**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 Re_{Δ}=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 Re_{Δ}=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=1´10^{-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=1´10^{-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=3×10^{-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=6×10^{-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=3×10^{-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 2^{nd} and 3^{rd} 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 3^{rd} row). These features are very
different from that of lower concentration where flow remains turbulent
throughout the wave cycle (see 2^{nd} row). The 4^{th}, 5^{th}
and 6^{th} 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.

__References__

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),
187–204.

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.