Abstract

The Gulf of Mexico (GOM) receives heat from the Caribbean Sea via the Yucatan–Loop Current (LC) system, and the corresponding ocean heat content (OHC) is important to weather and climate of the continental United States. However, the mechanisms that affect this heat influx and how it is distributed in the Gulf have not been studied. Using the Princeton Ocean Model, the authors show that a steady, uniform westward wind in the Gulf increases (∼100 KJ cm−2) the upper OHC (temperature T > 18°C) of the Gulf. This is because wind increases the water exchange between the Gulf and the Caribbean Sea, and the heat input into the Gulf is also increased, by about 50 TW. The westward heat transport to the western Gulf is ∼30 TW, and a substantial portion of this is due to wind-induced shelf currents, which converge to produce downwelling near the western coast. Finally, eddies are effective transporters of heat across the central Gulf. Wind forces larger LC and rings with deeper isotherms. This and downfront-wind mixing on the southern side of anticyclonic rings, northward spread of near-zero potential vorticity waters, and downwelling on the northern shelf break result in wide and deep eddies that transport large OHCs across the Gulf.

1. Introduction

Except in April through August, the Gulf of Mexico (GOM) loses heat across its surface to the atmosphere above; the annual-mean surface heat flux is a loss (Etter 1983). The Loop Current (LC) brings heat from the Caribbean Sea into the GOM through the Yucatan Channel, and eddies shed from the LC distribute this heat inside the Gulf (for a review of the LC and eddies, see Oey et al. 2005). Heat and moisture in the Gulf play an important role in modifying the climate of the continental United States (e.g., Ruiz-Barradas and Nigam 2005). The “Corn Belt” of the United States would probably not be so named without the GOM. Some of the most severe winter storms that affected the southern, eastern, and northeastern states of the United States [e.g., the Presidents’ Day snow storm of February 1979 (Bosart and Lin 1984), the blizzard of 1993 (Orlanski and Sheldon 1995) and the Christmas Eve snowstorm of 2004 (available online at http://www.srh.noaa.gov/hgx/?n=projects_xmasevesnow04)] had their genesis in the Gulf. The large ocean heat contents (OHC) of the LC and eddies also affect the development and intensity of tropical cyclones (e.g., Shay et al. 2000; Scharroo et al. 2005; Oey et al. 2006, 2007). Despite the importance of the topic, the mechanisms that affect heat influx into the GOM and the factors that govern how heat is distributed in the Gulf have not been studied. Etter (1983) estimated from observations the net heat flux divergence (influx from Yucatan Channel minus outflux through the Straits of Florida). Heat gains of about 50–80 W m−2 occur from January through May in one estimate, but in another estimate there are heat losses in January and February; the values are generally small in summer. There are large uncertainties in these estimates.

This work continues Chang and Oey’s (2010, hereafter CO2010) process model study that examines the effects of a spatially constant westward wind stress inside the GOM on transports and heat balances. Wind in the GOM is predominantly westward (Gutierrez de Velasco and Winant 1996). Though wind stress curl in the GOM is not zero [it is <0 (>0) north (south) of ∼23°N], we focus as a first attempt on effects of a uniform wind, which also considerably simplifies and clarifies the dynamics. CO2010 analyzed volume transports and found that wind lengthens the period of eddy shedding and increases the water exchange between the Gulf and the Caribbean Sea; because shedding is delayed, the LC accumulates more mass and sheds larger eddies. The present work examines if the local wind can significantly affect the transport and distribution of heat, not only through direct wind (and wave) mixing at the surface, but also through horizontal transports and other mechanisms that deepen isotherms.

The outline of the paper is as follows: Section 2 describes the numerical model. Section 3 contrasts the heat distributions for the NoWind and Wind experiments. In section 4, we analyze and explain in detail why the Wind experiment can produce a widespread increase in the upper ocean heat content in the Gulf. Section 5 gives the conclusions.

2. The numerical model

Details are already given in CO2010, so here we will be brief and highlight the main differences. The Princeton Ocean Model (POM; Mellor 2002) is used; this is time dependent and three dimensional based on the primitive equations assuming hydrostacy and Boussinesq approximation. The model forcing is constant inflow transport into the Cayman Sea and 0 (NoWind experiment) or constant westward wind stress. For the present process study, the westward wind stress is applied over the region west of 80°W only, with a constant value = −0.1 N m−2; this is stronger than the easterly mean wind stresses of about −0.07 N m−2 during fall–winter–spring months (Gutierrez de Velasco and Winant 1996), but it is not too unrealistic. The model produces eddy shedding with a nearly constant period of 8.1 months. The Mellor and Yamada (1982) turbulence closure scheme modified by Craig and Banner (1994) to parameterize wave-enhanced turbulence near the surface is used (Mellor and Blumberg 2004). Instead of setting the surface heat flux KH(∂T/∂z)|z=h equal to 0 (as done in CO2010), a monthly (pseudo) flux is specified by relaxing the sea surface temperature (SST) to its monthly climatological values (from NODC; available online at http://www.nodc.noaa.gov/OC5/WOA05/pr_woa05.html),

 
formula

where KH is the eddy diffusivity, h is the sea surface elevation, and αs = 10−6 s−1 (a relaxation time of about 10 days). This specification is used to mimic seasonal variation but primarily to serve as a long-term sink term; otherwise, the model Gulf’s heat content continuously increases. The treatment is identical in Wind and NoWind experiments; although the resulting surface heat flux differs, it is negligible <1 W m−2. The resulting mean surface heat loss is approximately 21 W m−2 [cf. this with Etter’s (1983) annual-mean loss of 24 W m−2]. As in CO2010, there is also an additional (primarily) heat sink due to the restoring term in the deep; that is, T for z < −1000 m is restored to climatological values with a time scale of 600 days. This term also serves as a long-term sink. To maintain quasi heat equilibrium over several shedding periods, any excess heat is removed by this deep relaxation term, as well as by the surface heat flux term. For example, as an eddy migrates into the western Gulf, bringing with it heat as deepened isotherms, the relaxation terms help to flatten the isotherms.

