1. Introduction
In Barkan et al. (2017, hereinafter Part I), we used a suite of realistic submesoscale-resolving numerical simulations to characterize surface submesoscale statistics and spatial patterns in the northern Gulf of Mexico (GoM) during winter and summer, with a particular emphasis on understanding the role played by the Mississippi–Atchafalaya River system (hereinafter rivers). The northern GoM has recently received much attention because of the 2010 Deepwater Horizon oil spill that took place in the De Soto Canyon. Following this catastrophic event, two major experiments attempted to quantify and understand the flow dynamics that determined the transport and dispersion mechanisms of contaminants in this region. The Grand Lagrangian Deployment (GLAD) experiment took place in the summer of 2012 and demonstrated, through the analysis of a large number of drifter trajectories, that submesoscale currents dominate the dispersion statistics in the northern GoM. More recently, in the winter of 2016, the Lagrangian Submesoscale Experiment (LASER) aimed at exploring a different season, focusing on both mean dispersion statistics and individual submesoscale features.
In Part I, the comparison between two statistically equilibrated solution sets with (With-River) and without (No-River) river forcing demonstrated that, on average, the rivers tend to suppress submesoscale currents in winter and enhance them in summer and that such tendencies increase with resolution. The suppression is most prominent wherever fresh river water is more abundant and outside of the mesoscale Loop Current eddies. This is the case in winter east of the Mississippi River delta or Bird’s Foot. In summer, the enhancement is stronger than the suppression during winter and quantifiable throughout most of the computational domain. These river effects are rationalized in terms of scaling arguments that relate submesoscale current magnitudes to the surface boundary layer depth and lateral buoyancy gradients. Riverine outflow enhances submesoscale currents by increasing lateral buoyancy gradients but suppresses them by decreasing boundary layer depth.
In this paper, we review the model setup (section 2) and analyze temperature–salinity relations with an emphasis on the role of submesoscale currents (section 3). In section 4, we investigate the cross-shelf transport mechanisms of fresh river water west of the Bird’s Foot and in the river jet region east of the Bird’s Foot. Finally, in section 5, we provide a summary of our findings.
2. Model setup
The numerical simulations are carried out with the Regional Oceanic Modeling System (ROMS; Shchepetkin and McWilliams 2005) using a nonlinear equation of state (Shchepetkin and McWilliams 2011) and a one-way nesting procedure (Mason et al. 2010) and focusing on solutions in the northern GoM region with an approximately 500-m, nearly isotropic, horizontal resolution. The vertical stretching parameters (see Table 1 in Part I) are designed to have vertical resolution of approximately 5–7 m in the near-surface boundary layer offshore and much finer nearshore. The atmospheric forcing is climatological with a QuikSCAT-based daily product of scatterometer wind stresses (Risien and Chelton 2008), CORE (Large and Yeager 2009) monthly heat flux atmospheric forcing, and HOAPS (Andersson et al. 2010) monthly freshwater atmospheric forcing. No tidal forcing is used, and a daily river forcing is applied based on daily river volume flux data from the USGS (http://waterdata.usgs.gov/nwis/rt) for the year 2010. The analysis is carried out based on 2 years of equilibrated solution sets for winter (January, February, March) and summer (June, July, August) months, with (With-River) and without (No-River) riverine forcing, using a twice-per-day output frequency. Additional information about the numerical setup is provided in Part I.
For the Lagrangian tracer simulations in this work, the advection is performed offline using the ROMS hourly averaged horizontal velocity field for the month of February and the larval transport Lagrangian model (LTRANS), version 2b (North et al. 2011). We consider multiple releases of 5019 particles seeded uniformly in circular clusters of 40-km diameter [more details available in Choi et al. (2017, hereinafter Part III)].
3. Temperature–salinity relations
The analysis of the numerical simulations at 500-m horizontal resolutions presented in Part I and the observations of extremely sharp surface temperature gradients made by M. J. Molemaker et al. (2017, unpublished manuscript) motivate us to investigate the temperature–salinity (T–S) relations in the northern GoM.
