Results of large-eddy simulation (LES) of Langmuir circulations (LC) in a wind-driven shear current in shallow water are reported. The LC are generated via the well-known Craik–Leibovich vortex force modelling the interaction between the Stokes drift, induced by surface gravity waves, and the shear current. LC in shallow water is defined as a flow in sufficiently shallow water that the interaction between the LC and the bottom boundary layer cannot be ignored, thus requiring resolution of the bottom boundary layer. After the introduction and a description of the governing equations, major differences in the statistical equilibrium dynamics of wind-driven shear flow and the same flow with LC (both with a bottom boundary layer) are highlighted. Three flows with LC will be discussed. In the first flow, the LC were generated by intermediate-depth waves (relative to the wavelength of the waves and the water depth). The amplitude and wavelength of these waves are representative of the conditions reported in the observations of A. E. Gargett & J. R. Wells in Part 1 (J. Fluid Mech. vol .000, 2007, p. 00). In the second flow, the LC were generated by shorter waves. In the third flow, the LC were generated by intermediate waves of greater amplitude than those in the first flow. The comparison between the different flows relies on visualizations and diagnostics including (i) profiles of mean velocity, (ii) profiles of resolved Reynolds stress components, (iii) autocorrelations, (iv) invariants of the resolved Reynolds stress anisotropy tensor and (v) balances of the transport equations for mean resolved turbulent kinetic energy and resolved Reynolds stresses. Additionally, dependencies of LES results on Reynolds number, subgrid-scale closure, size of the domain and grid resolution are addressed.In the shear flow without LC, downwind (streamwise) velocity fluctuations are characterized by streaks highly elongated in the downwind direction and alternating in sign in the crosswind (spanwise) direction. Forcing this flow with the Craik–Leibovich force generating LC leads to streaks with larger characteristic crosswind length scales consistent with those recorded by observations. In the flows with LC, in the mean, positive streaks exhibit strong intensification near the bottom and near the surface leading to intensified downwind velocity ‘jets’ in these regions. In the flow without LC, such intensification is noticeably absent. A revealing diagnostic of the structure of the turbulence is the depth trajectory of the invariants of the resolved Reynolds stress anisotropy tensor, which for a realizable flow must lie within the Lumley triangle. The trajectory for the flow without LC reveals the typical structure of shear-dominated turbulence in which the downwind component of the resolved normal Reynolds stresses is greater than the crosswind and vertical components. In the near bottom and surface regions, the trajectory for the flow with LC driven by wave and wind forcing conditions representative of the field observations reveals a two-component structure in which the downwind and crosswind components are of the same order and both are much greater than the vertical component. The two-component structure of the Langmuir turbulence predicted by LES is consistent with the observations in the bottom third of the water column above the bottom boundary layer.

Recent measurements at a cabled sea-floor node in 15 meters of water off the coast of New Jersey suggest that Langmuir supercells, Langmuir circulations that achieve vertical scales equal to the water depth under extended storms, are an important mechanism for major sediment resuspension events on the extensive shallow shelves off the eastern U.S. coast. Because sediment resuspension is a prelude to transport, supercell events are a necessary condition for major sediment transport. Such events may also contribute to shelf-sea exchange and to offshore gradation of benthic community structure in shallow seas.

Interaction between the wind-driven shear current and the Stokes drift velocity induced by surface gravity waves gives rise to Langmuir turbulence in the upper ocean. Langmuir turbulence consists of Langmuir circulation (LC) characterized by a wide range of scales. In unstratified shallow water, the largest scales of Langmuir turbulence engulf the entire water column and thus are referred to as full-depth LC. Large-eddy simulations (LESs) of Langmuir turbulence with full-depth LC in a wind-driven shear current have revealed that vertical mixing due to LC erodes the bottom log-law velocity profile, inducing a profile resembling a wake law. Furthermore, in the interior of the water column, two sources of Reynolds shear stress, turbulent (nonlocal) transport and local Stokes drift shear production, can combine to lead to negative mean velocity shear. Meanwhile, near the surface, Stokes drift shear serves to intensify small-scale eddies leading to enhanced vertical mixing and disruption of the surface log law. A K-profile parameterization (KPP) of the Reynolds shear stress comprising local and nonlocal components is introduced, capturing these basic mechanisms by which Langmuir turbulence in unstratified shallow water impacts the vertical mixing of momentum. Single-water-column, Reynolds-averaged Navier–Stokes simulations with the new parameterization are presented, showing good agreement with LES in terms of mean velocity. Results show that coefficients in the KPP may be parameterized based on attributes of the full-depth LC.

International audienceWe report on temporal large eddy simulations (TLES) of the turbulent channel flow of a dilute polymer solution modeled with the FENE-P (finitely extensible nonlinear elastic in the Peterlin approximation) constitutive equation. The large eddy simulations are based upon an approximate temporal deconvolution method [ Pruett et al., Phys. of Fluids, 18, 028104–1, (2006) ] for residual Newtonian stress modeling and secondary regularization for unresolved subfilter Newtonian stress. The filtered conformation tensor equation involves deconvolution for stretching and for the nonlinear spring force, as well as secondary regularization. Results are shown at a friction Reynolds number 180 for Weissenberg numbers and molecular extensibilities spanning the moderate to high drag reducing regimes. Excellent agreement is obtained between TLES and direct numerical simulations (DNS) in terms of percent drag reduction prediction. TLES is also able to reproduce the high level of anisotropy of turbulence, which confirms recent findings by Frohnapfel et al. [J. Fluid Mech. 577, 457 (2007) ] who present high anisotropy as a general mechanism to obtain significant drag reduction. The TLES model proves itself stable and its overall computational workload some 60 times less than DNS

Tubular anaerobic digesters are used in developing countries to produce biogas from livestock waste. In this research, field measurements and physical and biological process modeling studies were used to investigate transport and transformation mechanisms for particulate and soluble organic matter in household-scale tubular digesters in the Monteverde region of Costa Rica. Greater than 75% removal of volatile solids and biochemical oxygen demand (BOD 5) were observed. The high effluent quality was attributed to the formation of a biologically active floccular sludge layer, which allowed for separation of hydraulic and mean cell residence times (HRT and MCRT). A reduced order transport model was developed and validated using field tracer study data. Key assumptions of the reduced order model were verified via computational fluid dynamics (CFD) analysis. The mean HRT predicted by the reduced order model was 23 days and was in good agreement with the tracer experiment. A simplified floccular sludge biological process model was developed and used to estimate an average MCRT of 115 days. The results showed that household-scale tubular anaerobic digesters can provide enough biogas to meet households' cooking energy needs, which was consistent with field results. This is the first study to combine mathematical modeling with field studies of tubular anaerobic digester performance.

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High‐frequency internal waves generated by Langmuir motions over stratified water may be an important source of turbulent mixing below the surface mixed layer. Large eddy simulations of a developing mixed layer and inertial current are employed to investigate this phenomena. Uniform surface wind stress and parallel Stokes drift wave forcing rapidly establishes a turbulent mixed‐layer flow, which (as the inertial motion veers off the wind) generates high‐frequency internal waves in the stratified fluid below. The internal waves evolve such that their vector phase velocity matches the depth‐averaged mixed‐layer velocity that rotates as an inertial oscillation. The internal waves drain energy and momentum from the mixed layer on decay time‐scales that are comparable to those of near‐inertial oscillations. The high‐frequency waves, which are likely to be trapped in the transition layer, may significantly contribute to mixing there and thus provide a potentially important energy sink for mixed‐layer inertial motions.

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