After a long-term spinup (10 yr) when the model has reached a quasi-equilibrium state with regular eddy shedding from the LC, the calculation was continued for another 5 yr with and without the wind forcing (CO2010); that is, both experiments start from the same initial condition. The analyses below are based on these 5-yr data. There are 7 to 8 eddies shed in 5 yr for the NoWind experiment and 6 eddies shed for the Wind experiment.

3. Effects of wind on the upper ocean heat content

A succinct way of comparing the heat distribution in different experiments is to examine the upper OHC (Leipper and Volgenau 1972), which is defined as

 
formula

where ρr is a constant (reference) seawater density = 1025 kg m−3; Cp is the heat capacity of water = 4 kJ kg−1 °C−1; z18 denotes the depth of 18°C isotherm, which is approximately at z ≈ −300 m; and η is the sea surface elevation. The 18°C isotherm is chosen in anticipation that wind may significantly alter the heat content of water masses at deeper levels: for example, that contained in LC eddies. Thus defined, the OHC encompasses two effects related to heat distribution in the upper ocean. The OHC is large if the temperature is high and also if the warm water (T > 18°C) occupies a large portion of the water column (i.e., large z18). In our case, because the NoWind and Wind experiments have nearly the same surface heat fluxes, differences in OHC depend in part on how effectively warm waters are mixed and downwelled vertically and how they spread horizontally. Another factor is the heat flux from lateral boundaries, especially through the Yucatan Channel, where we will show that wind increases the heat input into the Gulf.

Figure 1 compares 5-yr-averaged OHCs between the NoWind and Wind experiments. It is well known that the LC has a high OHC (e.g., Oey et al. 2006), and Fig. 1 shows a further increase of about 100 KJ cm−2 for the Wind experiment. The more striking difference is in the western Gulf, where the OHC for the Wind experiment increases by approximately 70–100 KJ cm−2 and by 150 KJ cm−2 in the northwestern Gulf (Fig. 1b). In the model, eddies propagate southwestward (CO2010). Both experiments show a southwestward heat-transport path that is clearly related to the LC eddies, from west of the LC at ∼(26°N, 88°W), where model eddies are shed, to the southwestern Gulf at ∼(23°N, 94°W). Figure 1b suggests that eddies in the Wind experiment are deeper and wider. One sees also increased OHC near the western coast, which suggests horizontal and/or vertical heat-flow convergences there.

Fig. 1.

The 5-yr-averaged OHC (color and white contours every 100 KJ cm−2) for (a) NoWind and (b) Wind experiments. Black contour is the 200-m isobath.

Fig. 1.

The 5-yr-averaged OHC (color and white contours every 100 KJ cm−2) for (a) NoWind and (b) Wind experiments. Black contour is the 200-m isobath.

4. Why can wind produce widespread and enhanced OHC in the Gulf?

The increase in OHC for the Wind experiment (Fig. 1) is widespread and too large to be accounted for by direct wind (and wave) mixing at the surface. This is because the z18 is quite a bit larger (by approximately 4–5 times) than the mixed layer depth and therefore cannot be significantly affected by the latter. Except for the surface heat flux and the deep-layer restoring term, which are small and nearly the same for both experiments, there are no other heat sources (or sinks) inside the Gulf. The widespread increase in OHC must therefore be caused by increased heat influx from the Yucatan Channel and/or the Straits of Florida and then by an efficient redistribution of this heat throughout the Gulf.

How is the higher OHC in the Wind experiment transferred and distributed in the western Gulf? The mean surface heat transport (uT, υT) in the NoWind experiment (Fig. 2a) shows that heat from the LC is transported anticyclonically around the Gulf: southwestward along the southern Gulf by propagating LC eddies, northward along the western boundary current, and then eastward along the northern shelf edge. The corresponding circulation patterns are discussed in CO2010. Figure 2b shows that wind alters the heat transport and distribution and enhances the heat transport into the western Gulf.1 Heat is transported westward over the northern and southern shelves by the wind-induced westward shelf currents. These currents converge in the western Gulf, where they downwell and spread heat to the Gulf’s interior. Also, eddies in the Wind experiment transport more heat along the propagation track in the southern Gulf than the NoWind experiment, both at z = 0 (Figs. 2a,b) and z = −200 m (Figs. 2c,d). We deduce therefore that, in the Wind experiment, both eddy and shelf transports play an important role in the higher OHC seen in the western Gulf (Fig. 1b).

Fig. 2.

Heat transports (°C m s−1) for the (a),(c) NoWind and (b),(d) Wind experiments at (a),(b) z = 0 m and (c),(d) z = −200 m. Color is the magnitude of heat transport, and vectors show direction and strength.

Fig. 2.

Heat transports (°C m s−1) for the (a),(c) NoWind and (b),(d) Wind experiments at (a),(b) z = 0 m and (c),(d) z = −200 m. Color is the magnitude of heat transport, and vectors show direction and strength.

