The length scale equation in turbulence models

International audienceThe question of which length scale equation to use in models of turbulence has long been controversial and several approaches have been suggested and used in the past. In this paper, we demonstrate that all these approaches are equivalent and the inconsistencies in the use of some of these approaches arise from improper modeling of the diffusion term in the length scale equation. We formulate a general length scale equation, which encompasses all current approaches. This equation is devoid of inconsistencies and should prove useful in its general form, or one of its subsets, in turbulence closure modeling

Qualitative responses of a vortex core to tip blowing and intersecting airfoils

The qualitative responses of a trailing vortex core to change in its convective velocity produced by injection of air into the vortex core and by the flow field of a lifting surface in the path of the core are discussed. Flow pictures of the vortex core and vorticity measurements in the core show that an axial momentum injection of approximately 35% of the total wing drag alters the vortex structure and behavior quite drastically by effectively inducing a more rapid dispersion of the vorticity in the core. The data indicate that the phenomenon is governed by the rate of injection of the momentum rather than the mass flow rate. There also seems to be an optimum rate of injection beyond which increased injection does not bring about equally significant changes in the vortex core. Flow patterns of the region of interaction between the flow field of a lifting surface and the vortex core show two modes of vortex response; (1) the vortex core bends, following the streamline shape until it intercepts the wake of the wing where it is abruptly dispersed, or (2) the vortex core may be sliced into two similar vortices when the vortex hits the leading edge of the wing

Subtropical Mode Water in the 137°E Section

Rotational effects on turbulence structure and mixing are investigated using a second-moment closure model. Both explicit and implicit Coriolis terms are considered. A general criterion for rotational effects to be small is established in terms of local turbulent Rossby numbers. Characteristic length scales are determined for rotational effects and Monin–Obukhov type similarity theory is developed for rotating stratified flows. A one-dimensional version of the closure model is then applied to simulate oceanic mixed layer evolution. It is shown that the effects of rotation on mixed layer depth tend to be small because of the influence of stable stratification. These findings contradict a hypothesis of Garwood et al. that rotational effects on turbulence are responsible for the disparity in the mixed-layer depths between the eastern and western regions of the equatorial Pacific Ocean. The model is also applied to neutrally stratified flows to demonstrate that rotation can either stabilize or destabilize the flow

Langmuir cells and mixing in the upper ocean

The presence of surface gravity waves at the ocean surface has two important effects on turbulence in the oceanic mixed layer (ML): the wave breaking and the Langmuir cells (LC). Both these effects act as additional sources of turbulent kinetic energy (TKE) in the oceanic ML, and hence are important to mixing in the upper ocean. The breaking of high wave-number components of the wind wave spectrum provides an intense but sporadic source of turbulence in the upper surface; turbulence thus injected diffuses downward, while decaying rapidly, modifying oceanic near-surface properties which in turn could affect the air-sea transfer of heat and dissolved gases. LC provide another source of additional turbulence in the water column; they are counter-rotating cells inside the ML, with their axes roughly aligned in the direction of the wind (Langmuir I., Science, 87 (1938) 119). These structures are usually made evident by the presence of debris and foam in the convergence area of the cells, and are generated by the interaction of the wave-field–induced Stokes drift with the wind-induced shear stress. LC have long been thought to have a substantial influence on mixing in the upper ocean, but the difficulty in their parameterization have made ML modelers consistently ignore them in the past. However, recent Large Eddy Simulations (LES) studies suggest that it is possible to include their effect on mixing by simply adding additional production terms in the turbulence equations, thus enabling even 1D models to incorporate LC-driven turbulence. Since LC also modify the Coriolis terms in the mean momentum equations by the addition of a term involving the Stokes drift, their effect on the velocity structure in the ML is also quite significant and could have a major impact on the drift of objects and spilled oil in the upper ocean. In this paper we examine the effect of surface gravity waves on mixing in the upper ocean, focusing on Langmuir circulations, which is by far the dominant part of the surface wave contribution to mixing. Oceanic ML models incorporating these effects are applied to an observation station in the Northern Adriatic Sea to see what the extent of these effects might be. It is shown that the surface wave effects can indeed be significant; in particular, the modification of the velocity profile due to LC-generated turbulence can be large under certain conditions. However, the surface wave effects on the bulk properties of the ML, such as the associated temperature, while significant, are generally speaking well within the errors introduced by uncertainties in the external forcing of the models. This seems to be the reason why ML models, though pretty much ignoring surface wave effects until recently, have been reasonably successful in depicting the evolution of the mixed layer temperature (MLT) at various timescales

