Linear stability analysis of subaqueous bedforms using direct numerical simulations

We present results on the formation of ripples from linear stability analysis. The analysis is coupled with direct numerical simulations of turbulent open-channel flow over a fixed sinusoidal bed. The presence of the sediment bed is accounted for using the immersed boundary method. The simulations are used to extract the bed shear stress and consequently the sediment transport rate. The approach is different from traditional linear stability analysis in the sense that the phase lag between the bed topology and the sediment flux is obtained from the three-dimensional turbulent simulations. The stability analysis is performed on the Exner equation, whose input, the sediment flux, is provided from the simulations. We ran 11 simulations at a fixed shear Reynolds number of 180, but for different sediment bed wavelengths. The analysis allows us to sweep a large range of physical and modelling parameters to predict their effects on linear growth. The Froude number appears to be the critical controlling parameter in the early linear development of ripples, in contrast with the dominant role of particle Reynolds number during the equilibrium stage. We also present results from a wave packet analysis using a one-dimensional Gaussian ridge

On the Role of Sidewalls in the Transition From Straight to Sinuous Bedforms

We present results from direct numerical simulation on the transition from straight-crested to sinuous-crested bedforms. The numerical setup is representative of turbulent open channel flow over an erodible sediment bed at a shear Reynolds number of Reτ = 180. The immersed boundary method accounts for the presence of the bed. The simulations are two-way coupled such that the turbulent flow can erode and modify the bed, and in turn, the bed modifies the overlying flow. Coupling from the flow to the bed occurs through the Exner equation, while back coupling from the bed to the flow is achieved by imposing the no-slip and no-penetration condition at the immersed boundary. The simulation setup is similar to that by Zgheib et al. (2018a, https://doi.org/10.1002/2017JF004398) except for the presence of sidewalls to better mimic laboratory flume conditions. Sidewalls are observed to significantly increase bedform sinuosity. Key Points Lateral sidewalls significantly increase crestline sinuosity Influence of lateral domain extent on sinuosity is small but noticeable Influence of lateral extent is amplified in the presence of sidewall

Direct numerical simulation of cylindrical particle-laden gravity currents

We present results from direct numerical simulations (DNS) of cylindrical particle-laden gravity currents. We consider the case of a full depth release with monodisperse particles at a dilute concentration where particle–particle interactions may be neglected. The disperse phase is treated as a continuum and a two-fluid formulation is adopted. We present results from two simulations at Reynolds numbers of 3450 and 10,000. Our results are in good agreement with previously reported experiments and theoretical models. At early times in the simulations, we observe a set of rolled up vortices that advance at varying speeds. These Kelvin–Helmholtz (K–H) vortex tubes are generated at the surface and exhibit a counter-clockwise rotation. In addition to the K–H vortices, another set of clockwise rotating vortex tubes initiate at the bottom surface and play a major role in the near wall dynamics. These vortex structures have a strong influence on wall shear-stress and deposition pattern. Their relations are explored as well

Propagation and deposition of non-circular finite release particle-laden currents

The dynamics of non-axisymmetric turbidity currents is considered here for a range of Reynolds numbers of O (104) when based on the initial height of the release. The study comprises a series of experiments and highly resolved simulations for which a finite volume of particle-laden solution is released into fresh water. A mixture of water and polystyrene particles of mean diameter ̃=300m and mixture density ̃=1012kg/m3 is initially confined in a hollow cylinder at the centre of a large tank filled with fresh water. Cylinders with two different cross-sectional shapes, but equal cross-sectional areas, are examined: a circle and a rounded rectangle in which the sharp corners are smoothened. The time evolution of the front is recorded as well as the spatial distribution of the thickness of the final deposit via the use of a laser triangulation technique. The dynamics of the front and final deposits are significantly influenced by the initial geometry, displaying substantial azimuthal variation especially for the rectangular case where the current extends farther and deposits more particles along the initial minor axis of the rectangular cross section. Several parameters are varied to assess the dependence on the settling velocity, initial height aspect ratio, and volume fraction. Even though resuspension is not taken into account in our simulations, good agreement with experiments indicates that it does not play an important role in the front dynamics, in terms of velocity and extent of the current. However, wall shear stress measurements show that incipient motion of particles and particle transport along the bed are likely to occur in the body of the current and should be accounted to properly capture the final deposition profile of particles

On the spreading of non-canonical thermals from direct numerical simulations

We present results from direct numerical simulations on laminar and turbulent non-canonical thermals with an initial rectangular density distribution at a Reynolds number of Re = 500 and Re = 5000, respectively. We find the non-canonical shape to induce strong azimuthal variations in the thermal for both the laminar and turbulent cases. These include noticeable differences in downward and horizontal propagation speeds as well as differences in the strength of the vortex tube. These differences persist over a significant period of time and help generate a cross-flow component that is otherwise not present in canonical cases. The cross-flow component is in the opposite direction to that observed in gravity currents with the same initial density distribution. This is counterintuitive seeing that both flows are solely driven by buoyancy. By extracting the three-dimensional streamlines, we find the descending vortex tube to force the dense fluid to follow a helical path

Suspension-Driven gravity surges on horizontal surfaces: Effect of the initial shape