In the Wind experiment, the western Gulf’s OHC is increased through downwelling because of convergences of shelf currents at the western coast and also because of eddies, which depress isotherms as they enter the western Gulf. In CO2010, we show that the westward wind forces a returned eastward flow across the central Gulf toward the LC. The returned transport forces downwelling in the LC, which enables it to grow larger, resulting in larger eddies. Mean vertical velocities averaged over the LC in regions where water depths >3000 m are −1.3 and −1.2 m day−1 for the Wind and NoWind experiments, respectively. The difference (Wind minus NoWind) is only −0.1 m day−1; however, when accumulated over, for example, a half shedding period of about 135 days, before an eddy is shed, the isotherm deepening is about 13 m (in agreement with the z18 plots in CO2010). The larger eddy in the Wind experiment results in higher OHC as the eddy propagates westward and decays in the western Gulf (Fig. 1b). The higher OHC in Fig. 1b along the eddy propagation track and in the southwestern Gulf is in part due to this enlarged-eddy process in the Wind experiment (another mechanism will be shown later). On the other hand, near the western coast, the high OHC in the Wind experiment is primarily caused by shelf current convergences, by shelf currents that flow off the shelf edge between 19° and 28°N. Figure 3 compares the w profiles for the two experiments, area averaged west of 94°W, and clearly shows the stronger downwelling velocity for the Wind experiment, particularly in the upper 200 m. Note that there is downwelling in the upper 1200 m for both experiments and upwelling at deeper levels. This is a feature that is closely related to Gulf-wide oscillations forced by the LC and will be discussed in a future work (Chang and Oey 2011).

Fig. 3.

The 5-yr-mean vertical velocity profile (m day−1) area averaged over the western GOM west of 94°W and in water depths >200 m (i.e., exclude shelves) for the Wind (solid) and NoWind (dashed) experiments.

Fig. 3.

The 5-yr-mean vertical velocity profile (m day−1) area averaged over the western GOM west of 94°W and in water depths >200 m (i.e., exclude shelves) for the Wind (solid) and NoWind (dashed) experiments.

a. Quantitative analysis: Heat balance

To find out quantitatively the source of higher OHC and heat transport in the Wind experiment, we compute various terms in the heat equation,

 
formula

where t is time; T is the potential temperature; u is the velocity with zonal x, meridional y, and vertical z (positive upward with z = 0 at the sea surface) components (u, υ, w); q is the vertical eddy diffusive heat flux; and the last term is the restoring term for the deep layers. The term Tclim is climatological T, and α(z) is 0 in the upper 1000 m and smoothly asymptotes to 1.9 × 10−8 s−1 (=1/600 day−1) for z < −2000 m. The term α is used to provide additional eddy dissipation in the western Gulf, but its value is chosen to be small so that shorter-period dissipative and dispersive physics (e.g., side-wall friction and topographic Rossby waves) that also act to modify eddies are not affected.

Integrate Eq. (2) over the whole Gulf from the western coast to the Straits of Florida (between Cuba and Florida), from the Yucatan channel to the northern coast, and from bottom to surface and multiply by ρ0Cp, and we obtain

 
formula

The lhs is the rate of change of heat content, where Q is the heat content integrated over the entire Gulf. Because the zero point of the temperature scale is arbitrary, the Q has an arbitrary constant which is not shown (Montgomery 1954). The first and second terms on the rhs are the heat transports at Yucatan Channel and the Straits of Florida, respectively. The third term is the integral of the surface heat flux ρ0Cpqsurf over the surface area of the Gulf and the last term is the domain-integral of the restoring term.

Each term in (3) is computed. The surface heat flux qsurf gives rise to seasonal variation but its net function is to provide a heat sink (i.e., surface loss); its variation is small compared to the first two terms on the rhs of (3). The deep restoring term is weak but is kept to preserve long-term heat equilibrium; it is larger in the Wind experiment (because the corresponding OHC is larger). The main heat source into the GOM is from the LC. The net heat residing in the Gulf is therefore primarily controlled by the difference between heat input due to transport through the Yucatan channel and heat output due to transport through the Straits of Florida. The cross-sectional contours of temperature and (throughflow) velocity at Yucatan Channel (velocity υ and Straits of Florida (velocity u) are plotted in Fig. 4. The heat transports at these sections are dominated by near-surface values (because speeds are largest and temperatures are warmest there). In Yucatan Channel (Fig. 4a), the easterly wind produces northward Ekman transport, which in part explains why the Yucatan Current is stronger near the surface. However, this is not the major part, which is explained in more details below. The v velocity is stronger, and the current width is wider than in the NoWind experiment (Figs. 4a,b). The near-surface isotherms (gray curves, 28° and 26°C) are deeper in the Wind experiment in part because of wind-induced mixing but also because of altered geostrophic current required to support the stronger flow. Therefore, in the Wind experiment, the stronger inflow and warmer temperature contribute to higher heat transport through the Yucatan Channel. In the Straits of Florida, the high-speed, near-surface velocity is on the northern (i.e., Florida) side (Figs. 4c,d). We show in CO2010 that westward wind reduces the portion of the Straits of Florida transport derived from the currents along the shelf break of the northern Gulf and west Florida shelf. This reduction is seen in the decreased surface speed for the Wind experiment (Fig. 4c) compared to the NoWind experiment (Fig. 4d). However, in the Straits of Florida, westward wind advects near-surface warm water northward toward the Florida coast, and downwelling deepens isotherms. The result is that heat transports in the Straits of Florida for both the Wind and NoWind experiments are approximately the same, being 1.96 and 1.93 PW (1 PW = 1015 J s−1), respectively. The mean heat transports through Yucatan Channel are 2.04 and 1.96 PW for the Wind and NoWind experiments, respectively. Therefore, the net heat transport (Yucatan minus Florida) into the Gulf is 80 TW (1 TW = 1012 J s−1) for the Wind experiment and is 30 TW in the NoWind experiment. For convenience, these and other values (below) are listed in Table 1. If spread over the surface area of the Gulf AGulf ≈ 1.6 × 1012 m2, the net heat influx is 19 W m−2 for the NoWind experiment and 50 W m−2 for the Wind experiment. These agree quite well with Etter’s (1983) estimates. For the present study, of interest is the increase (Wind minus NoWind) of 50 TW, which corresponds to approximately 31 W m−2 if spread over AGulf. This is a significant amount in view of the annual-mean “net oceanic heat gain” (i.e., the Gulf is a heat source for the atmosphere) estimates in the GOM of about 21–27 W m−2 by Etter (1983). Thus, wind significantly modifies the heat content in the GOM.

