Testing Munk’s hypothesis for submesoscale eddy generation using observations in the North Atlantic

A high-resolution satellite image that reveals a train of coherent, submesoscale (6 km) vortices along the edge of an ocean front is examined in concert with hydrographic measurements in an effort to understand formation mechanisms of the submesoscale eddies. The infrared satellite image consists of ocean surface temperatures at inline image m resolution over the midlatitude North Atlantic (48.69°N, 16.19°W). Concomitant altimetric observations coupled with regular spacing of the eddies suggest the eddies result from mesoscale stirring, filamentation, and subsequent frontal instability. While horizontal shear or barotropic instability (BTI) is one mechanism for generating such eddies (Munk's hypothesis), we conclude from linear theory coupled with the in situ data that mixed layer or submesoscale baroclinic instability (BCI) is a more plausible explanation for the observed submesoscale vortices. Here we assume that the frontal disturbance remains in its linear growth stage and is accurately described by linear dynamics. This result likely has greater applicability to the open ocean, i.e., regions where the gradient Rossby number is reduced relative to its value along coasts and within strong current systems. Given that such waters comprise an appreciable percentage of the ocean surface and that energy and buoyancy fluxes differ under BTI and BCI, this result has wider implications for open-ocean energy/buoyancy budgets and parameterizations within ocean general circulation models. In summary, this work provides rare observational evidence of submesoscale eddy generation by BCI in the open ocean.


Introduction
Below, we provide supporting material. This includes example imagery during this period, clear-sky occurrences during the entire OSMOSIS period, evidence for connections (albeit speculative) to spiral eddies documented by Scully-Power [1986]; Munk et al. [2000], errors resulting from optimal interpolation of SeaSoar II measurements and estimates of the lateral shear across the front.
1 Clear-sky occurrences (September 2012-September 2013 As mentioned in the manuscript, we provide a list of periods classified as clear-sky according to our definition and which exceed two hours in duration (Table 1). We believe this may help in future analysis of the OSMOSIS record. Note: not all imagery obtained during these periods resulted in stellar imagery. Considerable information might be teased out by using more sophisticated processing in concert with geosynchronous data. Another option might be to identify coverage from the MODIS sensor onboard the Aqua spacecraft. This sensor has a spatial resolution near ∼1 km and would complement these data considerably. Another thing to note is that the visible portion of the electromagnetic spectrum on both the VIIRS and MODIS instruments provides information about chlorophyll concentration. Thus, consideration of an additional sensor could increase the chances of obtaining coincident chlorophyll and in situ (i.e., mooring-and glider-based) measurements. In summary, these clear-sky periods may be beneficial to the reader.
2 Additional infrared imagery Figure 1 provides several example SST images obtained from cross-referencing clearsky conditions with VIIRS onboard Suomi-NPP. Two examples are highlighted. One of these is the unstable front described in the main manuscript on 19 September 2012 (first row, second column). The second pertains to upwelling of waters within an anticyclonic mesoscale eddy west of the observation site during July and August 2013 (e.g., 12 July 2012; fourth row, third column) and which may be evidence of symmetric instability within the mesoscale eddy [Brannigan, 2016].

Spiral eddies in infrared measurements of sea surface temperature?
We stated within the manuscript that the occurrence of swirling vortices along the thermal front was most likely related to "spiral eddies" documented within optical images by Scully-Power [1986]; Munk et al. [2000]. Figure 2a illustrates an example of spiral eddies from the Apollo shuttle missions [Scully-Power, 1986]. Using image processing methods (e.g., morphological operations and normalization), we isolated tracer concentrations elevated above background levels. The resulting binary image is displayed in Figure 2b. Finally, we hand-drew contours of these tracers as objectively as possible, connecting previously unconnected segments ( Figure 2c). The tracer contour has appearance that is similar to the SST contour separating warm and cool waters in the study. In summary, while we cannot state for certain that the observed SST image provides evidence of spiral eddies in SST, we suspect they are produced by the same underlying phenomenon.

