A Multi-Envelope generalised coordinate system for numerical ocean modelling is introduced. In this system, computational levels are curved and adjusted to multiple 'virtual bottoms' (aka envelopes) rather than following geopotential levels or the actual bathymetry. This allows defining computational levels which are optimised to best represent different physical processes in different subdomains of the model. In particular, we show how it can be used to improve the representation of tracer advection in the ocean interior. The new vertical system is compared with a widely used z-partial step scheme. The modelling skill of the models is assessed by comparison with the analytical solutions or results produced by a model with a very high resolution z-level grid. Three idealised process-oriented numerical experiments are carried out. Experiments show that numerical errors produced by the new scheme are much smaller than those produced by the standard z-partial step scheme at a comparable vertical resolution. In particular, the new scheme shows superiority in simulating the formation of a cold intermediate In order to minimise the disadvantages of the various vertical coordinate sys-43 tems, further modifications were introduced either to the vertical grids themselves 44 or to the numerical representation of the governing equations. For example, the 45 introduction of shaved (Adcroft et al., 1997) or partial (Pacanowski et al., 1998) 46 cells which slightly change the shape of 'pure' z-coordinate grids was proposed to 47 improve the representation of bottom topography in z-models. The z-partial steps 48 approach is now widely used for global (Barnier et al., 2006) and regional (e.g., 49 Oddo et al. 2009; Trotta et al. 2016) ocean models. A stretched terrain-following s-50 coordinate system(Song and Haidvogel, 1994) and its several variants (e.g, Madec 51 et al. 1996; Siddorn and Furner 2013) as well as advanced methods in calculation 52 of pressure gradients (Shchepetkin, 2003) were developed to improve σ-coordinates 53 flexibility and accuracy. 54 The concept of a generalised vertical coordinate system (see for example Kasa-55 hara 1974 or Mellor et al. 2002) allowed in principle the development of vertical 56 grids of various complexity, as for example the hybrid vertical schemes where dif-57 ferent 'pure' grids were applied to different sub-domains of the ocean. The aim of 58 this was to better represent the differing physical processes which might prevail in 59 different sub-domains, by using one specific grid rather than another. Examples 60 of those methods are the HYCOM model (62 or the Song and Hou (2006) parametric vertical coordinate system. 63 The idea of Arbitrary Lagrangian-Eulerian (ALE) vertical coordinates (Hirt 64 et al., 1974) permitted the development of z * -(Adcroft and Campin, 2004) and 65z -coordinates (Leclair and Madec, 2011) and the adaptive σ-based coordinate 66 (Hofmeister et al., 2010). 67 A significant improvement in terrain-following schemes was achieved by in-68 troducing the id...
The development of a 3D computational mesh to improve the representation of dynamic processes: The Black Sea test case Bruciaferri, D
The sinking of dense shelf waters down the continental slope (or "cascading") contributes to oceanic water mass formation and carbon cycling. Cascading over steep bottom topography is studied here in numerical experiments using POLCOMS, a 3-D ocean circulation model using a terrain-following s-coordinate system. The model setup is based on a laboratory experiment of a continuous dense water flow from a central source on a conical slope in a rotating tank. The governing parameters of the experiments are the density difference between plume and ambient water, the flow rate, the speed of rotation and (in the model) diffusivity and viscosity. The descent of the dense flow as characterized by the length of the plume as a function of time is studied for a range of parameters. Very good agreement between the model and the laboratory results is shown in dimensional and nondimensional variables. It is confirmed that a hydrostatic model is capable of reproducing the essential physics of cascading on a very steep slope if the model correctly resolves velocity veering in the bottom boundary layer. Experiments changing the height of the bottom Ekman layer (by changing viscosity) and modifying the plume from a 2-layer system to a stratified regime (by enhancing diapycnal diffusion) confirm previous theories, demonstrate their limitations and offer new insights into the dynamics of cascading outside of the controlled laboratory conditions.
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