We present results from highly resolved direct numerical simulations of canonical (axisymmetric and planar) and non-canonical (rectangular) configurations of horizontal suspension-driven gravity surges. We show that the dynamics along the initial minor and major axis of a rectangular release are roughly similar to that of a planar and axisymmetric current, respectively. However, contrary to expectation, we observe under certain conditions the final extent of the deposit from finite releases to surpass that from an equivalent planar current. This is attributed to a converging flow of the particle-laden mixture toward the initial minor axis, a behaviour that was previously reported for scalar-driven currents on uniform slopes [31]. This flow is observed to be correlated with the travelling of a perturbation wave generated at the extremity of the longest side that reaches the front of the shortest side in a finite time. A semi-empirical explicit expression (based on established relations for planar and axisymmetric currents) is proposed to predict the extent of the deposit in the entire x-y plane. Finally, we observe that for the same initial volume of a suspension-driven gravity surge, a release of larger initial horizontal aspect-ratio is able to retain particles in suspension for longer periods of time

Long-lasting effect of initial configuration in gravitational spreading of material fronts

We present the results from laboratory experiments and fully resolved simulations pertaining to finite-release turbulent density flows with a non-axisymmetric initial shape. First, we demonstrate that the effects of the initial shape influence the current’s evolution well into the long-time phase which would corresponds to the inertial self-similar phase in the case of planar or axisymmetric configurations. Then, we identify the physical mechanisms responsible for this dependence and propose a new model capable of capturing the dynamics of such releases. Finally, we show that this dependence on the initial configuration is robust for various types of gravity currents over a wide range of parameters such as Reynolds number, density ratio, and aspect ratio

Front dynamics and entrainment of finite circular gravity currents on an unbounded uniform slope

We report on the dynamics of circular finite-release Boussinesq gravity currents on a uniform slope. The study comprises a series of highly resolved direct numerical simulations for a range of slope angles between 5∘ and 20∘ . The simulations were fixed at Reynolds number Re=5000 for all slopes considered. The temporal evolution of the front is compared to available experimental data. One of the interesting aspects of this study is the detection of a converging flow towards the centre of the gravity current. This converging flow is a result of the finite volume of the release coupled with the presence of a sloping boundary, which results in a second acceleration phase in the front velocity of the current. The details of the dynamics of this second acceleration and the redistribution of material in the current leading to its development will be discussed. These finite-release currents are invariably dominated by the head where most of the mixing and ambient entrainment occurs. We propose a simple method for defining the head of the current from which we extract various properties including the front Froude number and entrainment coefficient. The Froude number is seen to increase with steeper slopes, whereas the entrainment coefficient is observed to be weakly dependent on the bottom slope

Dynamics of non-circular finite-release gravity currents

The present work reports some new aspects of non-axisymmetric gravity currents obtained from laboratory experiments, fully resolved simulations and box models. Following the earlier work of Zgheib et al. (Theor. Comput. Fluid Dyn., vol. 28, 2014, pp. 521–529) which demonstrated that gravity currents initiating from non-axisymmetric cross-sectional geometries do not become axisymmetric, nor do they retain their initial shape during the slumping and inertial phases of spreading, we show that such non-axisymmetric currents eventually reach a self-similar regime during which (i) the local front propagation scales as t1/2 as in circular releases and (ii) the non-axisymmetric front has a self-similar shape that primarily depends on the aspect ratio of the initial release. Complementary experiments of non-Boussinesq currents and top-spreading currents suggest that this self-similar dynamics is independent of the density ratio, vertical aspect ratio, wall friction and Reynolds number Re , provided the last is large, i.e. Re⩾O(104) . The local instantaneous front Froude number obtained from the fully resolved simulations is compared to existing models of Froude functions. The recently reported extended box model is capable of capturing the dynamics of such non-axisymmetric flows. Here we use the extended box model to propose a relation for the self-similar horizontal aspect ratio χ∞ of the propagating front as a function of the initial horizontal aspect ratio χ0 , namely χ∞=1+(lnχ0)/3 . The experimental and numerical results are in good agreement with the proposed relation

A physics-based model for frost buildup under turbulent flow using direct numerical simulations

We present a new model for frost buildup under turbulent (and laminar) flow using direct numerical simulations. The physical model consists of two layers, the air and the frost. The air layer is fully resolved and consists of solving for the velocity, temperature, and vapor mass fraction fields. The frost layer thickness is resolved using conservation of mass and energy. Both phases are dynamically coupled using the immersed boundary method. Three-dimensional simulations are conducted in an open-channel configuration. A number of challenges need to be overcome to make these simulations feasible. First, to enforce far-field conditions of zero gradient and prescribed mean temperature and humidity, a source term is added to the energy and transport equations in the flow solver. Second, the mean frost thickness is subtracted after each time step to ensure a constant mean flow thickness and level of turbulence in the numerical domain. Third, a slow-time acceleration approach, which accelerates the frost buildup by a predetermined factor, is employed to bridge the gap between the fast turbulent and slow frost buildup time scales. Finally, a frost densification scheme is used to overcome the difficulties of vertically varying frost properties. The model is validated by comparing the frost thickness and frost thickness buildup rate over a period of one hour from a cooled flat plate experiment. Both quantities compare favorably with experiments