Fig. 4.

Temperature (colors; gray contours indicate 26° and 28°C) and along-channel–strait velocity (black contours; thick green contours indicate 1 and 1.4 m s−1) at the (a),(b) Yucatan Channel (upper 800 m only) and (c),(d) Straits of Florida for the (a),(c) Wind and (b),(d) NoWind experiments. The inset on the top left shows section locations, and also section c at 90°W and eddy-propagation track section d, which will be described later.

Fig. 4.

Temperature (colors; gray contours indicate 26° and 28°C) and along-channel–strait velocity (black contours; thick green contours indicate 1 and 1.4 m s−1) at the (a),(b) Yucatan Channel (upper 800 m only) and (c),(d) Straits of Florida for the (a),(c) Wind and (b),(d) NoWind experiments. The inset on the top left shows section locations, and also section c at 90°W and eddy-propagation track section d, which will be described later.

Table 1.

A summary of 5-yr-mean heat transports through the Yucatan Channel (>0 northward) and the Straits of Florida (>0 eastward); net influx into the GOM (Yucatan − Florida; >0 into GOM) and across 90°W (>0 eastward); and values for the “ensemble-mean eddies,” which are computed following individual eddies and then ensemble averaging them.

A summary of 5-yr-mean heat transports through the Yucatan Channel (>0 northward) and the Straits of Florida (>0 eastward); net influx into the GOM (Yucatan − Florida; >0 into GOM) and across 90°W (>0 eastward); and values for the “ensemble-mean eddies,” which are computed following individual eddies and then ensemble averaging them.
A summary of 5-yr-mean heat transports through the Yucatan Channel (>0 northward) and the Straits of Florida (>0 eastward); net influx into the GOM (Yucatan − Florida; >0 into GOM) and across 90°W (>0 eastward); and values for the “ensemble-mean eddies,” which are computed following individual eddies and then ensemble averaging them.

b. Why can wind within the Gulf produce a larger net heat input into the Gulf?

Irrespective of the wind, heat is transported into the Gulf via the Yucatan–LC system = ViTi, where Vi is the inflow volume transport in Sv (1 Sv ≡ 106 m3 s−1) and Ti is the temperature of the inflowing water from the Caribbean Sea. Most of this heat influx is balanced by outfluxes through the Straits of Florida, VFoTo, and the Yucatan Channel (i.e., back into the Caribbean Sea; see CO2010), VYoTo, where VFo and VYo are the outflow volume transports through the Straits of Florida and Yucatan Channel, respectively, and To is the temperature of the outflowing Gulf’s water. The convention is that the Vi, VFo, and VYo are all positive. In a simplified Gulf that is treated as a “box,” To is taken as the Gulf-averaged temperature. Inside the Gulf, eddies distribute heat, which is removed by the Gulf’s interior heat loss (−QI < 0), which in the model is the sum of surface heat loss ∫∫qsurf dx dy (<0) plus heat adjustment due to the restoring term in (3) −∫∫∫α(TTclim) dx dy dz (which predominantly is also <0—i.e., a loss—because eddy isopycnals are flattened to climatology). After a quasi-steady state is reached, the heat balance is

 
formula

which (because Vi = VYo + VFo) gives

 
formula

The values of QI for Wind and NoWind are approximately the same, but the Caribbean and Gulf temperature difference (TiTo) is smaller for the Wind experiment, as a comparison of Figs. 1a,b indicates. Equation (5) suggests then that

 
formula

We obtained this same result but using a different approach in CO2010. There we show that, in the NoWind experiment, the eddy transport Qeddy that is returned to the eastern Gulf is nearly equally partitioned between the Yucatan Channel and the Straits of Florida. In the Wind experiment, on the other hand, 70% of Qeddy flows out of the Yucatan Channel into the Caribbean Sea and only 30% flows out of the Straits of Florida (see CO2010 for why this is so). In other words, wind promotes a more vigorous exchange between the GOM and the Caribbean Sea. Inequality (6) then follows because Qeddy and the net inflow into the Yucatan Channel (which balances the net outflow through the Straits of Florida) are both very nearly the same with or without wind: that is, Qeddy|WindQeddy|NoWind, and (ViVYo)|Wind ≈ (ViVYo)|NoWind. The increased heat content in the Wind experiment (Fig. 1b) compared to the NoWind experiment (Fig. 1a) is explained then by stronger inflow of warmer Caribbean Sea Water and stronger outflow of (slightly) cooler Gulf Water through the Yucatan Channel.

In reality, QI in Eq. (5) should become larger for the Wind experiment because of increased evaporation and latent heat loss, which are not included in our simple model. However, this would only increase Vi (assuming that the additional heat loss equally affects the Caribbean Sea and the Gulf) and further increases the heat exchange between the two basins; our conclusions remain unchanged.

c. Heat flux across 90°W

We now examine how heat is redistributed into the western GOM (west of 90°W). To understand the roles of flows on shelves and deep basin, as well as of eddies and wind in the zonal transports of heat across the Gulf, the latitudinal section at 90°W is partitioned into upper and deep layers separated by z = −800 m. This depth is chosen because the LC and warm rings are mainly in the upper 800 m. The section is also divided into northern and southern shelves where water depths are less than 200 m and the middle basin with depths greater than 200 m (note that, although we use the term “shelf,” in most instances large transports are over the outer shelf and shelf break with water depths > 75 m). The 5-yr-averaged heat transports are computed.