A schematic illustrating the ranges spanned by the density ratio 
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
A schematic illustrating the ranges spanned by the density ratio
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
A schematic illustrating the ranges spanned by the density ratio
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
Ferrari and Rudnick (2000) and Rudnick and Martin (2002) have shown that typical 
Representative snapshots of Tux during winter and summer for the With-River and No-River solutions are shown in Fig. 2. The spatial maps of Tuy are very similar (not shown) so that (6) is a good approximation in these solutions.2 During winter, the With-River solution shows a clear signature of the Mississippi plume with values between 0 and π/4 (Fig. 2a). This indicates that the river outflow is opposing but dominated by salinity gradients. The same is true on the shelf both east and west of the Bird’s Foot. Away from the river mouths, Tux is close to π/2, indicating that the density gradients there are temperature dominated. In the No-River solution (Fig. 2b) values are much larger than π/4 throughout most of the computational domain, indicating that the density gradients are temperature dominated. The nearly zero Tux values very close to shore are associated with the elevated levels of precipitation along the coast (Fig. 3). The reinforcing and temperature-dominated signal near the southern boundary is associated with the Loop Current that brings warmer and fresher waters of Caribbean origin.
A snapshot of Tux [(5)] at the surface during (a) winter and (c) summer for the With-River solution and during (b) winter and (d) summer for the No-River solution.
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
A snapshot of Tux [(5)] at the surface during (a) winter and (c) summer for the With-River solution and during (b) winter and (d) summer for the No-River solution.
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
A snapshot of Tux [(5)] at the surface during (a) winter and (c) summer for the With-River solution and during (b) winter and (d) summer for the No-River solution.
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
Climatological HOAPS (Andersson et al. 2010) monthly mean surface freshwater flux (E − P) in (a) January and (b) September, the months corresponding to the winter and summer Tux snapshots, respectively, in Fig. 2.
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
Climatological HOAPS (Andersson et al. 2010) monthly mean surface freshwater flux (E − P) in (a) January and (b) September, the months corresponding to the winter and summer Tux snapshots, respectively, in Fig. 2.
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
Climatological HOAPS (Andersson et al. 2010) monthly mean surface freshwater flux (E − P) in (a) January and (b) September, the months corresponding to the winter and summer Tux snapshots, respectively, in Fig. 2.
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
During summer, Tux in the With-River solution is mainly positive with values between 0 and π/4 (Fig. 2c), suggesting that salinity dominates the density gradients in this season. This results from the river outflows being at their maximum. In the No-River solution, density gradients are mainly dominated by temperature, except for a narrow region very close to the shelf, where precipitation contributes freshwater anomalies (Fig. 3), and for the edges of the mesoscale structures that are compensated.
The PDFs of Tux during winter and summer are shown in Fig. 4. We distinguish between shelf regions, defined as shallower than 150 m, and offshore regions, defined as deeper than 500 m. The PDFs of Tuy are nearly identical (not shown), which further supports the validity of the approximation [(6)] in our solutions. None of the PDFs, except for the offshore No-River solution during summer, have a peak near π/4, suggesting that the northern GoM does not exhibit the more commonly observed compensated signal in the mixed layer. In winter the PDF shapes offshore support a clear temperature-dominated signal independent of the riverine forcing and resemble the one measured by Rudnick and Martin (2002) for a subpolar front in the western northern Atlantic in April. In the remaining panels, the PDFs in the With-River and No-River solutions differ, highlighting that the rivers govern the T–S distribution in the northern GoM.
PDFs of Tux [(5)]. Shelf regions are defined as shallower than 150 m, and offshore regions are defined as deeper than 500 m.
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
PDFs of Tux [(5)]. Shelf regions are defined as shallower than 150 m, and offshore regions are defined as deeper than 500 m.
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
PDFs of Tux [(5)]. Shelf regions are defined as shallower than 150 m, and offshore regions are defined as deeper than 500 m.
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
During winter, on the shelf, the With-River PDF exhibits a weaker temperature-dominated signal, compared to the offshore one, together with a salinity-dominated and opposing peak that is associated with the riverine forcing. In the No-River solution, the temperature-dominated peaks are much more pronounced, illustrating that the warmer offshore water (Fig. 4, offshore winter panel) can reach all the way to the shelf in the absence of river outflow. The salinity-dominated peak is more symmetric and concentrated around Tux = 0, compared with the With-River PDF, and is associated with nearshore precipitation patterns (Fig. 3).
During summer, the differences between the offshore PDFs in the No-River and With-River solutions are quite striking. In the With-River solution, the signal is mainly opposing and salinity dominated with most of the values between 0 and π/4. This illustrates the increased influence of the rivers in summer (see also Fig. 2). In the No-River solution, the PDF peak shifts to the compensation value of +π/4 with a secondary peak in the opposing and temperature-dominated range.3 On the shelf, both With-River and No-River PDFs have a clear salinity-dominated signal that is wider in the With-River solution, similar to winter. In addition, a temperature-dominated signal is only present in the No-River PDF, suggesting again that temperature-dominated water masses have the potential to reach the shore in the absence of river forcing.
