Alberto Scotti

Generalized Smagorinsky model for anisotropic grids

The Smagorinsky subgrid model is revised to properly account for grid anisotropy, using energy equilibrium considerations in isotropic turbulence. For moderate resolution anisotropies, Deardorff’s estimate involving an equivalent grid scale Δeq=(Δ1Δ2Δ3)1/3 is given a rigorous basis. For more general grid anisotropies, the Smagorinsky eddy viscosity is recast as νT=[csΔeqf(a1, a2)]2‖S‖, where f(a1,a2) is a function of the grid aspect ratios a1 and a2, and ‖S‖ is the resolved strain rate magnitude. The asymptotic behavior of νT at several limits of the aspect ratios are examined. Approximation formulas are developed so that f(a1,a2) can easily be evaluated in practice, for arbitrary values of a1 and a2. It is argued that these results should be used in conjunction with the dynamic model of Germano et al. whenever the anisotropy of the test‐filter differs significantly from that of the basic grid.

The formation and fate of internal waves in the South China Sea

Internal gravity waves, the subsurface analogue of the familiar surface gravity waves that break on beaches, are ubiquitous in the ocean. Because of their strong vertical and horizontal currents, and the turbulent mixing caused by their breaking, they affect a panoply of ocean processes, such as the supply of nutrients for photosynthesis, sediment and pollutant transport and acoustic transmission; they also pose hazards for man-made structures in the ocean. Generated primarily by the wind and the tides, internal waves can travel thousands of kilometres from their sources before breaking, making it challenging to observe them and to include them in numerical climate models, which are sensitive to their effects. For over a decade, studies have targeted the South China Sea, where the oceans’ most powerful known internal waves are generated in the Luzon Strait and steepen dramatically as they propagate west. Confusion has persisted regarding their mechanism of generation, variability and energy budget, however, owing to the lack of in situ data from the Luzon Strait, where extreme flow conditions make measurements difficult. Here we use new observations and numerical models to (1) show that the waves begin as sinusoidal disturbances rather than arising from sharp hydraulic phenomena, (2) reveal the existence of >200-metre-high breaking internal waves in the region of generation that give rise to turbulence levels >10,000 times that in the open ocean, (3) determine that the Kuroshio western boundary current noticeably refracts the internal wave field emanating from the Luzon Strait, and (4) demonstrate a factor-of-two agreement between modelled and observed energy fluxes, which allows us to produce an observationally supported energy budget of the region. Together, these findings give a cradle-to-grave picture of internal waves on a basin scale, which will support further improvements of their representation in numerical climate predictions.

Numerical simulation of pulsating turbulent channel flow

Direct and large-eddy simulations of the Navier–Stokes equations are used to study the pulsating flow in a channel. The cases examined span a wide range of frequencies of the driving pressure gradient, and encompass different physical behaviors, from the quasi-Stokes flow observed at high frequencies, to a quasisteady behavior at the lowest ones. The validity of the dynamic Smagorinsky model to study this kind of unsteady flow is established by a posteriori comparison with direct simulations and experimental data. It is shown that the fluctuations generated in the near-wall region by the unsteady pressure gradient do not propagate beyond a certain distance lt from the wall, which can be estimated quite accurately by a simple eddy viscosity argument. No substantial departure from the Stokes regime at very high frequency (ω+ as high as 0.1) is observed. The time-dependent characteristics of the flow are examined in detail, as well as the topology of the coherent structures.

Observations of nonlinear internal waves on the outer New England continental shelf during the summer Shelfbreak Primer study

Observations are presented of nonlinear internal waves on the outer New England continental shelf during the summer Shelfbreak Primer study conducted between July 26 and August 5, 1996. Current and temperature measurements were made with an upward looking acoustic Doppler current profiler (ADCP) located on the 147 m isobath near the shelfbreak and three vertical thermistor moorings located upshelf. Data from the ADCP and two nearby thermistor chains show energetic internal tides propagating at roughly 0.9 m s 21 to the north-northwest, nearly perpendicular to the local topography with 10 -15 cm s 21 horizontal currents and 15-30 m vertical displacements. These waves evolve rapidly within a 5.8 km range into an undular internal tidal bore. Cross-isobath barotropic tidal currents, responsible for generating the internal tides are in the 5-12 cm s 21 range. The bore formation is highly variable. There is evidence of a correlation between internal tide steepening and a shelfbreak front jet orientation that is oppositely directed to the internal tide propagation. There is no correlation between steepening and the jets vertical shear. Statistics of the undular bores show rms travel time fluctuations from 0.8 to 1.7 hours and average tidal bore durations from 12 to 9 hours. The average undular bore speed is 0.9 m s 21 , with an rms fluctuation of 0.4 m s 21 . The number of high-frequency waves in the bore varies from 0 to 8 near the shelfbreak and increases to 30 waves 26.7 km upshelf. The observed distribution function of temporal spacing between high-frequency internal waves is spread between 4 and 20 min.

Entrainment and suspension of sediments into a turbulent flow over ripples

We have analysed the trajectories of small particles released into a turbulent flow over a wavy wall in order to clarify the role of coherent structures in controlling the suspension and entrainment of sediments when ripples are present. LES was used to simulate the turbulent flow, while the motion of individual particles was calculated in a Lagrangian framework considering the effects of drag, lift and added mass. The results show that the process of suspension can be divided into two phases: the formation of a cloud in the lee of the ripples and the subsequent ejection of the particles across the shear layer capping the sediment cloud. Strong vortical structures on the upslope are shown to control the amounts of sediment entrained along the upslope, which feed the cloud. The implications for modelling are discussed.