In the NoWind experiment, heat is transported westward into the western Gulf on the southern shelf (−8.3 TW) and in the upper layer of the middle basin (−38.5 TW) and eastward over the northern shelf (34 TW; Fig. 5a). In the Wind experiment, westward heat transport is over the shallow shelves only, −61.8 and −12.9 TW for the southern and northern shelves, respectively, and heat is transported eastward (32.1 TW) in the upper layer of the middle basin (Fig. 5b). As explained in CO2010, wind forces a returned (i.e., eastward) flow in the middle basin. There is an excess (Wind minus NoWind) of westward heat transport of −30 TW in the upper layer when the model is forced by wind; most of it is contributed by the shelf heat transports. In the deep layer, transports are weak and eastward in both the Wind and NoWind experiments. See Table 1 for a summary of the above calculations.

Fig. 5.

The (a),(b) 5-yr-mean, (c),(d) active-eddy composite-mean, and (e),(f) decaying-eddy composite-mean heat transports (TW) at 90°W for the (left) NoWind and (right) Wind experiments. The dashed line separates the upper and lower layers. See text for details.

Fig. 5.

The (a),(b) 5-yr-mean, (c),(d) active-eddy composite-mean, and (e),(f) decaying-eddy composite-mean heat transports (TW) at 90°W for the (left) NoWind and (right) Wind experiments. The dashed line separates the upper and lower layers. See text for details.

Westward-propagating warm eddies from the LC bring large amounts of heat to the western Gulf. To see the effects of eddies, we composite the heat transport into two periods (CO2010): 1) active-eddy state when eddies just separate from the LC and are crossing the 90°W section (Figs. 5c,d) and 2) the remaining, decaying-eddy state when eddies are decaying in the western Gulf and the LC is reforming in the east (Figs. 5e,f). During the active-eddy state, westward upper-layer heat transports through the middle basin are large, −187.2 and −120.2 TW for the NoWind and Wind experiments, respectively. Because the Wind experiment has a returned (i.e., eastward) mean flow in the central Gulf in the upper layer (CO2010), its heat transport is partially cancelled and therefore is weaker than the NoWind experiment. This does not mean, however, that eddies in the NoWind experiment transport more heat to the west than the Wind experiment, because the composite cannot separate eddy and wind effects; the appropriate calculation will be done below. In the deep layer, the compensating flow transports heat eastward, +26.4 TW for NoWind and +21.7 TW for Wind (Figs. 5c,d). Nonetheless, contrasting the above values with the corresponding middle-basin heat transports in the upper layer, +4.7 TW (NoWind) and +76.3 TW (Wind) during the decaying-eddy state (Figs. 5e,f), and taking the weak deep-layer contributions [−3.6 TW (NoWind) and +1.8 TW (Wind)] into account, we see that eddies are substantial transporters of heat, providing approximately 125 W m−2 or more as they enter the western Gulf (1000 km × 800 km).

The eddy heat transport Heddy is estimated by calculating the heat carried by individual eddies as they propagate westward, in the same way that Qeddy was estimated in CO2010, except that heat content is used instead of volume. This gives Heddy = −0.85 PW for the Wind experiment and −0.82 PW in the NoWind experiment. As in the case of Qeddy, the Heddy values do not differ much in both experiments because eddies in the Wind experiment are larger and have higher heat content (the ensemble mean = 2.2 × 1021 J; Table 1), but they propagate slower (because of the opposing eastward returned flow in the central Gulf) than eddies in the NoWind experiment (the ensemble mean heat content = 1.4 × 1021 J). Note that the magnitude of Heddy is larger than the middle-basin, upper-layer heat transport estimated in Fig. 5c during the active-eddy state, because the latter is a composite-mean value (cf. CO2010).

On the shelves, heat transport in the NoWind experiment (Fig. 5c) is dominated by eastward flow over the northern shelf (and shelf break), +31.8 TW, as part of the Gulf-scale anticyclonic gyre (CO2010). In the Wind experiment, heat transports over the southern and northern shelves are westward, −55.1 and −2.8 TW, respectively (Fig. 5d). Again, shelf currents play an important role in the heat transports. Together with the heat transports through the middle basin, the active-eddy composite gives a net westward heat transport of approximately −180 TW for Wind and −155 TW for NoWind in the upper layer, contributing approximately 200 W m−2 or more to the western Gulf.

In contrast, during the decaying-eddy state (Figs. 5e,f), heat transports in the upper layer in the middle basin become eastward, +4.7 TW (NoWind) and +76.3 TW (Wind), and heat transports are weak in the deep layer. In conjunction with the results for the active-eddy state (Figs. 5c,d), we conclude that rings are important transporters of heat from the LC to the western GOM. In the decaying-eddy state, wind-driven shelf transports remain substantial (Fig. 5f) and indicate clearly the “W shape” (from the vantage of an observer high above the western coast looking eastward over the Gulf’s water) double-gyre recirculation: westward over the northern and southern shelves and eastward in the central basin.

That wind-forced shelf currents are important in transporting heat westward may also be deduced by comparing the two composites in Figs. 5c–f. In the upper layer of the middle basin, westward heat transports are weaker for the Wind experiment. The net (including shelves and the weak deep contributions), however, is stronger westward for the Wind experiment. The reason is due to the shelf contributions, because they are persistent (under the steady westward wind). For the active-eddy composite, the net heat transports are −156.4 (Wind) and −130.3 TW (NoWind); for the decaying-eddy composite, they are −1.4 (Wind) and 25.5 TW (NoWind).

d. How does wind modify eddies and upper thermal structures?

We noted above when calculating Heddy that the eddy heat content in the Wind experiment is higher than in the NoWind experiment. The eddy isotherms are therefore deeper and/or wider in the Wind experiment. We can deduce this (instead of calculating Heddy) in another way, as follows. In the active-eddy composites (as in Figs. 5c,d) for volume transports (see CO2010, their Figs. 4c,d), the ratio of NoWind to Wind transports in the upper layer is (−1.92/−0.93) ≈ 2. If the heat contents in both experiments were the same, then the corresponding ratio for heat transports would also be close to 2. In fact, the ratio (from Figs. 5c,d) is quite a bit smaller, (−187/−120) ≈ 1.6, which suggests that heat contents of eddies in the Wind experiment are higher (cf. Table 1). We now analyze in some detail the processes by which wind modifies eddies and upper thermal structures of the Gulf and how then the modifications lead to the higher OHC seen in Fig. 1b.