Relating T–S compensation to submesoscale currents
To more accurately interpret the Turner angles with respect to submesoscale currents, we focus on flow features with temperature and salinity gradients that are strong compared with background values. To this end we compute the conditional PDFs only where α2∇hT2 + β2∇hS2 values are larger than a tenth of the mean value. This threshold is chosen to be the value in the cumulative distribution function of α2∇hT2 + β2∇hS2, where the slope flattens out (not shown) and includes approximately 8% of the domain. These frontal Tux PDFs are shown in Fig. 5. The large differences between the With-River and No-River solutions in all cases demonstrate the significant role of rivers in governing the surface submesoscale flow in the northern GoM during both summer and winter.
Conditional PDFs of Tux [(5)] computed in flow regions where α2∇hT2 + β2∇hS2 is larger than a tenth of the mean (see section 3 for detail). Shelf regions are defined as shallower than 150 m, and offshore regions are defined as deeper than 500 m.
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
Conditional PDFs of Tux [(5)] computed in flow regions where α2∇hT2 + β2∇hS2 is larger than a tenth of the mean (see section 3 for detail). Shelf regions are defined as shallower than 150 m, and offshore regions are defined as deeper than 500 m.
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
Conditional PDFs of Tux [(5)] computed in flow regions where α2∇hT2 + β2∇hS2 is larger than a tenth of the mean (see section 3 for detail). Shelf regions are defined as shallower than 150 m, and offshore regions are defined as deeper than 500 m.
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
In winter, the conditional PDFs of the With-River and No-River solutions are considerably different offshore, while they were nearly identical when computed over the entire domain (Fig. 4, offshore winter). This illustrates the care that must be practiced when interpreting Turner angle PDFs with respect to submesoscale currents. In the No-River solution, the temperature-dominated signal remains, implying that it is indeed a frontal signal. In the With-River solution, however, the peak at −π/2 is substantially reduced, whereas a new peak emerges in the salinity-dominated and opposing range that is associated with the freshwater river fronts. On the shelf, the changes to the No-River frontal PDF are again minor compared with the PDF of the entire region (Fig. 4, shelf winter), whereas for the With-River solution the temperature-dominated peaks are completely eliminated. This illustrates that the rivers prevent the offshore, temperature-dominated water masses from reaching the shelf at the surface.
In summer, the With-River solution has very similar frontal PDFs on the shelf and offshore, although the distribution is less symmetric offshore and is skewed toward the opposing range. Furthermore, the temperature-dominated tails seen in the general PDFs during summer (Fig. 4, bottom panels) are now completely missing. In the No-River solution, the perfectly compensated signal at +π/4 offshore as well as the temperature-dominated one are more pronounced in the frontal PDFs. This compensated signal corresponds to the edges of the mesoscale structures shown in Fig. 2d. On the shelf, the temperature-dominated peaks are reduced compared with the general PDFs, and the peak around zero is wider and quite similar to the With-River one, suggesting that it is largely dominated by evaporation minus precipitation (E − P) forcing.
A crucial assumption of the physical model describing how compensation arises in the mixed layer (section 3) is that the horizontal eddy diffusivity scales nonlinearly with the horizontal buoyancy gradient (Ferrari and Young 1997). Under this assumption, the eddy diffusivity in locations where the spice gradient is much larger (or smaller) than the buoyancy gradient will tend to dissipate buoyancy much faster than spice and consequently align temperature and salinity gradients, thereby leading to compensation (Ferrari and Paparella 2003). This suggests that in regions with large positive T–S covariance 
To investigate this argument in our solutions, representative snapshots of the T–S covariance 
Representative snapshots of the T–S covariance 
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
Representative snapshots of the T–S covariance
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
Representative snapshots of the T–S covariance
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
To test this hypothesis we compute a Hovmöller diagram of the Tux PDFs during the first 18 days of February in the With-River solution offshore (Fig. 7). To focus on submesoscale structures, we only account for flow regions where α2∇hT2 + β2∇hS2 is larger than a tenth of the spatial mean at every output time. Overall, a persistent temperature-dominated signal, associated with the offshore temperature-dominated fronts, is found, as shown in Fig. 8 (top). In addition, there is a clear tendency toward an opposing signal, in agreement with the seasonal-averaged frontal PDF (Fig. 5, offshore winter). A diurnal cycle in the PDFs around Tux ≈ −π/2 is also visible; however, its analysis is deferred to a future study. Most interestingly, we note an evolution in the PDFs from a salinity-dominated signal around day 6 toward a nearly compensated signal around day 9. This evolution toward compensation corresponds to offshore advection of the river-forced, salinity-dominated gradients that are stirred and mixed with the surrounding Loop Current temperature-dominated gradients (Fig. 8, top). In addition, the APE stored in the salinity-dominated fronts is gradually being released (positive wb in Fig. 8, bottom), consistent with submesoscale restratification processes.