Preface: Oceanographic processes on the continental shelf: observations and modeling

No abstract available

Lagrangian predictability of high-resolution regional models: the special case of the Gulf of Mexico

The Lagrangian prediction skill (model ability to reproduce Lagrangian drifter trajectories) of the nowcast/forecast system developed for the Gulf of Mexico at the University of Colorado at Boulder is examined through comparison with real drifter observations. Model prediction error (MPE), singular values (SVs) and irreversible-skill time (IT) are used as quantitative measures of the examination. Divergent (poloidal) and nondivergent (toroidal) components of the circulation attractor at 50m depth are analyzed and compared with the Lagrangian drifter buoy data using the empirical orthogonal function (EOF) decomposition and the measures, respectively. Irregular (probably, chaotic) dynamics of the circulation attractor reproduced by the nowcast/forecast system is analyzed through Lyapunov dimension, global entropies, toroidal and poloidal kinetic energies. The results allow assuming exponential growth of prediction error on the attractor. On the other hand, the <it>q</it>-th moment of MPE grows by the power law with exponent of 3<it>q</it>/4. The probability density function (PDF) of MPE has a symmetrical but non-Gaussian shape for both the short and long prediction times and for spatial scales ranging from 20km to 300km. The phenomenological model of MPE based on a diffusion-like equation is developed. The PDF of IT is non-symmetric with a long tail stretched towards large ITs. The power decay of the tail was faster than 2 for long prediction times

Chlorophyll dispersal by eddy-eddy interactions in the Gulf of Mexico

1] A Lagrangian analysis of the transport and dispersal of plumes observed in satellite-derived ocean color images was conducted using a data-assimilating model of the Gulf of Mexico. The interaction between pervasive cyclonic and anticyclonic eddies in the Gulf generated advective paths that connect remote shelf regions. These paths aligned remarkably well with the plume events recorded with the chlorophyll-a ocean color product from SeaWiFS. Two such events were studied. In one event material was transported in a thin strip between the northern wall of the Loop Current and an adjacent cyclone, connecting the eastern Campheche shelf (off the Yucatan Peninsula) and South Florida shelves. The other event began off the Louisiana shelf break as a small plume traced by chlorophyll and then developed into a long and thin feature which meandered to the shelf break off the northern Yucatan Peninsula, moving between a large anticyclone and several adjacent cyclones. These results indicate that inter-eddy advection plays a crucial role in developing the ocean color patterns observed in the satellite ocean color data

Transcriptomic analysis of milk somatic cells in mastitis resistant and susceptible sheep upon challenge with Staphylococcus epidermidis and Staphylococcus aureus

<p>Abstract</p> <p>Background</p> <p>The existence of a genetic basis for host responses to bacterial intramammary infections has been widely documented, but the underlying mechanisms and the genes are still largely unknown. Previously, two divergent lines of sheep selected for high/low milk somatic cell scores have been shown to be respectively susceptible and resistant to intramammary infections by <it>Staphylococcus spp</it>. Transcriptional profiling with an 15K ovine-specific microarray of the milk somatic cells of susceptible and resistant sheep infected successively by <it>S. epidermidis </it>and <it>S. aureus </it>was performed in order to enhance our understanding of the molecular and cellular events associated with mastitis resistance.</p> <p>Results</p> <p>The bacteriological titre was lower in the resistant than in the susceptible animals in the 48 hours following inoculation, although milk somatic cell concentration was similar. Gene expression was analysed in milk somatic cells, mainly represented by neutrophils, collected 12 hours post-challenge. A high number of differentially expressed genes between the two challenges indicated that more T cells are recruited upon inoculation by <it>S. aureus </it>than <it>S. epidermidis</it>. A total of 52 genes were significantly differentially expressed between the resistant and susceptible animals. Further Gene Ontology analysis indicated that differentially expressed genes were associated with immune and inflammatory responses, leukocyte adhesion, cell migration, and signal transduction. Close biological relationships could be established between most genes using gene network analysis. Furthermore, gene expression suggests that the cell turn-over, as a consequence of apoptosis/granulopoiesis, may be enhanced in the resistant line when compared to the susceptible line.</p> <p>Conclusions</p> <p>Gene profiling in resistant and susceptible lines has provided good candidates for mapping the biological pathways and genes underlying genetically determined resistance and susceptibility towards <it>Staphylococcus </it>infections, and opens new fields for further investigation.</p