We examine the section d of Fig. 4 (inset), along which model eddies propagate. Westward wind acting on warm eddies with anticyclonic vorticity ζ < 0 is “downfront” on the southern side of the eddy and “upfront” on its northern side. A downfront wind produces upward flux (i.e., loss) of potential vorticity near the surface, resulting in strong convective mixing (Thomas 2005) that thickens the surface approximately 50–100-m warm layer. The upfront wind on the northern side of the eddy produces a thin stable layer near the surface. However, wind forces downwelling over the continental slope and shelf of the northern Gulf, and this process will also be studied.

Therefore, along track d (shown in Fig. 4), because it is on the southern side of eddies and the wind is downfront, large differences between the Wind and NoWind heat transports are expected (Fig. 2). The 5-yr-mean vertical-section contours of temperature along track d show a thicker near-surface warm layer in the Wind experiment (Fig. 6a). The isotherms are deeper by about 20–30 m in the Wind experiment than in the NoWind experiment (Fig. 6b). The temperature difference (Fig. 6c) is larger than 1°C from z = −30 m to z = −200 m; the maximum difference of about 1.4°C is at z ≈ −100 m. Close to the surface, the difference is small. The deeper isotherms result in higher OHC in the Wind experiment. The deep penetration of heat in the Wind experiment is not due to the surface heat flux, because this is very nearly the same in both experiments. It is also not caused by direct wind-induced turbulence, which can only account for mixing near the surface (∼30 m), where we have just seen that the difference between the two experiments is small.

Fig. 6.

Upper 350-m temperature (°C) along the southern eddy propagation track (d in Fig. 4 inset) for (a) Wind and (b) NoWind experiments and (c) their difference.

Fig. 6.

Upper 350-m temperature (°C) along the southern eddy propagation track (d in Fig. 4 inset) for (a) Wind and (b) NoWind experiments and (c) their difference.

e. Can wind acting on rings give rise to a deeper penetration of heat?

To address this, we compare Wind and NoWind experiments at the 90°W section through which every model ring must pass. Figure 7 shows the active-eddy composites of temperature and Ertel’s potential vorticity (PV), which is given by

 
formula

where ζa is absolute vorticity vector (ζx, ζy, ζz), ρ is the potential density, and ρr is the reference density = 1025 kg m−3. Strongly stratified fluid tends to have large negative PV, whereas fluid of gravitational, inertial, or symmetric instability tends to have small (i.e., near 0 or even positive) PV. The PVs in Figs. 7a,b are negative (i.e., stable) in both experiments. This is in part due to the ensemble averaging, which tends to erase shorter-period, near 0, or even positive PVs. However, the near-surface PV values in the Wind experiment are nearer to 0; hence, the fluid has undergone more mixing than in the NoWind experiment. This is clearly seen in Fig. 7c, which plots the PV difference (PVD; Wind − NoWind). Near the surface (approximately 50–100 m) and south of the eddy center near 26°N, a region of positive PVD can be seen (Fig. 7c). (Here we focus on portion of the 90°W section south of the eddy center and defer to the next section explanations of processes involved in the northern portion: e.g., the positive PVD seen in Fig. 7c over the northern slope and shelf break.) The positive PVD shows a strong PV loss in the upper layer in the Wind experiment compared to the NoWind experiment. The positive PVD penetrates deepest (to z ≈ −150 m) immediately south of the eddy center near where the z component anticyclonic relative vorticity ζz is strongest (not shown). Immediately north of the eddy center, however, PVD is weak and shallow. The sharp northward decrease in the thickness of layer of positive PVD across the eddy center, across which the eddy’s zonal velocity changes sign, strongly supports the idea of a PV loss (gain) on the southern (northern) side of the eddy where, in our case, the wind is downfront (upfront; Thomas 2005). Figure 7c also shows that the PVD changes sign at z ≈ −100 m, below which the Wind experiment therefore displays stronger stratification. The reason is because, as near-surface isotherms deepen and stretch, isotherms immediately below are compressed. The deepening of isotherms in the near-surface, approximately 300-m water column in the Wind experiment is clearly seen in Fig. 7d, which should be compared with Fig. 7e for the NoWind experiment. Their difference (Fig. 7f) shows a wide region of warming from the Campeche continental slope (in the south) to 25.5°N (just south of the eddy center). A warming of +2°C from depths of z ≈ −200 to −50 m and of +1°C penetrating to a depth of z ≈ −300 m can be seen.

Fig. 7.

Vertical-section at 90°W of (a),(b) PV and (d),(e) T for the (a),(d) Wind and (b),(e) NoWind experiments and (c),(f) the corresponding differences. The thick white contours on the T plots are 18° and 26°C. Variables are composite averages during the active-eddy state (see text).

Fig. 7.

Vertical-section at 90°W of (a),(b) PV and (d),(e) T for the (a),(d) Wind and (b),(e) NoWind experiments and (c),(f) the corresponding differences. The thick white contours on the T plots are 18° and 26°C. Variables are composite averages during the active-eddy state (see text).

