3D Turbulence-resolving simulation of fine sediment transport in oscillatory boundary layer



Conventional modeling approaches based on Reynolds-averaged Navier-Stokes equations with eddy-viscosity type turbulence closures are not able to predict various processes occur during wave-driven high concentration fluid mud transport, e.g., laminarization of wave boundary layer due to strong sediment-induced stable density stratification. This is partially because it is difficult to parameterize all the scales of turbulence when intense turbulence-sediment interactions occur at various scales.


A DNS code (e.g., Cortese & Balanchandar 1995; Cantero et al. 2008, 2009) has been successfully revised to simulate oscillatory boundary layer with fine sediment transport of various concentrations. Simulation results[1] match very well with prior DNS results reported by Spalart and Baldwin (1988) at ReΔ=1000, which give us the confidence of the new modification made to the code. Numerical model is further used to study interactions between carrier flow turbulence and sediment transport. The numerical model compute nondimensionalized equations but results are discussed here in terms of dimensional quantities. At a fixed ReΔ=1000, which corresponds to wave period of 10 sec and wave velocity amplitude of 0.56 m/s, we carry out a series of simulations for dimensional particle settling velocity of 0.5 mm/s at different sediment concentrations represented by bulk Richardson number Ri. At Ri=110-4, which corresponds to near bed sediment concentration of about 10 g/l (see <C>=10 g/l case shown in Figure 1), sediment-induced stable density stratification attenuates flow turbulence and reduces mixing of sediment near the top of the wave boundary layer, which gives the formation of sharp concentration gradient, i.e., lutocline. It is worth mentioning that another simulation with Ri=0 (i.e., very dilute sediment concentration such that sediment is passive to carrier turbulence flow) shows more or less well-mixed concentration profile without the formation of lutocline (not shown here). Hence, this test case also gives a qualitative estimate on the minimum concentration (<C> about O(1) g/l) in which particle cannot be considered as passive to the carrier flow turbulence. In spite of the formation of lutocline at Ri=110-4, turbulence in the wave boundary layer is not affected by sediment and mean flow velocity is almost identical to clear fluid condition.


At Ri=310-4 (near bed concentration <C> about 100 g/l, see Figure 1), sediment-induced density stratification is strong enough to attenuate turbulence in the entire wave boundary layer. Flow tends to be laminarized and mean flow velocity profiles become similar to laminar solution. However, flow instability, which can be seen clearly both in turbulent coherent structure and instantaneous particle concentration (e.g., see the iso-surface of concentration shown in the third panel in Figure 1), occurs during flow reversal which trigger large turbulence production and particle suspension that last about one-third of the wave period. Finally at Ri=610-4 (near bed concentration much more than 100 g/l), oscillatory boundary layer flow become laminarized throughout the wave cycle due to intense sediment-induced stable density stratification. At Ri=310-4 or greater (<C> larger than about 50 g/l), turbulence is attenuated across the entire oscillatory boundary layer and hence the oscillatory boundary layer thickness and friction are reduced due to sediment-induced stable density stratification. This study identifies several distinct regimes of sediment-laden oscillatory boundary layer according to different magnitudes of bulk Richardson number (or sediment concentration). Although the exact value of Ri for these regimes must depends on Reynolds number and settling velocity, the characteristics of these regimes are useful to explain wave-driven cohesive sediment transport process observed in coastal environments.






Figure 1: Simulation results for a medium concentration case (near bed concentration <C> 10 g/l) and a high concentration case (<C> 50 g/l). The top row: time-series of free-stream velocity and associated phases; The 2nd and 3rd rows: iso-surface of particle concentration for the case of <C> 10 g/l, and <C> 50 g/l at three different phases. When sediment concentration is large, flow laminarizes under wave crest but shear instability occurs during flow reversal (see 3rd row). These features are very different from that of lower concentration where flow remains turbulent throughout the wave cycle (see 2nd row). The 4th, 5th and 6th rows are averaged concentration, streamwise velocity and RMS streamwise turbulent velocity fluctuations profiles at three different phases. Significant damping of turbulence due to sediment-induced density stratification causes laminarization of velocity and reduction of wave boundary layer thickness.



[1]: 3D numerical simulations are carried out by C. E. Ozdemir as part of his PhD research.



Cortese, T. & Balachandar, S., 1995 High performance spectral simulation of turbulent flows in massively parallel machines with distributed memory. International Journal of Supercomputer Applications 9 (3), 187204.

Cantero, M.I., S. Balachandar & M. Garcia. 2008 An Eulerian-Eulerian model for gravity currents driven by inertial particles. Int. J. Multiphase Flow. 34,484-501.

Cantero, M.I., S. Balachandar, A. Cantelli, C. Pirmez, & G. Parker, 2009 Turbidity current with a roof: Direct numerical simulation of self-stratified turbulent channel flow driven by suspended sediment. J. Geophys. Res. 114, C03008.

Spalart, P. R. & Baldwin, B. S. 1988 Direct simulation of a turbulent oscillating boundary layer. Turbulent Shear Flows 6 Springer.