Hovmöller diagram of Tux and 
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
Hovmöller diagram of Tux and
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
Hovmöller diagram of Tux and
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
Snapshots of (top) Tux and (bottom) wb at four times relative to 1 Feb in the With-River solution, which corresponds to the evolving nearly compensated peak in Fig. 7. The river water, which is salinity dominated when (top left) entering the domain, gradually evolves toward compensation as it is (top right) advected offshore. The corresponding wb signal is (bottom left) positive and strongest at earliest time and (bottom right) gradually decreases with time.
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
Snapshots of (top) Tux and (bottom) wb at four times relative to 1 Feb in the With-River solution, which corresponds to the evolving nearly compensated peak in Fig. 7. The river water, which is salinity dominated when (top left) entering the domain, gradually evolves toward compensation as it is (top right) advected offshore. The corresponding wb signal is (bottom left) positive and strongest at earliest time and (bottom right) gradually decreases with time.
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
Snapshots of (top) Tux and (bottom) wb at four times relative to 1 Feb in the With-River solution, which corresponds to the evolving nearly compensated peak in Fig. 7. The river water, which is salinity dominated when (top left) entering the domain, gradually evolves toward compensation as it is (top right) advected offshore. The corresponding wb signal is (bottom left) positive and strongest at earliest time and (bottom right) gradually decreases with time.
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
To further examine this process we interpolate the Eulerian Tux values onto Lagrangian particles that are released near the Mississippi River mouth. This allows us to better track the Turner angle evolution of the river water during its offshore advection. The Hovmöller diagrams as a function of time and distance from the particle release location (Figs. 9a,b) illustrate more clearly the gradual evolution toward compensation seen in Fig. 7. When the PDFs are averaged over 2 days and 100 km (Figs. 9c,d), we note an evolution from a unimodal, salinity-dominated distribution at early times and short distances from the source, toward a bimodal, temperature-dominated and nearly compensated distribution at later times and longer distances from the source. The maintenance of a nearly compensated signal in the Lagrangian Turner angle PDFs is consistent with the argument proposed by previous authors (Ferrari and Young 1997) and implies that the continuous release of APE (Fig. 8, bottom) and subsequent lateral diffusion destroy buoyancy gradients more effectively than spice gradients. The evolution toward a temperature-dominated peak illustrates a lateral mixing of advected river waters that gradually reduces salinity gradients.
Hovmöller diagram of Tux PDFs, interpolated onto Lagrangian particles, as a function of (a) time and (b) distance from the release location (red circle in Fig. 11). (c),(d) A subsample of the PDFs shown in (a) and (b) using a 2-day average in time and a 100-km average in space.
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
Hovmöller diagram of Tux PDFs, interpolated onto Lagrangian particles, as a function of (a) time and (b) distance from the release location (red circle in Fig. 11). (c),(d) A subsample of the PDFs shown in (a) and (b) using a 2-day average in time and a 100-km average in space.
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
Hovmöller diagram of Tux PDFs, interpolated onto Lagrangian particles, as a function of (a) time and (b) distance from the release location (red circle in Fig. 11). (c),(d) A subsample of the PDFs shown in (a) and (b) using a 2-day average in time and a 100-km average in space.
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
4. Cross-shelf transport mechanisms of fresh river water in winter
In this section, we investigate in detail the cross-shelf transport of riverine waters during winter, the period of the LASER experiment. In this season, a fast moving, well-defined plume or jet of freshwater forms in the With-River solution (see the opposing and salinity-dominated peak in Figs. 7 and 8 and the salinity gradient animation available in the supplemental information as animation 1). Such a jet is typically oriented in the northwest–southeast direction and at times can reach across the entire computational domain, in agreement with observations by Hu et al. (2005). We propose mechanistic models that approximate this cross-shelf transport, distinguishing between the region to the west of the Bird’s Foot and the Mississippi River jet.
