Thomas Pähtz

Why do particle clouds generate electric charges

Granular flows, such as in silos or desert sandstorms, can form charged particle clouds in the presence of an electric field. Simulations and experiments on inert grains explain how significant electrical charges are able to accumulate.

The apparent roughness of a sand surface blown by wind from an analytical model of saltation

We present an analytical model of aeolian sand transport. The model quantifies the momentum transfer from the wind to the transported sand by providing expressions for the thickness of the saltation layer and the apparent surface roughness. These expressions are derived from basic physical principles and a small number of assumptions. The model further predicts the sand transport rate (mass flux) and the impact threshold (the smallest value of the wind shear velocity at which saltation can be sustained). We show that, in contrast to previous studies, the present models predictions are in very good agreement with a range of experiments, as well as with numerical simulations of aeolian saltation. Because of its physical basis, we anticipate that our model will find application in studies of aeolian sand transport on both Earth and Mars.

Jump at the onset of saltation.

We reveal that the transition in the saturated flux for aeolian saltation is generically discontinuous by explicitly simulating particle motion in turbulent flow. This is the first time that a jump in the saturated flux has been observed. The discontinuity is followed by a coexistence interval with two metastable solutions. The modification of the wind profile due to momentum exchange exhibits a maximum at high shear strength.

Flux Saturation Length of Sediment Transport

Sediment transport along the surface drives geophysical phenomena as diverse as wind erosion and dune formation. The main length scale controlling the dynamics of sediment erosion and deposition is the saturation length Ls, which characterizes the flux response to a change in transport conditions. Here we derive, for the first time, an expression predicting Ls as a function of the average sediment velocity under different physical environments. Our expression accounts for both the characteristics of sediment entrainment and the saturation of particle and fluid velocities, and has only two physical parameters which can be estimated directly from independent experiments. We show that our expression is consistent with measurements of Ls in both aeolian and subaqueous transport regimes over at least 5 orders of magnitude in the ratio of fluid and particle density, including on Mars.

Midair collisions enhance saltation.

Here we address the old question in aeolian particle transport about the role of midair collisions. We find that, surprisingly, these collisions do enhance the overall flux substantially. The effect depends strongly on restitution coefficient and wind speed. We can explain this observation as a consequence of a soft bed of grains which floats above the ground and reflects the highest flying particles. We make the unexpected observation that the flux is maximized at an intermediate restitution coefficient of about 0.7, which is comparable to values experimentally measured for collisions between sand grains.

Analytical model for flux saturation in sediment transport.

The transport of sediment by a fluid along the surface is responsible for dune formation, dust entrainment, and a rich diversity of patterns on the bottom of oceans, rivers, and planetary surfaces. Most previous models of sediment transport have focused on the equilibrium (or saturated) particle flux. However, the morphodynamics of sediment landscapes emerging due to surface transport of sediment is controlled by situations out of equilibrium. In particular, it is controlled by the saturation length characterizing the distance it takes for the particle flux to reach a new equilibrium after a change in flow conditions. The saturation of mass density of particles entrained into transport and the relaxation of particle and fluid velocities constitute the main relevant relaxation mechanisms leading to saturation of the sediment flux. Here we present a theoretical model for sediment transport which, for the first time, accounts for both these relaxation mechanisms and for the different types of sediment entrainment prevailing under different environmental conditions. Our analytical treatment allows us to derive a closed expression for the saturation length of sediment flux, which is general and thus can be applied under different physical conditions.

Is it appropriate to model turbidity currents with the three‐equation model?

The three-equation model (TEM) was developed in the 1980s to model turbidity currents (TCs) and has been widely used ever since. However, its physical justification was questioned because self-accelerating TCs simulated with the steady TEM seemed to violate the turbulent kinetic energy balance. This violation was considered as a result of very strong sediment erosion that consumes more turbulent kinetic energy than is produced. To confine bed erosion and thus remedy this issue, the four-equation model (FEM) was introduced by assuming a proportionality between the bed shear stress and the turbulent kinetic energy. Here we analytically proof that self-accelerating TCs simulated with the original steady TEM actually never violate the turbulent kinetic energy balance, provided that the bed drag coefficient is not unrealistically low. We find that stronger bed erosion, surprisingly, leads to more production of turbulent kinetic energy due to conversion of potential energy of eroded material into kinetic energy of the current. Furthermore, we analytically show that, for asymptotically supercritical flow conditions, the original steady TEM always produces self-accelerating TCs if the upstream boundary conditions (“ignition” values) are chosen appropriately, while it never does so for asymptotically subcritical flow conditions. We numerically show that our novel method to obtain the ignition values even works for Richardson numbers very near to unity. Our study also includes a comparison of the TEM and FEM closures for the bed shear stress to simulation data of a coupled Large Eddy and Discrete Element Model of sediment transport in water, which suggests that the TEM closure might be more realistic than the FEM closure.

Discrete Element Method simulations of the saturation of aeolian sand transport

The saturation length of aeolian sand transport (Ls), characterizing the distance needed by wind-blown sand to adapt to changes in the wind shear, is essential for accurate modeling of the morphodynamics of Earths sandy landscapes and for explaining the formation and shape of sand dunes. In the last decade, it has become a widely accepted hypothesis that Ls is proportional to the characteristic distance needed by transported particles to reach the wind speed (the “drag length”). Here we challenge this hypothesis. From extensive numerical Discrete Element Method simulations, we find that, for medium and strong winds, Ls∝Vs2/g, where Vs is the saturated value of the average speed of sand particles traveling above the surface and g is the gravitational constant. We show that this proportionality is consistent with a recent analytical model, in which the drag length is just one of four similarly important length scales relevant for sand transport saturation.

Well-balanced and flexible morphological modeling of swash hydrodynamics and sediment transport

Abstract Existing numerical models of the swash zone are relatively inflexible in dealing with sediment transport due to a high dependence of the deployed numerical schemes on empirical sediment transport relations. Moreover, these models are usually not well-balanced, meaning they are unable to correctly simulate quiescent flow. Here a well-balanced and flexible morphological model for the swash zone is presented. The nonlinear shallow water equations and the Exner equation are discretized by the shock-capturing finite volume method, in which the numerical flux and the bed slope source term are estimated by a well-balanced version of the SLIC (slope limited centered) scheme that does not depend on empirical sediment transport relations. The satisfaction of the well-balanced property is demonstrated through simulating quiescent coastal flow. The quantitative accuracy of the model in reproducing key parameters (i.e., the notional shoreline position, the swash depth, the flow velocity, the overtopping flow volume, the beach change depth and the sediment transport rate) is shown to be satisfactory through comparisons against analytical solutions, experimental data as well as previous numerical solutions. This work facilitates an improved modeling framework for the swash hydrodynamics and sediment transport.

Fluid forces or impacts: What governs the entrainment of soil particles in sediment transport mediated by a Newtonian fluid?

To sustain steady sediment transport, the loss of transported particles that become trapped in the soil bed must be balanced by the entrainment of bed particles through fluid forces or energetic impacts of transported particles. Here we show that the transition to fully impact-sustained transport occurs at a critical impact number