Analysis

Figure 1 shows a snapshot (on 1 July 2013) of the surface vorticity in the GoM produced by a data-assim-

ilative simulation based on the U.S. Navy Coastal Ocean Model (NCOM) at 1-km resolution (for details

cf., e.g., Beron-Vera and LaCasce, 2016). Note the wealth of structures spanning mesoscales (50–200

km) and marginally submesoscales (10–25 km). An outstanding mesoscale structure is the anticyclonic

ring shed from the LC in the center of the domain . The presence of marginally submesoscale structures is

ubiquitous in the GoM, including the Yucatan Channel. Note for instance the chain of Karman-like vor-

tices immediately upstream of Cozumel Island. Similar vortex streets are seen downstream of the west -

ernmost tip of Cuba in other dates. And sequences of vorticity snapshots reveal further that the transport

across the Channel is accomplished by a convoluted mixture of seemingly coherent vortices and fila-

ments. Satellite-derived ocean color imagery, when available, reveals some of these simulated aspects of

the surface circulation as is evident in the inset in Figure 1. With a spatial resolution of O(1) km and a

temporal resolution of O(1) hr, HFR-derived surface currents in the region will provide a unique opportu-

nity to investigate their significance, further explore their occurrence down into the submesoscale range,

and also get insight into the physics underlying them.

The analysis of HFR-derived surface currents will be done along two different lines. One line will make

use of nonlinear dynamics methods designed to reveal coherent flow structures in an observed-indepen-

dent (or objective) manner. Both Lagrangian (Haller and Beron-Vera, 2012; 2014; Haller et al., 2016) and

Eulerian (Serra-Haller-16) methods for revealing coherent structures objectively are available. Eulerian

methods do not require trajectory integration and thus are particularly well suited to dealing with velocity

fields defined on a limited spatial domains that are open as is the case of HFR-derived flow. The La -

grangian methods in turn enable transport assessments. Recent application of the Lagrangian methods

(Beron-Vera et al., 2018) has revealed from the NCOM velocities in the region (marginally) subme-

soscale vortices with the ability of transporting coherently fluid from the southern coast of Cuba into the

Caribbean Sea and then into the Yucatan Channel area. We will seek to reveal similar structures there to

evaluate their transport across the Channel into the GoM. There is novel technology to frame this objec-

tively as well (Karrasch, 2016; Hofherr and Karrasch, 2018) and we will consider it. Clearly transport

here will necessarily restrict to two-space dimensions given the nature of the velocity data. However ro -

bust coherent structures in such data can be expected not to be confined at the ocean surface. We will

seek to verify this in velocity data measured by the ADCP to be used in HFR-derived velocity validation.

The transport across the Yucatan Channel is a critical forcing of the GoM LC system and the LC in par-

ticular. Thus framing it with precision is important for informing circulation models.

A second line of analysis will focus on the computation of kinetic energy (E) wavenumber (k) spectra and

fluxes to diagnose characteristics of the submesoscale surface currents as inferred from the HFRs. This is

important to shed light on the way that energy is transferred from large to dissipative scales, which is a

subject of intense debate in oceanography and in particular that of the GoM (Poje et al., 2014; Beron-Vera

and LaCasce, 2016). It is well known (cf., e.g., Callies and Ferrari, 2013, for the exposition that follows)

that interior quasigeostrophic (QG) turbulence predicts E ~ k−3 below the Rossby deformation scale

(about 45 km in the GoM) with a downscale enstrophy cascade. Surface QG turbulence, by contrast, pre-

dicts E ~ k−5/3 with energy cascading downscale. Ageostrophic effects leading to frontogenesis can make

E flatter (E ~ k−2 ) and most importantly reverse the direction of the energy cascade of a surface QG-like

flow from upscale in the QG limit to downscale. The instability of a wintertime deep mixed layer can

also make E ~ k−2 but with eddies are confined between the ocean surface and the mixed-layer base as

opposed to surface QG where the eddies are confined toward the surface. Internal waves are another

source of submesoscale variability with E ~ k−2 in the short-wave limit and flatten out at scales larger

than about 10 km. There are relationships between the one-dimensional spectra of longitudinal and trans-

verse components of kinetic energy (Callies and Ferrari, 2013) as well as recent wave-vortex and

Helmholtz decompositions (Buhler et al., 2015; Lindborg, 2015) that help constrain the dominant mecha-

nism of submesoscale energy production, which will be considered.

References

Beron-Vera, F. J., Hadjighasem, A., Xia, Q., Olascoaga, M. J. and Haller, G. (2018a). Coherent La-grangian swirls among submesoescale motions. Proc. Natl. Acad. Sci. USA, doi:10.1073/pnas.1701392115.

Beron-Vera, F. J. and LaCasce, J. H. (2016). Statistics of simulated and observed pair separa-tions in the Gulf of Mexico. J. Phys. Oceanogr. 46 (7), 2183–2199.

Callies, J. and Ferrari, R. (2013). Interpreting energy and tracer spectra of upper-ocean turbu-lence in the submesoscale range (1–200 km). J. Phys. Oceanogr. 43, 2456–2474.

Haller, G. (2015). Lagrangian coherent structures. Ann. Rev. Fluid Mech. 47, 137–162.

Haller, G. and Beron-Vera, F. J. (2013). Coherent Lagrangian vortices: The black holes of turbulence. J. Fluid Mech. 731, R4.

Haller, G. and Beron-Vera, F. J. (2012). Geodesic theory of transport barriers in two-dimensional flows. Physica D 241, 1680–1702.

Haller, G., Hadjighasem, A., Farazmand, M. and Huhn, F. (2016). Defining coherent vortices objectively from the vorticity. J. Fluid Mech. 795, 136–173.

Hofherr, F. and Karrasch, D. (2018). Lagrangian transport through surfaces in compressible flows. SIAM Journal on Applied Dynamical Systems 17, 526–546.

Karrasch, D. (2016). Lagrangian transport through surfaces in volume-preserving flows. SIAM J. Appl. Math. 76, 11781190.

Poje, A. C., Ozgokmen, T. M., Lipphart, Jr., B., Haus, B., Ryan, E., Haza, A. C., Jacobs, G., A. Reniers, M. J. O., Novelli, G., Griffa, A., Beron-Vera, F. J., Chen, S., Hogan, P., Coelho, E., Kirwan, Jr., A., Hunt -ley, H. and Mariano, A. (2014). The nature of surface dispersion near the Deepwater Horizon oil spill. Proc. Nat. Acad. Sci. USA 111, 12693–12698.

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Figure 1. A snapshot on 1 July 2013 of sea surface vorticity produced a data-assimilative simulation of the GoM based on the U.S. Navy Coastal Ocean Model (NCOM) at 1-km resolution. Indicated is a do-main including the Yucatan Channel where HFR-derived surface currents will be available for analysis. The inset shows a MODIS (Moderate Resolution Imaging Spectroradiometer) derived chlorophyll-a concentration map on 18 February 2014.