In summer, the jet pattern is not as well defined and does not reach as far offshore in our simulations. In general, the dynamics of the Mississippi River jet and its offshore extent depend on local winds and the location of the Loop Current eddies (Schiller et al. 2011) and do not exhibit a clear correlation with a specific season. This suggests that the lack of a far-extending plume in our solutions during summer represents a specific numerical realization and that the jet-driven projectile-like ballistic process described below (section 4b) is not confined to the winter months only. In any event, the horizontal resolution of our 500-m solutions allows us to adequately represent shelf dynamics during winter only (see section 4 of Part I for details). Finer resolution than used here is required to resolve in detailed cross-shelf transport processes in summer when the mixed layer depth is shallow. The corresponding analysis is therefore not attempted.
a. West of the Bird’s Foot: A diffusive process
(a) Winter-mean salinity in the With-River solution and (b) the corresponding cross-gradient salinity diffusivity 
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
(a) Winter-mean salinity in the With-River solution and (b) the corresponding cross-gradient salinity diffusivity
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
(a) Winter-mean salinity in the With-River solution and (b) the corresponding cross-gradient salinity diffusivity
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
b. The Mississippi River jet: A ballistic process
The distinct river jet signature in the salinity contours east of the Bird’s Foot (Fig. 10a) and the generally negative 
Salinity gradient magnitude |∇hS| in log scale, time averaged over the Lagrangian release period (1 to 10 Feb). Red circle indicates the release location of 5019 particles, which was repeated once per day during the Lagrangian release period. White dots indicate the daily mean location of the particles that were used for the analysis in Figs. 12 and 13 (see section 4b for detail).
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
Salinity gradient magnitude |∇hS| in log scale, time averaged over the Lagrangian release period (1 to 10 Feb). Red circle indicates the release location of 5019 particles, which was repeated once per day during the Lagrangian release period. White dots indicate the daily mean location of the particles that were used for the analysis in Figs. 12 and 13 (see section 4b for detail).
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
Salinity gradient magnitude |∇hS| in log scale, time averaged over the Lagrangian release period (1 to 10 Feb). Red circle indicates the release location of 5019 particles, which was repeated once per day during the Lagrangian release period. White dots indicate the daily mean location of the particles that were used for the analysis in Figs. 12 and 13 (see section 4b for detail).
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
(a) Salinity S, (b) potential temperature T, and (c) potential density ρ averaged on particles as function of time (denoted by white dots in Fig. 11). (d)–(f) Gradient magnitudes of the fields in the top panels. Error bars indicate one standard deviation over eight particle deployments. Solid red line indicates the exponential fit to the data (solid black). Text inset indicates the corresponding e-folding scale.
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
(a) Salinity S, (b) potential temperature T, and (c) potential density ρ averaged on particles as function of time (denoted by white dots in Fig. 11). (d)–(f) Gradient magnitudes of the fields in the top panels. Error bars indicate one standard deviation over eight particle deployments. Solid red line indicates the exponential fit to the data (solid black). Text inset indicates the corresponding e-folding scale.
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
(a) Salinity S, (b) potential temperature T, and (c) potential density ρ averaged on particles as function of time (denoted by white dots in Fig. 11). (d)–(f) Gradient magnitudes of the fields in the top panels. Error bars indicate one standard deviation over eight particle deployments. Solid red line indicates the exponential fit to the data (solid black). Text inset indicates the corresponding e-folding scale.
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
As in Fig. 12, but computed as a function of distance from the release site (red circle in Fig. 11).
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
As in Fig. 12, but computed as a function of distance from the release site (red circle in Fig. 11).
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
As in Fig. 12, but computed as a function of distance from the release site (red circle in Fig. 11).
Citation: Journal of Physical Oceanography 47, 9; 10.1175/JPO-D-17-0040.1
5. Summary
Realistic, submesoscale-resolving, numerical simulations are used to investigate submesoscale dynamics in the northern Gulf of Mexico (GoM), the location of the 2010 Deepwater Horizon oil spill as well as the GLAD and LASER field experiments. In Part I, we examined how the Mississippi–Atchafalaya River system (rivers) impacts submesoscale currents, analyzing two solutions with (With-River) and without (No-River) river forcing at two horizontal resolutions: 500 and 1500 m. We found that both river forcing and mesoscale variability impact the generation of submesoscale circulations in the northern GoM during winter and summer. Here, the second of three companion papers, we analyze the temperature–salinity (T–S) relations and cross-shelf freshwater transport focusing on the 500-m horizontal resolution set to provide an alternative quantification for the effects of the rivers in governing the dynamics in this region. In support of Part I, we find that river forcing has a key role in determining T–S distributions and in governing cross-shelf transport processes in the northern GoM.
