river bed morphology, for large eddy simulation, roughness parameterization, sediment entrainment and deposition studies, and understanding interactions between flow and vegetation in relation to conveyance studies. Copyright © 2002 John Wiley & Sons, Ltd.

Development of channel organization and roughness following sediment pulses in single‐thread, gravel bed rivers

Large, episodic inputs of coarse sediment (sediment pulses) in forested, mountain streams may result in changes in the size and arrangement of bed forms and in channel roughness. A conceptual model of channel organization delineates trajectories of response to sediment pulses for many types of gravel bed channels. Channels exhibited self‐organizing behavior to various degrees based on channel gradient, presence of large in‐channel wood or other forcing elements, the size of the sediment pulse, and the number of bed‐mobilizing flows since disturbance. Typical channel changes following a sediment pulse were initial decreases in water depth, in variability of bed elevations, and in the regularity of bed form spacing. Trajectories of change subsequently showed increased average water depth, more variable and complex bed topography, and increased uniformity of bed form spacing. Bed form spacing in streams with abundant forcing elements developed at a shorter spatial scale (two to five channel widths) than in streams without such forcing mechanisms (five to 10 channel widths). Channel roughness increased as bed forms developed.

Delineation of a complexly dipping temperate glacier bed using short-pulse radar arrays

AbstractWe have defined the complex bed topography for a section of a small temperate glacier using 50 MHz monostatic short-pulse radar data and a synthetic-aperture array-processing method. The data were collected on a 100 m by 340 m array grid in the upper stem of Gulkana Glacier, central Alaska, U.S.A. The array processing was based on a modified three-dimensional (3-D) Kirchhoff migration integral and implemented with a synthetic-aperture approach that uses sequences of overlapping sub-arrays to generate depth images in vertical planes. Typical sub-array beam patterns are generally <5° at the −6 dB level, giving a flashlight-like searching capability without distorting the wavelet shape. The bed topography was constructed using normal reflections picked from 3-D array depth images. In some instances reflections were imaged outside the data-cover-age area. The bed surface dips steeply, both parallel and transverse to the direction of ice flow. The maximum observed depth is roughly 140 m. The 3-D method resolved bed dips up to 45°. In regions of steepest dip, it improved depth accuracy by 36% compared with raw data, and by 15% compared with standard two-dimensional (2-D) migration. Over 12 dB of signal-to-noise improvement and improved spatial resolution was achieved compared to raw data and 2-D migration. False bottom layering seen in the raw data and in 2-D migrations is not observed in the 3-D array results. Furthermore, loss of bottom reflections is shown by the 3-D migration to be attributable to the dip and curvature of the reflector, and not scattering losses or signal clutter from englacial inclusions.

Irregular bed forms in steep, rough channels: 2. Field observations

A linear stability analysis using a flow model appropriate for steep, rough channels suggests that initial wavelength selection of alternate bars is strong for extant flow conditions in North Boulder Creek, Colorado. This is due in part to effects of velocity correlation terms in the streamwise momentum balance that involve deviations in velocity components about depth‐averaged values. The analysis also suggests that alternate bars and midchannel bars can “compete” during initial bed form growth at low sediment transport rates. These points are consistent with the observation that alternate and midchannel bar forms in North Boulder Creek have comparable topographic relief, as revealed by spectral analysis of the bed topography. Moreover, the dominant wavelengths of these bar forms match the fastest growing wavelengths predicted by the stability analysis. However, whereas the alternate bar topography can be attributed to free‐bar growth, much of the midchannel bar topography probably is a forced‐bar topography that is related to flow accelerations associated with variations in channel width. The complex bed topography of North Boulder Creek thus consists of a decipherable mixture of bed forms that have evolved as free alternate bars together with forced bars whose positions and geometries are fixed in relation to variations in channel width or to large immobile boulders.