f. Wind-induced heat transport over the northern shelf break and slope

North of the eddy center, especially over the northern continental slope and outer shelf (north of ∼27°N), the Wind experiment shows deepened isotherms (approximately 50–100 m deep) that coincide with the region of positive PVD near the surface (Fig. 7). Against the shelf break, the temperature difference (Wind − NoWind) reaches +5°C. Westward wind is upfront north of the eddy’s center and is downwelling favorable with respect to the northern coast. Upfront wind advects warm water to the north in a thin Ekman layer with stable stratification underneath (see below). However, Fig. 7d shows that the thickness of warm layer on the northern side of the eddy is comparable to that on the southern side. The reason is that, against the northern coast and the continental shelf break, warmer water downwells into the bottom boundary layer (BBL), where it flows offshore under cooler water, resulting in strong mixing over the sloping bottom (Allen and Newberger 1996) as well as a PV loss; that is, PV tends toward zero and PVD increases. A bottom front can be seen anchored over the shelf break over the 100-m isobath (see the 26°C isotherm white contour in Fig. 7d). The bottom front is in geostrophic balance with a westward flow (not shown) that transports heat westward along the shelf break and outer shelf. We now examine these (and other) processes that lead to deepened isotherms and enhanced heat transport over the northern Gulf.

g. A process model

We wish to demonstrate that the upfront wind on the northern side of a warm eddy produces a thin Ekman layer with stable stratification beneath the layer and propagates away from the eddy and that downwelling produces large mixing with near-zero PVs, as well as a bottom front that anchors at the continental shelf break. An idealized numerical model with POM is set up to study the mechanisms. The model is two dimensional in a cross-slope and vertical yz section. The bottom topography mimics the continental shelf and slope at 90°W (Fig. 8a). The model’s y length is 500 km, and a maximum depth of 450 m is used. The minimum depth Hmin = 50 m is at the coast y = 0 and 500 km; all ∂/∂x terms are 0. The horizontal grid size (Δy) is 2 km. In the vertical, 300 equally spaced sigma layers are used.

Fig. 8.

Idealized experiment of westward wind blowing over a warm eddy in a south–north (0 < y < 500 km) basin with continental slopes at both ends: (a) initial temperature at day 60 and (b),(d),(f) subsequent evolution (shown for the right half of the eddy only or upfront wind) at days 70, 100, and 130 (thick white contour is 22°C isotherm). (c),(e),(g) The corresponding PV evolution is also given; white contours are −10−8 and −4 × 10−8 m−1 s−1.

Fig. 8.

Idealized experiment of westward wind blowing over a warm eddy in a south–north (0 < y < 500 km) basin with continental slopes at both ends: (a) initial temperature at day 60 and (b),(d),(f) subsequent evolution (shown for the right half of the eddy only or upfront wind) at days 70, 100, and 130 (thick white contour is 22°C isotherm). (c),(e),(g) The corresponding PV evolution is also given; white contours are −10−8 and −4 × 10−8 m−1 s−1.

The initial temperature is obtained as follows: A warm eddy is analytically specified; it has two fronts centered at y = yf , yf2 = 150, 350 km; and with y scale ≈ Lyf = 20 km,

 
formula

The domain-averaged kinetic energy indicates that a quasi-steady state is reached at approximately day 50 (not shown). Day 60 is therefore taken as the initial eddy condition (Fig. 8a) upon which a westward wind forcing is applied. The wind stress is spatially constant and is gradually increased to a constant |τ0| = 10−4 m2 s−2 over 5 days,

 
formula
 
formula

where t is in days, t0= 60 days is the initial time corresponding to Fig. 8a, and tτ = 20 days. Our interest is in frontal movement caused by Ekman flows and the subsequent interaction with the shelf break, so to simplify the problem the Coriolis parameter f is set to be constant = 6.2 × 10−5 s−1, corresponding to a latitude ≈25°N. Also, salinity is set constant at 35 psu, and heat and salt fluxes are 0 at the surface, coasts, and ocean bottom. The downfront-wind solution is also simulated on the southern side of the eddy; the development of strong mixing due to slantwise convection with near-zero PV there will be seen to affect also the solution on the upfront side.

Figures 8b–g show contours of temperature (left column) and PV at various times for 250 km ≤ y < 500 km (northern side of eddy). To show details of the Ekman frontal movement and the subsequent interaction with the shelf break, the upper 200 m is shown. At day 70 (i.e., 10 days after the wind begins; Figs. 8b,c), a thin warm layer of eddy water intrudes onto the coast. The layer is capped underneath by strong stratification, which can be seen as a wavy “ribbon” of large and negative PV (deep blue color, Fig. 8c) extending to the coast. The ribbon’s wavy pattern can be shown to be due to upwelling coupled with Ekman advection at the front (Chang and Oey 2010). By this time, downwelling also has begun near the coast and all along the bottom of the shelf and slope. A thick BBL is seen characterized by isotherms intersecting the bottom and near-zero and positive PV, also near the bottom. The along-shelf velocity is westward in geostrophic balance with the bottom front (not shown). The corresponding plots at days 100 and 130 (Figs. 8d–g) show the subsequent evolution of the downwelling flow and the thickening of the BBL. By these times, the bottom front is fully established. Behind (i.e., to the left of) and above the wavy PV ribbon is a thickening layer of strong mixing characterized by near-zero and positive PV and vertical isotherms. These well-mixed, near-zero PV waters are advected from the southern side of the eddy, where the wind is downfront. Figure 9 shows turbulence kinetic energy q2, PV, and the streamfunction at day 80 (20 days after wind is turned on) when these near-zero PV waters begin to intrude northward (i.e., to the right). The plot is for the upper 200 m, but for the entire y section. The strong and deep mixing (to z ≈ −150 m) with small-scale recirculation cells where PV ≥ 0 on the southern side of the eddy (130 km < y < 200 km) are clearly seen. The cells are indicative of slantwise instability with positive PV. Note also the mixing and PV ≈ 0 in the BBL over the northern shelf break, mentioned above. It is (i) the formation of these near-zero PV waters in the BBL of the continental shelf break by downwelling and (ii) their advection from the downfront-wind side of the eddy that explains why there is also a thick warm layer near the surface on the northern side of the eddy.

Fig. 9.

(top) Turbulence energy q2 [contour interval = 2 × 10−4 m2 s−2; color is log10(q2)] and (bottom) Ertel’s PV (color and white contours −10−8 and −4 × 10−8 m−1 s−1) and streamfunction (black contours; interval = 0.25 m2 s−1) for idealized experiment at day 80.

