Energetics of lateral eddy diffusion/advection：Part Ⅲ. Energetics of horizontal and isopycnal diffusion/advection

Gravitational Potential Energy （GPE） change due to horizontal/isopycnal eddy diffusion and advection is examined. Horizontal/isopycnal eddy diffusion is conceptually separated into two steps： stirring and sub scale diffusion. GPE changes associated with these two steps are analyzed. In addition, GPE changes due to stirring and subscale diffusion associated with horizontal/isopycnal advection in the Eulerian coordinates are analyzed. These formulae are applied to the SODA data for the world oceans. Our analysis indicates that horizontal/isopycnal advection in Eulerian coordinates can introduce large artificial diffusion in the model. It is shown that GPE source/sink in isopycnal coordinates is closely linked to physical property distribution, such as temperature, salinity and velocity. In comparison with z-coordinates, GPE source/sink due to stir ring/cabbeling associated with isopycnal diffusion/advection is much smaller. Although isopycnal coordi nates may be a better choice in terms of handling lateral diffusion, advection terms in the traditional Eule rian coordinates can produce artificial source of GPE due to cabbeling associated with advection. Reducing such numerical errors remains a grand challenge.     

Energetics of lateral eddy diffusion/advection：Part Ⅰ. Thermodynamics and energetics of vertical eddy diffusion

Two important nonlinear properties of seawater thermodynamics linked to changes of water density, cabbeling and elasticity(compressibility), are discussed. Eddy diffusion and advection lead to changes in density; as a result, gravitational potential energy of the system is changed. Therefore, cabbeling and elasticity play key roles in the energetics of lateral eddy diffusion and advection. Vertical eddy diffusion is one of the key elements in the mechanical energy balance of the global oceans. Vertical eddy diffusion can be conceptually separated into two steps: stirring and subscale diffusion. Vertical eddy stirring pushes cold/dense water upward and warm/light water downward; thus, gravitational potential energy is increased. During the second steps, water masses from different places mix through subscale diffusion, and water density is increased due to cabbeling. Using WOA01 climatology and assuming the vertical eddy diffusivity is equal to a constant value of 2×103 Pa2/s, the total amount of gravitational potential energy increase due to vertical stirring in the world oceans is estimated at 263 GW. Cabbeling associated with vertical subscale diffusion is a sink of gravitational potential energy, and the total value of energy lost is estimated at 73 GW. Therefore, the net source of gravitational potential energy due to vertical eddy diffusion for the world oceans is estimated at 189 GW.     

Energetics of lateral eddy diffusion/advection：Part Ⅳ. Energetics of diffusion/advection in sigma coordinates and other coordinates

Gravitational potential energy （GPE） source and sink due to stirring and cabbeling associated with sigma dif fusion/ advection is analyzed. It is shown that GPE source and sink is too big, and they are not closely linked to physical property distribution, such as temperature, salinity and velocity. Although the most frequently quoted advantage of sigma coordinate models are their capability of dealing with topography; the exces sive amount of GPE source and sink due to stirring and cabbeling associated with sigma diffusion/advec tion diagnosed from our analysis raises a very serious question whether the way lateral diffusion/advection simulated in the sigma coordinates model is physically acceptable. GPE source and sink in three coordinates is dramatically different in their magnitude and patterns. Overall, in terms of simulating lateral eddy diffu sion and advection isopycnal coordinates is the best choice and sigma coordinates is the worst. The physical reason of the excessive GPE source and sink in sigma coordinates is further explored in details. However, even in the isopycnal coordinates, simulation based on the Eulerian coordinates can be contaminated by the numerical errors associated with the advection terms.     

南海冷涡区域SST及冷涡动能、有效重力位能对热带气旋的响应

选择了12个个例,分析了冷涡区域海表面温度(sea surface temperature, SST)对热带气旋(tropical cyclone, TC)的响应。在TC的影响下,冷涡区域SST降低的最大值在2.7—9.15℃,冷涡平均降温1.35—5.89℃。冷涡SST降低与TC移动速度有很好的反向关联,移动速度越慢,冷涡SST降低越多。冷涡SST降低与TC平均最大风速有较好的正向关联,最大风速越大,冷涡SST降低越多。TC对冷涡的能量改变起着重要的作用,TC经过冷涡后,冷涡的动能(eddy kinetic energy, EKE)、有效重力位能(available gravitational potential energy, AGPE)有明显增长,并且EKE的增长小于AGPE的增长。TC作用前后EKE、AGPE的增长与冷涡区域SST降低的平均呈正向关联,表明在TC的影响下,冷涡的EKE、AGPE的改变能够反映SST降低的程度,或者说SST降低的多少能够反映冷涡EKE、AGPE改变的程度。