Andries Paarlberg

A parameterization of flow separation over subaqueous dunes

Flow separation plays a key role in the development of dunes, and modeling the complicated flow behavior inside the flow separation zone requires much computational effort. To make a first step toward modeling dune development at reasonable temporal and spatial scales, a parameterization of the shape of the flow separation zone over two-dimensional dunes is proposed herein, in order to avoid modeling the complex flow inside the flow separation zone. Flow separation behind dunes, with an angle-of-repose slip face, is characterized by a large circulating leeside eddy, where a separation streamline forms the upper boundary of the recirculating eddy. Experimental data of turbulent flow over two-dimensional subaqueous bed forms are used to parameterize this separation streamline. The bed forms have various heights and height to length ratios, and a wide range of flow conditions is analyzed. This paper shows that the shape of the flow separation zone can be approximated by a third-order polynomial as a function of the distance away from the flow separation point. The coefficients of the polynomial can be estimated, independent of flow conditions, on the basis of bed form shape at the flow separation point and a constant angle of the separation streamline at the flow reattachment point.

Modeling river dune evolution using a parameterization of flow separation

This paper presents an idealized morphodynamic model to predict river dune evolution. The flow field is solved in a vertical plane assuming hydrostatic pressure conditions. The sediment transport is computed using a Meyer-Peter–Muller type of equation, including gravitational bed slope effects and a critical bed shear stress. To avoid the necessity of modeling the complex flow inside the flow separation zone, we follow an approach similar to one used earlier to simulate the dynamics of wind-blown desert dunes. In case of flow separation, the separation streamline acts as an artificial bed and sediment avalanches down the leeside distributing evenly on the leeside at the angle of repose. Model results show that bed slope effects play a crucial role in the determination of the fastest-growing wavelength from a linear analysis. Flow separation is shown to be crucial to take into account if the dune lee exceeds a certain threshold slope. If flow separation is not included, dune shapes are incorrectly predicted and the dune height saturates at an early stage of bed form evolution, yielding an underprediction of dune height and time to equilibrium. The local bed slope at the dune crest plays a critical role for obtaining an equilibrium dune height. The simulation model is able to predict the main characteristics of dune evolution, such as dune asymmetry, dune growth, and saturation at a certain dune height. Dune dimensions, migration rates, and times to equilibrium compare reasonably well to various data sets.

Flow separation and shear stress over angle‐of‐repose bed forms: A numerical investigation

Large asymmetric bed forms commonly develop in rivers. The turbulence associated with flow separation that develops over their steep lee side is responsible for the form shear stress which can represent a substantial part of total shear stress in rivers. This paper uses the Delft3D modeling system to investigate the effects of bed form geometry and forcing conditions on flow separation length and associated turbulence, and bed form shear stress over angle-of-repose (30° lee side angle) bed forms. The model was validated with lab measurements that showed sufficient agreement to be used for a systematic analysis. The influence of flow velocity, bed roughness, relative height (bed form height/water depth), and aspect ratio (bed form height/length) on the variations of the normalized length of the flow separation zone, the extent of the wake region (where the turbulent kinetic energy (TKE) was more than 70% of the maximum TKE), the average TKE within the wake region and the form shear stress were investigated. Form shear stress was found not to scale with the size of the flow separation zone but to be related to the product of the normalized extent of the wake region (extent of the wake region/extent of water body above the bed form) and the average TKE within the wake region. The results add to understanding of the hydrodynamics of bed forms and may be used for the development of better parameterizations of small-scale processes for application in large-scale studies.

Characterising natural bedform morphology and its influence on flow

Bedforms such as dunes and ripples are ubiquitous in rivers and coastal seas, and commonly described as triangular shapes from which height and length are calculated to estimate hydrodynamic and sediment dynamic parameters. Natural bedforms, however, present a far more complicated morphology; the difference between natural bedform shape and the often assumed triangular shape is usually neglected, and how this may affect the flow is unknown. This study investigates the shapes of natural bedforms and how they influence flow and shear stress, based on four datasets extracted from earlier studies on two rivers (the Rio Paraná in Argentina, and the Lower Rhine in The Netherlands). The most commonly occurring morphological elements are a sinusoidal stoss side made of one segment and a lee side made of two segments, a gently sloping upper lee side and a relatively steep (6 to 21°) slip face. A non-hydrostatic numerical model, set up using Delft3D, served to simulate the flow over fixed bedforms with various morphologies derived from the identified morphological elements. Both shear stress and turbulence increase with increasing slip face angle and are only marginally affected by the dimensions and positions of the upper and lower lee side. The average slip face angle determined from the bed profiles is 14°, over which there is no permanent flow separation. Shear stress and turbulence above natural bedforms are higher than above a flat bed but much lower than over the often assumed 30° lee side angle.