Fig. 9.

(top) Turbulence energy q2 [contour interval = 2 × 10−4 m2 s−2; color is log10(q2)] and (bottom) Ertel’s PV (color and white contours −10−8 and −4 × 10−8 m−1 s−1) and streamfunction (black contours; interval = 0.25 m2 s−1) for idealized experiment at day 80.

An LC ring at 90°W is not stationary. However, a typical ring takes about 30–60 days to traverse its entire diameter (about 300 km) past 90°W; this is similar to the response time of the processes described in the idealized experiment. Therefore, the active-eddy composite shown in Fig. 7 may be thought as being an average of events that contain mechanisms described in the idealized experiment of Figs. 8 and 9. (We have also verified this supposition with plots similar to Figs. 8 and 9 but applied to individual rings that cross 90°W.) Therefore, the processes that lead to the widened eddy and thickened upper-layer thermal structure in the Wind experiment compared to the NoWind experiment, seen in Figs. 7d,e, may be summarized as follows: Downfront wind on the southern side of the eddy leads to PV losses there. The corresponding waters of strong mixing and near-zero PV are advected northward near the surface (as well as propagated westward with the eddy, as discussed in Fig. 6), in a time scale of O(approximately 10–30 days), and contribute to the thickened warm layer north of the eddy. North of the eddy, the initial [O(10 days)] response to wind is the development of a thin sheet (ribbon) of highly stratified water with large and negative PVs under the thin Ekman layer. In the subsequent approximately 20–30 days, downwelling ensues at the northern coast and over the shelf break. A bottom front is formed by large mixing in the BBL in part because of warm waters being advected under cooler layer of waters but also because of slantwise instability with positive PV (Fig. 9; see Allen and Newberger 1996). The tendency for the near-bottom PV to approach 0 and positive values may also be interpreted as being caused by PV losses through the ocean bottom because of the frictional stresses (Thomas 2005).

5. Discussion and conclusions

This paper explores the role of a steady, spatially constant westward wind in the GOM in modifying the ocean heat content inside the Gulf. A previous study in CO2010 has shown that westward wind increases the volume exchange between the Gulf and the Caribbean Sea. A conceptual model is then that this increased exchange also increases inflow of warm Caribbean Sea Water and outflow of (slightly) cooler Gulf Water, resulting in an increased heat transport into the Gulf of about 50 TW compared to the NoWind experiment, or about 31 W m−2 if spread over the area of the Gulf. The net increase due to wind in westward heat transport across 90°W to the western Gulf is approximately 30 TW, or about 38 W m−2 if spread over the area of the western Gulf. Wind-induced currents along the southern and northern shelves of the Gulf play an important role in this westward heat redistribution. The shelf currents converge in the western coast, produce downwelling as they flow off the shelf edge, and return eastward across the central Gulf. Propagating eddies are also effective transporters of heat across the deep Gulf. Because wind forces the LC to accumulate more mass (CO2010), the corresponding eddies are larger with deeper isotherms. Moreover, westward wind produces PV loss across the sea surface on the southern side of an anticyclonic eddy, where the wind is downfront. The PV loss results in near-zero PVs and in slantwise convection cells that efficiently mix the surface approximately 50–100-m warm layer. The model indicates that westward wind transports these well-mixed waters with near-zero PVs northward in the surface Ekman layer. When coupled with the downwelling over the northern Gulf coast and continental shelf break, the well-mixed warm waters can be more efficiently spread across the entire northern GOM (Fig. 1b).

In the GOM, westward wind is strong in winter and weak in summer (Gutierrez de Velasco and Winant 1996). Our results suggest that, during fall and winter, wind can play a very important role in increasing the heat input into the Gulf and in redistributing heat to the western Gulf. The difference between the Wind and NoWind experiments of approximately 31–38 W m−2 heat influx into the GOM and the western Gulf is a substantial portion of the observed annual-mean “net oceanic heat gain” of approximately 21–27 W m−2 by Etter (1983). It will be interesting in future work to examine the impact of years of weak and strong winter winds on the interannual variability of the regional U.S. climate.

The asymmetry in mixing in Fig. 9 between the downfront-wind and upfront-wind sides of an eddy is a new finding that appears to have its counterpart in old observational data. Elliott (1982) wondered how the Caribbean Subtropical Underwater (SUW) at a depth of z ≈ −200 m, well below the seasonal thermocline, may be mixed and transformed into the Gulf “Common” Water within an LC ring; he proposed deep winter convection. Elliott’s Brunt–Väisälä frequency contours across the ring (his Fig. 12) shows remarkable asymmetry with a deep low-stability water column to the left (i.e., southwest) of the ring’s center (located slightly to the left of observational station 38) and high stability to the right, similar to Fig. 9. The model suggests slantwise convection with near-zero PVs, perhaps in addition to or even instead of winter convection in explaining the observed deep mixing. Future work should further examine the importance of this process in redistributing heat (and other tracers).

Acknowledgments

We thank the two anonymous reviewers for providing useful comments. This research is supported by the Minerals Management Service Contracts M08PC20007, M07PC13311, and M08PC20043 (SAIC 4400159982). YLC received a fellowship from the Graduate Student Study Abroad Program (NSC97-2917-I-003-103) of the National Science Council of Taiwan. Computations were done at NOAA/GFDL, Princeton.

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Footnotes

Corresponding author address: L.-Y. Oey, Princeton University, Sayre Hall, 300 Forrestal Rd., Princeton, NJ 08544. Email: lyo@princeton.edu

1

Wind-induced sea level setup at the western Gulf (assuming steady state and absence of other dynamical processes, etc.) ≈ 5 × 10−3 m, or about 2.5-m isopycnal deepening. This is small (1%) compared with the heat-induced change (≈25 m) being discussed.