Eddy-mean flow energy exchange depends on three variables

Eddies are large, rotating currents that contribute to ocean mixing and transport of heat and salt in seawater. Importantly, eddies modify ocean circulation and can influence climate variability by interacting with larger, more dominant ocean currents, or mean flow.

When eddies and large ocean currents interact with one another, they exchange energy, momentum and enstrophy, a measure of the strength of the swirling motion in fluids. In order to better model the dynamics between eddies and the larger mean flow, however, scientists must find a way to accurately simulate the exchange between the two types of currents.

In order to better understand and calculate eddy-mean flow energy exchange, scientists from the Tianjin University, The University of California and the Massachusetts Institute of Technology designed a research study to identify how specific variations in mean flow influence eddy-mean flow feedback and found a new way to characterize eddies in an energy flow model. The team recently published their study in the journal Ocean-Land-Atmosphere Research.

“The design of non-eddy-resolving numerical models requires a good understanding and an appropriate representation of the eddy-mean flow feedback. This [research] aims to solve two questions: 1) What is the relative importance of the along-stream and cross-stream variations in mean flow to eddy-mean kinetic energy exchange? [and] 2) Are there explicit mathematical formulas that link the eddy-mean energy exchange terms of the Lorenz energy diagram with parameters for eddy geometry?” said Ru Chen, professor at Tianjin University and first author of the research paper.

Specifically, large mean flow ocean currents often vary in the along-mean flow direction (along-stream) and in the cross-mean flow direction (cross-stream) in the real world, and these variations contribute to the exchange of energy between eddies and mean flow. The research team scrutinized these variations and their effects on eddy-mean energy exchange in the context of the Lorenz energy diagram, a comprehensive model that accounts for the variables and processes responsible for energy exchange in a fluid system.

“The eddy-mean kinetic energy exchange term can be [separated] into three parts: one associated with the cross-stream variation in mean flow, one associated with the along-stream variation in mean flow, and one associated with the variation in mean flow direction. All… three parts contribute considerably to eddy mean kinetic energy exchange and are linked with parameters for eddy geometry,” said Chen.

The research team also succeeded in creating a kinematic framework for eddy-mean energy exchange that describes the motion of large ocean and eddy currents without accounting for the forces acting on each current or their physical properties. In their Lorenz energy diagram framework, the eddy energy change rate is expressed as a function of geometric eddy parameters through explicit formulas, which is a unique approach.

“The framework we developed is a new tool that could be useful for improvements in eddy parameterization and for eddy-mean flow interaction studies,” said Chen. One reason is that the framework can offer more basic interpretations and conceptual diagrams of eddy geometry patterns in the Lorenz energy diagram.

The research team’s framework may also encourage the creation of eddy parameterization schemes that include mixing nonlocality, or the degree to which mixing in a system is nonlocal. Ellipses, or visual representation of the energy transfer between different ocean currents, of eddy momentum can be anisotropic, or have different physical properties when measured in different directions. Interestingly, eddy momentum ellipses can resemble mixing nonlocality ellipses in certain flow regimes, or different ways that fluids move.

The results of this study will also help advance efforts to enhance geometric approaches to ocean eddy-mean energy exchange models built on the Gent-McWilliams scheme, a mathematical model developed to simulate the effects of eddies on larger ocean currents.

“In the future, the geometric formulas of other terms in the Lorenz energy diagram can be explored to geometrically interpret the nonlocality of eddy-mean flow interaction. The generation of eddy enstrophy may also be expressed in a form that involves geometric parameters using a similar procedure. These work[s] would offer new tools for geometrically interpreting eddy-mean energy exchange and ultimately advance the development of eddy parameterizations,” said Chen.

Yi Yang, Qianqian Geng and Junyi Wang from the Tianjin Key Laboratory for Marine Environmental Research and Service at the School of Marine Science and Technology at Tianjin University in Tianjin, China; Andrew Stewart from The University of California, Los Angeles, CA; and Glenn Flierl from the Massachusetts Institute of Technology in Cambridge, MA also contributed to this research.

This work was supported by the National Natural Science Foundation of China (grant number 42076007) and by the First-Class University Construction Fund.