On the interpretation of energy and energy fluxes of nonlinear internal waves: an example from Massachusetts Bay

A self-consistent formalism to estimate baroclinic energy densities and fluxes resulting from the propagation of internal waves of arbitrary amplitude is derived using the concept of available potential energy. The method can be applied to numerical, laboratory or field data. The total energy flux is shown to be the sum of the linear ∂

Modeling unsteady turbulent flows over ripples: Reynolds‐averaged Navier‐Stokes equations (RANS) versus large‐eddy simulation (LES)

(1) In this paper we consider the problem of modeling a turbulent pulsating boundary layer over ripples. We compare the results of two modeling strategies, Wilcoxs kw Reynolds-Averaged Navier-Stokes equations (RANS) and large-eddy simulation (LES) employing the Lagrangian dynamic eddy viscosity model. The geometry and parameters employed are relevant to nearshore oceanic flows, and the results are discussed in relation to the problem of sediment transport. Generally, RANS and LES agree well only with regard to the vertical profiles of the streamwise component of the velocity. Large discrepancies were found in all the other quantities considered (e.g., vertical velocity, turbulent kinetic energy, and Reynolds stress). In particular, RANS severely underpredicted the magnitude of the Reynolds stress and overpredicted the amplitude of the oscillations in the vertical velocity. We also found that often the trends exhibited by RANS and LES when the frequency and/or amplitude of the driving conditions was varied were at odds. Since comparison with available experiments indicates that LES is able to accurately model this kind of flows, we conclude that the RANS model is not appropriate to model the suspension and transport of sediment under conditions similar to the ones presented in this study. INDEX TERMS: 4568 Oceanography: Physical: Turbulence, diffusion, and mixing processes; 4558 Oceanography: Physical: Sediment transport; 3210 Mathematical Geophysics: Modeling; 3220 Mathematical Geophysics: Nonlinear dynamics; 3230 Mathematical Geophysics: Numerical solutions; KEYWORDS: turbulence, numerical modeling, sediment transport

Direct numerical simulation of turbulent channel flows with boundary roughened with virtual sandpaper

A method to simulate the effects of a roughened surface on a turbulent boundary layer is introduced. The method is easy to implement, does not increase the numerical overhead of the code, and affects the mean velocity in an a priori predictable way. A single parameter k is sufficient to fully characterize the roughness. The procedure has been tested in turbulent channel flows at Reτ=1000, with roughness heights k+ spanning the transitional regime. The properties of the rough flow agree well with experimental data.

Plankton accumulation and transport in propagating nonlinear internal fronts

Accumulation and transport of plankton in fronts propagating across-shore is a process of considerable ecological importance for many inhabitants of the littoral zone, since it links the offshore larval pool with the juvenile and adult inshore habitat. Several field studies have shown that larval plankton accumulates in fronts, but have failed to give a conclusive proof that effective Lagrangian transport takes place. A few process-oriented numerical studies have lent support to the idea, but the scope of their results is limited by the two-dimensional nature of the flows considered and by the simple model used to account for the behavior of plankton. In this paper, we relax both constraints. We solve the three-dimensional Navier-Stokes equation to compute the time dependent velocity field, and we use an empirically based model for the behavior of plankton. Our results show that accumulation and transport is possible, even for larvae characterized by sustained swimming speeds that are small compared with the speed of propagation of the front. We introduce a simple model to characterize the accumulation along the front, which includes both entrainment and detrainment. The model accurately represents accumulation calculated from the numerical runs, and provide a simple tool to estimate transport under a variety of circumstances. We also investigate the spatial distribution of plankton along and across the front and show that it is very patchy and dependent on the swimming speed of plankton, with important implications for interpreting results from field experiments.

Generation and propagation of nonlinear internal waves in Massachusetts Bay

[1] During the summer, nonlinear internal waves (NLIWs) are commonly observed propagating in Massachusetts Bay. The topography of the area is unique in the sense that the generation area (over Stellwagen Bank) is only 25 km away from the shoaling area, and thus it represents an excellent natural laboratory to study the life cycle of NLIWs. To assist in the interpretation of the data collected during the 1998 Massachusetts Bay Internal Wave Experiment (MBIWE98), a fully nonlinear and nonhydrostatic model covering the generation/shoaling region was developed, to investigate the response of the system to the range of background and driving conditions observed. Simplified models were also used to elucidate the role of nonlinearity and dispersion in shaping the NLIW field. This paper concentrates on the generation process and the subsequent evolution inthe basin. Themodel was foundtoreproducewell the range of propagation characteristics observed (arrival time, propagation speed, amplitude), and provided a coherent framework to interpret the observations. Comparison with a fully nonlinear hydrostatic model shows that during the generation and initial evolution of the waves as they move away from Stellwagen Bank, dispersive effects play a negligible role. Thus the problem can be well understood considering the geometry of the characteristics along which the Riemann invariants of the hydrostatic problem propagate. Dispersion plays a role only during the evolution of the undular bore in the middle of Stellwagen Basin. The consequences for modeling NLIWs within hydrostatic models are briefly discussed at the end.