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

Comments on “A generic length-scale equation for geophysical turbulence models” by L. Umlauf and H. Burchard

Umlauf and Burchard (2003) present a generic length-scale equation... for use in two-equation models of turbulence. However, because of the traditional form used for the diffusion term, it can be used at present for only negative values of n. We show that a simple modification of the diffusion term is sufficient to insure a more universal generic length-scale equation that is valid for all values of m and n, including positive values of n. We also show that an appropriate combination of exponents m and n will enable the generic length-scale equation to simulate any desired length-scale equation..

A Time-Dependent Λ

The prevailing constant Λ-G cosmological model agrees with observational evidence including the observed red shift, Big Bang Nucleosynthesis (BBN), and the current rate of acceleration. It assumes that matter contributes 27% to the current density of the universe, with the rest (73%) coming from dark energy represented by the Einstein cosmological parameter Λ in the governing Friedmann-Robertson-Walker equations, derived from Einstein’s equations of general relativity. However, the principal problem is the extremely small value of the cosmological parameter (~10−52 m2). Moreover, the dark energy density represented by Λ is presumed to have remained unchanged as the universe expanded by 26 orders of magnitude. Attempts to overcome this deficiency often invoke a variable Λ-G model. Cosmic constraints from action principles require that either both G and Λ remain time-invariant or both vary in time. Here, we propose a variable Λ-G cosmological model consistent with the latest red shift data, the current acceleration rate, and BBN, provided the split between matter and dark energy is 18% and 82%. Λ decreases (Λ~τ-2, where τ is the normalized cosmic time) and G increases (G~τn) with cosmic time. The model results depend only on the chosen value of Λ at present and in the far future and not directly on G

North Indian Ocean variability during the Indian Ocean dipole

International audienceThe circulation in the North Indian Ocean (NIO henceforth) is highly seasonally variable. Periodically reversing monsoon winds (southwesterly during summer and northeasterly during winter) give rise to seasonally reversing current systems off the coast of Somalia and India. In addition to this annual monsoon cycle, the NIO circulation varies semiannually because of equatorial currents reversing four times each year. These descriptions are typical, but how does the NIO circulation behave during anomalous years, during an Indian Ocean dipole (IOD) for instance? Unfortunately, in situ observational data are rather sparse and reliance has to be placed on numerical models to understand this variability. In this paper, we estimate the surface current variability from a 12-year hindcast of the NIO for 1993?2004 using a 1/2° resolution circulation model that assimilates both altimetric sea surface height anomalies and sea surface temperature. Presented in this paper is an examination of surface currents in the NIO basin during the IOD. During the non-IOD period of 2000?2004, the typical equatorial circulation of the NIO reverses four times each year and transports water across the basin preventing a large sea surface temperature difference between the western and eastern NIO. Conversely, IOD years are noted for strong easterly and westerly wind outbursts along the equator. The impact of these outbursts on the NIO circulation is to reverse the direction of the currents ? when compared to non-IOD years ? during the summer for negative IOD events (1996 and 1998) and during the fall for positive IOD events (1994 and 1997). This reversal of current direction leads to large temperature differences between the western and eastern NIO

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

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

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

No abstract available

Innovando en la comercialización de materia prima en el ramo alimenticio: plan de negocios de la empresa Las Delicias de Nayarit S.A. de C.V.

Trabajo realizado en la empresa familiar Las Delicias de Nayarit, dedicada a comercializar materias primas para la industria de la panificación, repostería, heladería y food service. Se formuló un plan de negocios basado en las cuatro finalidades de la empresa según Carlos Llanos Cifuentes (1975): el desarrollo de las personas que integran la empresa y las que se relacionan con ella; el servicio a la comunidad, la generación de un valor económico agregado y la capacidad de dar continuidad y dotarla de capacidad de permanencia

Death of three Loop Current rings

The life cycle of large anticyclonic rings in the Gulf of Mexico (GOM) is widely described by pinch off from the Loop Current, migration across the Gulf and eventual spin down along the western slope. Extensive observational and modeling efforts provide a relatively consistent picture of rings pinching off from the Loop Current and of complex interaction between anticyclones and cyclones driven by bathymetry along the western and northwestern shelf. The observational record for Loop Current rings (LCRs) during the intermediate period of westward translation is less clear. A number of studies recognize distinct anomalies in LCR characteristics in deep water as the rings enter the western Gulf near 92-94W. These include abrupt changes in the geometry of observed drifter trajectories and derived eddy parameter fits as well as changes in both ring translation speeds and the estimated rate of ring decay. Such observations are consistent with intense interaction and mass exchange between the rings and other coherent mesoscale features known to be present in the western Gulf. We test the hypothesis that interactions with the ambient mesoscale field can lead to rapid loss of coherence of some LCRs well before they reach the \u27eddy graveyard\u27 in the western Gulf. We use the data-assimilating, eddy-resolving numerical GOM model described by Kantha et al. (2005) to assess the fates of readily identified LCRs Fourchon, Juggernaut, and Millenium during the period July 1998 to August 2001. Lagrangian metrics, including relative dispersion of small drifter clusters seeded in the ring cores, analysis of evolving blobs seeded in the ring cores, and finite-scale Lyapunov exponents, are used to track model ring evolution. These metrics clearly show that interactions with existing mesoscale cyclones and anticyclones caused Fourchon and Juggernaut to break up near 92W on advective time scales. In addition, Millenium also experienced an intense deformation, stirring, and mixing episode near 92W. Blob studies showed that the core fluid of Millenium was ultimately dispersed over much of the western basin. Our results show that some LCRs may break up through interactions with existing western Gulf cyclones and anticyclones prior to reaching the western slope