Interpolation of SeaSoar II measurements
While useful for understanding the horizontal and vertical structure of ocean fronts, interpolation of discrete measurements from SeaSoar II yield density and velocity fields that are smoothed relative to true values. In particular, the lateral smoothing inherent in the Barnes analysis employed here [Barnes, 1964[Barnes, , 1994] may bias eddy scales obtained in the BTI analysis; its effect on the widths of the horizontally-sheared regions, a and b, is paramount. 4 In order to quantify the lower bound for these quantities, we simulated a jet-like velocity field consisting of constant-vorticity sheets and conducted an optimal interpolation of these data. A comparison of original and processed fields is shown in Figure 3. For a jet-like profile having sheared widths a ′ = b ′ = 8.3 km, the result after the Barnes analysis is a Gaussian-like profile with widths a = b = 20.0 km. That is, the resulting jet has shear width approximately 2.4 times its original scale. We have rounded this to 3.0 to be conservative. Given our estimated shear widths of a = 20.0 and b = 25.0 km, this implies the true widths are no smaller than a ′ = 6.7 and b ′ = 8.3 km, respectively. Note, that the magnitude of the flow is reduced, as well. This suggests the unbiased shear parameter to use for the BTI model is larger: U ′ o ≈ 2U o = (2)(0.24) m/s = 0.48 m/s. We did not use this value within the text since this parameter modifies only the growth rate and not the scale of the most unstable mode. We did, however, use it to estimate the gradient Rossby number (below).
We emphasize that the shear widths obtained above are somewhat conservative. We have done this in order to be explicit about how the horizontal shear model used in the manuscript does not explain the observed eddy sizes. In reality, the true shear widths are likely closer to 20/2.5 = 8 km.

Magnitude of lateral shear across the front
For completion, we document higher-order derivatives of the SeaSoar II data. In general, we are not confident of small-scale features observed in these quantities. This is because the errors arising during the interpolation scheme will tend to amplify when spatial gradients are taken. Nevertheless, the general magnitude of horizontal shear across the front should be well-represented by these estimates. Note: where other optimal interpolation schemes intro-duce errors, we have minimized many of these by using the Barnes analysis [Barnes, 1964[Barnes, , 1994. Figure 4 depicts the gradient Rossby number, Ro = ζ/f ≈ −f −1 ∂u/∂y, estimated from the SeaSoar II data. Note that amplitudes do not exceed 0.125. However, given the smoothing inherent in the interpolation scheme, we estimate lower and upper bounds on this value of 0.1-0.55. These bounds can be obtained as follows. We first subtract from the total current magnitude the background value to obtain U o = 0.24 m s −1 . For the upper bound, we multiply by 2 to obtain U ′ o = 2U o m s −1 , whereas we retain U o only for the lower bound. Finally, we divide by the product of f and the shear width, a. In this calculation, we used a = 8.0 km (upper bound) and a = 20 km (lower bound). [For example, for the upper bound, For geophysical flows, a necessary but insufficient criterion for instability is that the crossfront gradient of potential vorticity, ∂q/∂y, change sign somewhere within the flow. For baroclinic instability, this quantity will be dominated by the cross-front gradient of vertical shear, ∂ 2 u/∂z∂y, whereas for barotropic instability, it will be dominated by the cross-front gradient of relative vorticity, ∂ 2 u/∂y 2 . In Figure 5, we depict the meridional (i.e., cross-front) gradient of potential vorticity, q y = ∂q/∂y. While interpretation of this graphic is beyond the scope of this study, we include it as supporting material since it suggests a two-dimensional instability analysis may be needed. Two features are suggested in this field. First, there is a large change in sign of q y at the pycnocline (all cross-front distances, depths 40-50 m), reflecting the dominance of baroclinic instability. Second, there is a more subtle decrease in this quantity on the northward side of the front (cross-front distances 0-7 km, depths 0-30 m), reflecting the smaller but potential importance of barotropic shear on the northern side of the front. Note: as q y is a second-order derivative, we encourage only qualitative interpretation of this graphic and have therefore provided it only as supporting material.     -7-