Reply to: “Comments on ‘A generic length-scale equation for geophysical turbulence models’ ”by L. Kantha and S. Carniel

Recently, Kantha and Carniel (2003) commented on some earlier work of Kantha (2003) and Umlauf and Burchard (2003) on the formulation of a generalized length-scale equation in Reynolds stress models for geophysical flows. With the present short note, we respond to their major criticism of the Umlauf and Burchard (2003) generic two-equation model..

Estuarine exchange flow is related to mixing through the salinity variance budget

Author Posting. © American Meteorological Society, 2018. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 48 (2018): 1375-1384, doi:10.1175/JPO-D-17-0266.1.The relationship between net mixing and the estuarine exchange flow may be quantified using a salinity variance budget. Here “mixing” is defined as the rate of destruction of volume-integrated salinity variance, and the exchange flow is quantified using the total exchange flow. These concepts are explored using an idealized 3D model estuary. It is shown that in steady state (e.g., averaging over the spring–neap cycle) the volume-integrated mixing is approximately given by Mixing ≅ SinSoutQr, where Sin and Sout are the representative salinities of in- and outflowing layers at the mouth and Qr is the river volume flux. This relationship provides an extension of the familiar Knudsen relation, in which the exchange flow is diagnosed based on knowledge of these same three quantities, quantitatively linking mixing to the exchange flow.The work was supported by the National Science Foundation through Grants OCE-1736242 to PM and OCE-1736539 to WRG and by the German Research Foundation through Grants TRR 181 and GRK 2000 to HB

Sur la stabilité des E-feuilletages

Dans ce travail, nous résolvons un cas particulier du problème standard de la théorie des feuilletages qui est de trouver des conditions pour la stabilité d’une feuille compacte: une feuille compacte est stable si elle possède un système fondamental de voisinages saturés par rapport à la relation d’équivalence définie par les feuilles du feuilletage. Comme de nombreuses variétés différentiables ne possèdent pas de feuilletage, au sens classique, non trivial, nous nous intéressons à des feuilletages avec singularités et plus particulièrement aux E-feuilletages : un E-feuilletage F a la propriété d’être localement décrit par une application holomorphe appelée F-carte qui sépare les feuilles, c’est-à-dire une application qui factorise localement la projection canonique sur l’espace des feuilles. Ces feuilletages ont été étudiés pour la première fois dans la thèse de Egger. Pour une feuille compacte d’un E-feuilletage F, il n’est pas possible de définir un groupe d’holonomie car il n’y a pas de compatibilité biholomorphe entre les Fcartes. La compatibilité entre deux F-cartes fj :Uj −→ Vj, j = 1, 2, est donnée par une famille d’applications (uj :Z −→ Vj)j∈{1,2} appelée mont. Le comportement de F autour d’une feuille compacte est décrit par une famille finie de monts appelée massif que nous obtenons en recouvrant la feuille par un nombre fini de F-cartes. Nous reprenons et continuons dans cette thèse le travail de Egger en proposant une étude catégorique plus poussée des massifs. Ceci nous permet de définir différemment et plus simplement les germes d’holonomie, l’analogue au groupe d’holonomie que Egger a introduit. Les germes d’holonomie, dans le sens o`u nous les avons définis, nous donnent aussi un critère de stabilité. L’étude des germes d’holonomie définie par des E-feuilletages compacts de codimension 1 nous permet alors de démontrer que tous ces feuilletages sont stables: un feuilletage compact est stable si toutes ses feuilles sont stables. Il suit du théorème de Mattei-Moussu et du critère de simplicité de Reiffen que tous les feuilletages holomorphes compacts de codimension 1 définis sur une variété sont des E-feuilletages, nous avons donc trouvé une nouvelle démonstration de la stabilité de ces feuilletages.In this work, we solve a particular case of a standard problem of the theory of foliations which is to find conditions for the stability of a compact leaf. A compact leaf is stable if it possesses a fundamental system of neighborhoods saturated with respect to the equivalence relation defined by the leaves of the foliation. Since a lot of manifolds do not possess any foliation in the classical sense, that is not trivial, we study foliations with singularities and in particular the E-foliations. An E-foliation has the property to be locally described by a holomorphic mapping named F-chart which separates the leaves, i.e. a mapping that factorizes locally the canonical projection on the leafs space. This foliations have been studied first by Egger in his thesis. For a compact leaf of an E-foliation F it is not possible to define a holonomy group since there is no biholomorphic compatibility between the F-charts. The compatibility between two F-charts fj :Uj −→ Vj, j = 1, 2, is given by a family of applications (uj :Z −→ Vj)j∈{1,2} named a mountain. In order to know the behavior around a compact leaf we cover it with a finite number of F-charts and we obtain a finite family of mountains named massif. We develop further and complement the work of Egger proposing a more advanced categorical study of the massifs. This allows us to define the holonomy germs, i.e. the analogue to the holonomy group Egger introduced, in a different and simpler way. The holonomy germs, in the sense we defined them, also give a stability criterion. The study of the holonomy germs defined by 1-codimensional compact E-foliations allows us to prove the stability of these foliations. A compact foliation is stable if all its leaves are stable. The theorem of Mattei-Moussu and the simplicity criterion of Reiffen imply that all the 1-codimensional compact foliations defined on a manifold are E-foliations. Thus we have found a new proof of their stability

