Diffusivity from SMLT
This protocol is extracted from research article:
Ocean mesoscale mixing linked to climate variability
Sci Adv, Jan 23, 2019; DOI: 10.1126/sciadv.aav5014

Here, we applied SMLT to attempt to reconstruct the temporal variability observed in Koc from simple physical principles. We hypothesize that the main aspects of the flow, which vary in time within Eqs. 4 and 3, are U and urms (derived from large scale and small scale components of the velocity according to the decomposition described earlier) and assume that Leddy, γ, Γ, and cw do not vary in time. In this case, the diffusivity formula Eq. 4 can be written asEmbedded Image(6)

For small amplitude variability, we can linearize this to findEmbedded Image(7)where the overbar indicates the long-term time mean and the Δ is a time fluctuation.

We find ΔK0 and ΔS by Taylor expansion. ΔK0 is trivialEmbedded Image(8)

The suppression factor requires a bit more algebraEmbedded Image(9)

If not otherwise noted, then the diffusivity variability and its contributions (e.g., ΔK, Embedded Image, and Embedded Image) are shown with the mean diffusivity Embedded Image (derived from long-term means of U and urms according to Eqs. 4 and 3) added.

In this study, we used constant values for Γ = 0.35, γ = 1/4 days [see (19)]. The Doppler shifted phase speed is calculated as Embedded Image, calculated using the depth- and time-averaged zonal flow Embedded Image and the first baroclinic Rossby radius LD, both estimated from an ocean state estimate [as in (19)]. The observed eddy length-scale was estimated from altimetry observations (41) [see also (19)].

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