Applications

This code was developed with the goal of analyse and extract the energy contained by Eddies and jets in the ocean. However it can be used for a variety of processes. To know more about these processes, please se below:

Kinetic Energy decomposition

In many parts of the ocean, transient processes contain more kinetic energy (commonly known as eddy kinetic energy, or \(EKE\)) than the men kinetic energy (\(MKE\)). Variations in the oceanic energy balance can be diagnosed through \(EKE\), which allows the analysis of positive or negative feedbacks on climate change. However, one difficulty in determining the role of eddies in the ocean transient adjustment to climate change is the lack of a process-based definition of \(EKE\).

The aim of this algorithm is to decompose and analyse \(EKE\) according to different ocean processes. Specifically, the separation of kinetic energy will be recustructed using a 2D gaussian fitting for each closedd eddy detected (\(EKE_{eddy}\)) from the eddy kinetic energy due to meandering jets (\(EKE_{jets}\)) and the background eddy kinetic energy (\(EKE_{background}\)):

\[EKE = EKE_{eddy} + \underbrace{EKE_{jets} + EKE_{background}}_{EKE_{residual}}\]

However, this decomposition represents several challenges like:

• Second order terms which maybe important in the energy balance.

\[KE = MKE + EKE\]

Expanding this equation we obtain:

\[KE = MKE + EKE_{eddy} + \underbrace{EKE_{jets} + EKE_{background}}_{EKE_{residual}} + EKE'_{O^1}\]

Replacing the kinetic energy definition:

\[\hspace{-3cm}\frac{1}{2}\rho_0 (u^2+v^2) = \frac{1}{2}\rho_0 (\bar{u}^2 + \bar{v}^2) + \frac{1}{2}\rho_0 (u_{eddy}^2 + v_{eddy}^2) +\]

\[\hspace{2.7cm}\frac{1}{2}\rho_0 (u_{jets}^2 + v_{jets}^2) + \frac{1}{2}\rho_0 (u_{background}^2 + v_{background}^2) +\]

\[\hspace{0.6cm}\rho_0 (\bar{u}u_{eddy} + \bar{v}v_{eddy}) + \rho_0 (\bar{u}u_{jets} + \bar{v}v_{jets}) +\]

\[\hspace{4cm}\rho_0 (\bar{u}u_{background} + \bar{v}v_{background}) + \rho_0 (u_{eddy}u_{jets} + v_{eddy}v_{jets}) +\]

\[\hspace{0cm} \rho_0 (u_{eddy}u_{background} + v_{eddy}v_{background}) +\]

\[\hspace{-0.6cm} \rho_0 (u_{jets}u_{background} + v_{jets}v_{background})\]

where \(u = \bar{u} + u_{eddy} + u_{jet} + u_{background}\). Assuming \(\iff\) \(\bar{EKE'_{O^1}} \rightarrow 0\) \(\implies\) we can ingore those terms. However, this implications is really hard to prove unless we define an exact way to extract the velocity field for each eddy.

Because of this, the first approach to this problem will be the decomposition of the components.

Heatwaves

Oceanic Tracers

Regional Studies