Modular System for Shelves and Coasts (MOSSCO v1.0) - a flexible and multi-component framework for coupled coastal ocean ecosystem modelling

Shelf and coastal sea processes extend from the atmosphere through the water column and into the sea bed. These processes are driven by physical, chemical, and biological interactions at local scales, and they are influenced by transport and cross strong spatial gradients. The linkages between domains and many different processes are not adequately described in current model systems. Their limited integration level in part reflects lacking modularity and flexibility; this shortcoming hinders the exchange of data and model components and has historically imposed supremacy of specific physical driver models. We here present the Modular System for Shelves and Coasts (MOSSCO, http://www.mossco.de), a novel domain and process coupling system tailored---but not limited--- to the coupling challenges of and applications in the coastal ocean. MOSSCO builds on the existing coupling technology Earth System Modeling Framework and on the Framework for Aquatic Biogeochemical Models, thereby creating a unique level of modularity in both domain and process coupling; the new framework adds rich metadata, flexible scheduling, configurations that allow several tens of models to be coupled, and tested setups for coastal coupled applications. That way, MOSSCO addresses the technology needs of a growing marine coastal Earth System community that encompasses very different disciplines, numerical tools, and research questions.Comment: 30 pages, 6 figures, submitted to Geoscientific Model Development Discussion

Realistic Multiannual Simulations of the Coupled North Sea and Baltic Sea System Using the Getm Model

This report presents a brief summary of modelling work done for the North Sea/Baltic Sea area within the institutional action ECOMAR (Monitoring and assessment of marine ecosystems) at the Joint Research Centre (JRC). First the underlying model equations are briefly recalled. Then different model setups for the coupled North Sea - Baltic Sea system using the General Estuary Transport Model (GETM) are described.JRC.H.3-Global environement monitorin

Numerical discretization of rotated diffusion operators in ocean models

A method to improve the behavior of the numerical discretization of a rotated diffusion operator such as, for example, the isopycnal diffusion parameterization used in large-scale ocean models based on the so-called z-coordinate system is presented. The authors then focus exclusively on the dynamically passive tracers and analyze some different approaches to the numerical discretization. Monotonic schemes are designed but are found to be rather complex, while simpler, linear schemes are shown to produce unphysical undershooting and overshooting. It is suggested that the choice of an appropriate discretization method depends on the importance of the rotated diffusion in a given simulation, whether the field to be diffused is dynamically active or not

Scientific cruise report Elisabeth Mann-Borgese SUMMIX-MESO

Objectives: It was intended to investigate the meso-scale and sub-meso-scale dynamics of the upper layers (upper 80 m) in the central Baltic Sea, using towed instruments and acoustic profilers, to better understand the physical conditions for cyanobacteria blooms. Under optimal weather conditions, we intended to carry out 10 one-day quasi-synoptic surveys by cruising in large meandering patterns (see fig. 1) covering areas of 15 X 15 nautical miles or 8 X 8 nautical miles, depending on the survey mode, see below. This cruise was the meso-scale component of the two-ship SUMMIX experiment together with RV Meteor (Physical and biochemical exchange-, mixing- and transformation processes in the central Baltic Sea during summer stratification and their controls on the cyanobacterial summer bloom) which was intended to be located at a fixed position nearby RV Elisabeth Mann Borgese in order to survey the water column in high vertical, spatial and parameter resolution, including biogeochemical experiments on board. In addition to the physical parameters, also vertical and horizontal zooplankton net tows as well as water samples taken by CTD bottles were planned

The impact of advection schemes on restratifiction due to lateral shear and baroclinic instabilities

This paper quantifies spurious dissipation and mixing of various advection schemes in idealised experiments of lateral shear and baroclinic instabilities in numerical simulations of a re-entrant Eady channel for configurations with large and small Rossby numbers. In addition, a two-dimensional barotropic shear instability test case is used to examine numerical dissipation of momentum advection in isolation, without any baroclinic effects. Effects of advection schemes on the evolution of background potential energy and the dynamics of the restratification process are analysed. The advection schemes for momentum and tracers are considered using several different methods including a recently developed local dissipation analysis. As highly accurate but computationally demanding schemes we apply WENO and MP5, and as more efficient lower-order total variation diminishing (TVD) schemes we use among others the SPL-max-View the MathML source13 and a third-order-upwind scheme. The analysis shows that the MP5 and SPL-max-View the MathML source13 schemes provide the most accurate results. Following our comprehensive analysis of computational costs, the MP5 scheme is approximately 2.3 times more expensive in our implementation. In contrast to the configuration with a small Rossby number, in which significant differences between schemes are apparent, the different advection schemes behave similarly for a larger Rossby number. Regions of high numerical dissipation are shown to be associated with low grid Reynolds numbers. The major outcome of the present study is that generally positive global numerical dissipation and positive background potential energy evolution delay the restratification process