Energetics of lateral eddy diffusion/advection:Part Ⅱ. Numerical diffusion/diffusivity and gravitational potential energy change due to isopycnal diffusion
doi: 10.1007/s13131-014-0410-0
Energetics of lateral eddy diffusion/advection:Part Ⅱ. Numerical diffusion/diffusivity and gravitational potential energy change due to isopycnal diffusion
-
摘要: Study of oceanic circulation and climate requires models which can simulate tracer eddy diffusion and advection accurately. It is shown that the traditional Eulerian coordinates can introduce large artificial horizontal diffusivity/viscosity due to the incorrect alignment of the axis. Therefore, such models can smear sharp fronts and introduce other numerical artifacts. For simulation with relatively low resolution, large lateral diffusion was explicitly used in models;therefore, such numerical diffusion may not be a problem. However, with the increase of horizontal resolution, the artificial diffusivity/viscosity associated with horizontal advection in the commonly used Eulerian coordinates may become one of the most challenging obstacles for modeling the ocean circulation accurately. Isopycnal eddy diffusion (mixing) has been widely used in numerical models. The common wisdom is that mixing along isopycnal is energy free. However, a careful examination reveals that this is not the case. In fact, eddy diffusion can be conceptually separated into two steps: stirring and subscale diffusion. Due to the thermobaric effect, stirring, or exchanging water masses, along isopycnal surface is associated with the change of GPE in the mean state. This is a new type of instability, called the thermobaric instability. In addition, due to cabbeling subscale diffusion of water parcels always leads to the release of GPE. The release of GPE due to isopycnal stirring and subscale diffusion may lead to the thermobaric instability.Abstract: Study of oceanic circulation and climate requires models which can simulate tracer eddy diffusion and advection accurately. It is shown that the traditional Eulerian coordinates can introduce large artificial horizontal diffusivity/viscosity due to the incorrect alignment of the axis. Therefore, such models can smear sharp fronts and introduce other numerical artifacts. For simulation with relatively low resolution, large lateral diffusion was explicitly used in models;therefore, such numerical diffusion may not be a problem. However, with the increase of horizontal resolution, the artificial diffusivity/viscosity associated with horizontal advection in the commonly used Eulerian coordinates may become one of the most challenging obstacles for modeling the ocean circulation accurately. Isopycnal eddy diffusion (mixing) has been widely used in numerical models. The common wisdom is that mixing along isopycnal is energy free. However, a careful examination reveals that this is not the case. In fact, eddy diffusion can be conceptually separated into two steps: stirring and subscale diffusion. Due to the thermobaric effect, stirring, or exchanging water masses, along isopycnal surface is associated with the change of GPE in the mean state. This is a new type of instability, called the thermobaric instability. In addition, due to cabbeling subscale diffusion of water parcels always leads to the release of GPE. The release of GPE due to isopycnal stirring and subscale diffusion may lead to the thermobaric instability.
-
Bryan F. 1987. Parameter sensitivity of primitive equation ocean circulation models. J Phys Oceanogr, 17: 970-984 Carton J A, Giese B S. 2008. A reanalysis of ocean climate using simple ocean data assimilation (SODA). Mon Weather Rev, 136: 2999-3017 Conkright M E, Locarnini R A, Garcia H E, et al. 2002. World Ocean Atlas 2001: Objective analysis, data statistics, and figures, CD-ROM Documentation. National Oceanographic Data Center, Silver Spring, MD, 17 Eden C, Willebrand J. 1999. Neutral density revisited. Deep-Sea Res Pt II, 46: 33-54 Forster T D, Carmack E C. 1976. Frontal zone mixing and Antarctic bottom water formation in the southern Weddell Sea. Deep-Sea Res, 23: 301-317 Gent P R, McWilliams J C. 1990. Isopycnal mixing in ocean circulation models. J Phys Oceanogr, 20: 150-155 Huang R X. 2014a. Adiabatic density surface, neutral density surface, potential density surface and mixing path. Manuscript submitted to Journal of tropical oceanography Huang R X. 2014b. Energetics of lateral eddy diffusion/advection: Part Ⅰ. Thermodynamics and energetics of vertical eddy diffusion. Acta Oceanol Sin, 33 (3): 1-18 Hui W H. 2007. The unified coordinate system in computational fluid dynamics. Commu Compu Phys, 2: 577-610 Hui W H, Li P Y, Li Z W. 1999. A unified coordinate system for solving the two-dimensional Euler equations. J Comput Phys, 153: 596 Hui W H, Kudriakov S. 2001. A unified coordinate system for solving the three-dimensional Euler equations. J Comput Phys, 172: 235 Hui W H, Xu K. 2012. Computational Fluid Dynamics Based On The Unified Coordinates. Beijing: Science Press, 198 McDougall T J. 1987a. Neutral surfaces. J Phys Oceanogr, 17: 1950-1964 McDougall T J. 1987b. The vertical motion of submesoscale coherent vorticies across neutral surfaces. J Phys Oceanogr, 17: 2334-2342 McDougall T J. 1987c. Thermobaricity, cabbeling, and water-mass conversion. J Geophys Res, 92: 5448-5464 Nycander N. 2011. Energy conversion, mixing energy, and neutral surfaces with a nonlinear equation of state. J Phys Oceanogr, 41: 28-41 Ledwell J R, Watson A J, Law C S. 1998. Mixing of a tracer in the pycnocline. J Geopys Res, 103: 21499-21529 Lumpkin R, Treguier A-M, Speer K. 2002. Lagrangian eddy scales in the Northern Atlantic Ocean. J Phys Oceanogr, 32: 2425-2440 Obuko A. 1971: Oceanic diffusion diagrams. Deep-Sea Res, 18: 789-802 Qian Y-K, Peng S, Li Y. 2013. Eulerian and Lagrangian statistics in the South China Sea as deduced from surface drifters. J Phys Oceanogr, 43: 726-743 Ruddick B, Kerr O. 2003: Oceanic thermohaline intrusions: theory. Progr Oceanogr, 56: 483-497 Ruddick B, Richards K. 2003: Oceanic thermohaline intrusions: observations. Progr Oceanogr, 56: 499-527 Spivakovskaya D, Heemink A W, Deleersnijder E. 2007. Lagrangian modelling of multi-dimensional advection-diffusion with space-varying diffusivities: theory and idealized test cases, 57(3): 189-203 Tulloch R, Ferrari R, Jahn O, et al. 2013. Direct estimate of lateral eddy diffusivity upstream of Drake Passage, manuscript Wagner D H. 1987. Equivalence of Eulerian and Lagrangian equations of gas dynamics for weak solutions. J Differ Equations, 68: 118-136 Zheng C, Wang P P. 1999. MT3DMS: a modular three-dimensional multispecies transport model for simulation of advection, dispersion and chemical reactions of contaminants in groundwater systems;documentation and user's guide. Alabama Univ University
点击查看大图
计量
- 文章访问数: 1032
- HTML全文浏览量: 36
- PDF下载量: 1218
- 被引次数: 0