First, we examine Turner angle statistics [(3)] in both simulations and show that the surface PDFs do not exhibit the commonly observed mixed layer compensated peak near +π/4 (Rudnick and Martin 2002). During winter, the With-River solution has a nearshore, salinity-dominated signal, which is associated with the river waters, and an offshore, temperature-dominated signal, which is associated with Loop Current waters. In the absence of river forcing, the surface, nearshore, salinity-dominated signal is reduced, and the offshore, temperature-dominated signal can reach closer to shore. In summer, the With-River solution is characterized by a salinity-dominated peak both nearshore and offshore that is associated with the increased river influence. In the No-River solution, both a compensated peak and a temperature-dominated peak are found offshore. The compensated signal is observed at the edges of larger mesoscale structures, and the temperature-dominated signal is associated with the fronts and filaments that, similar to winter, are able to propagate closer to shore. There are substantial differences between With-River and No-River Turner angle PDFs, highlighting the significance of freshwater input in controlling T–S relations in the northern GoM.
To interpret T–S relations with respect to submesoscale currents, we examine conditional Turner angle PDFs in flow regions where temperature and salinity gradients are large relative to their surroundings. The conditional PDFs are found to be quite different than the general ones, emphasizing the care that must be practiced when interpreting Turner angle statistics with respect to submesoscale dynamics. It has been previously suggested (Ferrari and Rudnick 2000) that restratification processes in the mixed layer, which are often linked to submesoscale current generation (Fox-Kemper et al. 2008), together with an assumed horizontal diffusivity that scales nonlinearly with the lateral buoyancy gradient (Ferrari and Young 1997), can explain the commonly observed compensated signal in the ocean mixed layer. By assuming that all of the slumping of isopycnals and isospices during a submesoscale-inducing APE release will result in the destruction of density and spice gradients by such nonlinear diffusion, we are able to propose a scaling estimate [(7)] for the submesoscale-induced compensation that is based on the magnitude of the temperature–salinity covariance 
In winter, the river fronts’ evolution toward compensation is accompanied by an additional process that mixes river water, reduces the salinity gradients, and leads to a temperature-dominated signal away from the river mouth. This mixing process is facilitated by a jet of riverine water that often extends far offshore and transports the freshwater to regions were temperature-dominated fronts abound. The occurrence of frequent, far-extending advection of fresh riverine water by the Mississippi jet in winter motivates us to examine whether the cross-shelf freshwater transport mechanisms will differ in the jet and outside of it, west of the Bird’s Foot. We found that to the west of the Bird’s Foot the cross-shelf transport of river water is well modeled by a diffusive process, whereas in the jet it is better represented by a ballistic process. The jet-driven ballistic process is estimated to be substantially more efficient (as much as two orders of magnitudes whenever the jet is well developed) in transporting freshwater offshore.
Acknowledgments
This work was made possible by a grant from the Gulf of Mexico Research Initiative through the CARTHE Consortium. Data are publicly available through the Gulf of Mexico Research Initiative Information and Data Cooperative (GRIIDC) online (at https://data.gulfresearchinitiative.org; https://doi.org/10.7266/N7PK0DK2, https://doi.org/10.7266/N7F18X4S, https://doi.org/10.7266/N75H7DQ5, https://doi.org/10.7266/N7JS9NVS, https://doi.org/10.7266/N79885FW, and https://doi.org/10.7266/N7CN720V for the Lagrangian data). RB, JCM, and AFS are further supported by ONR N000141410626. The Extreme Science and Engineering Discovery Environment (XSEDE) provided support for computing.
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This definition of the Turner angle is different from the original definition (Ruddick 1983), which is based on the ratio of vertical derivatives of temperature and salinity.
In principle, it is possible to diagnose θ = arctan[
We checked the mixed layer T–S diagrams in both seasons and found the isopycnals to be nearly straight, suggesting that cabbeling effects are less important here compared with other regions of the ocean (Thomas and Shakespeare 2015).
