Numerical studies are described of the flows generated by a sphere moving vertically in a uniformly stratified fluid. It is found that the axisymmetric standing vortex usually found in homogeneous fluids at moderate Reynolds numbers (25 [les ] Re [les ] 200) is completely collapsed by stable stratification, generating a strong vertical jet. This is consistent with our experimental visualizations. For Re = 200 the complete collapse of the vortex occurs at Froude number F ≃ 19, and the critical Froude number decreases slowly as Re increases. The Froude number and the Reynolds number are here defined by F = W/Na and Re = 2Wa/v, with W being the descent velocity of the sphere, N the Brunt–Väisälä frequency, a the radius of the sphere and v the kinematic viscosity coefficient. The inviscid processes, including the generation of the vertical jet, have been investigated by Eames & Hunt (1997) in the context of weak stratification without buoyancy effects. They showed the existence of a singularity of vorticity and density gradient on the rear axis of the flow and also the impossibility of realizing a steady state. When there is no density diffusion, all the isopycnal surfaces which existed initially in front of the sphere accumulate very near the front surface because of density conservation and the fluid in those thin layers generates a rear jet when returning to its original position. In the present study, however, the fluid has diffusivity and the buoyancy effects also exist. The density diffusion prevents the extreme piling up of the isopycnal surfaces and allows the existence of a steady solution, preventing the generation of a singularity or a jet. On the other hand, the buoyancy effect works to increase the vertical velocity to the rear of the sphere by converting the potential energy to vertical kinetic energy, leading to the formation of a strong jet. We found that the collapse of the vortex and the generation of the jet occurs at much weaker stratifications than those necessary for the generation of strong lee waves, showing that jet formation is independent of the internal waves. At low Froude numbers (F [les ] 2) the lee wave patterns showed good agreement with the linear wave theory and the previous experiments by Mowbray & Rarity (1967). At very low Froude numbers (F [les ] 1) the drag on a sphere increases rapidly, partly due to the lee wave drag but mainly due to the large velocity of the jet. The jet causes a reduction of the pressure on the rear surface of the sphere, which leads to the increase of pressure drag. High velocity is induced also just outside the boundary layer of the sphere so that the frictional drag increases even more significantly than the pressure drag.
The first attempt to establish a relation between the Loop Current extension and deep flows in Yucatan Channel was made by Maul et al. [1985]; it was unsuccessful, probably because of the low spatial resolution of their observations. From September 8, 1999, to June 17, 2000, eight moorings with acoustic Doppler current profilers, current meters, and thermometers were deployed across the Yucatan Channel. The data from these arrays were used to compute time series of the transports below the level of the deepest isotherm observed in the Florida Straits, as required by a simple box model that restricts deep exchanges with the Gulf of Mexico to the Yucatan Channel. The surface extension of the Loop Current was inferred from 3 day advanced very high resolution radiometer imagery from October to May, when temperature gradients were sufficient to map the warm water unambiguously. The deep transports appear at first unrelated to the rate of change of the Loop Current extension, but filtering the series with a 20 day running mean increases the correlation between the low‐pass series to 0.62, and up to 0.83 with a lag of 8.5 days, with Loop Current changes leading the deep flows. The cumulative deep transport, a quantity that favors lower frequencies, is very well related (correlations >0.9) to the surface extension of the Loop Current, also with a lag of about a week. These lags are not statistically significant but suggest a timescale for internal adjustment processes in the Gulf of Mexico. The empirical orthogonal function of the current best related to the area extension of the Loop Current represents a unidirectional flow across the entire deep section, flowing either toward or from the Gulf of Mexico, and includes a strong expression of the Yucatan Undercurrent.
[1] The structure and variability of the velocity and temperature fields in Yucatan Channel are analyzed using data from an eight-mooring array deployed from August 1999 to June 2000. The area-averaged kinetic energy and transport fluctuations spectra show that the extrema of these quantities do not coincide, and that flow variability is dominated by highly energetic processes with weak transport contributions. Transport fluctuations peak in the 20-40 and 5-10 day period bands, but show no clear correlation with the local wind-stress forcing. Empirical orthogonal function (EOF) analysis of the along-channel velocity component shows that approximately 55% of the total velocity variance is retained in the first two EOFs, which depict tripolar (the center of the channel is out of phase with the sides) and dipolar structures. A multivariate complex EOF analysis of low-passed temperature and velocity components suggests the tripole-dipole structures are the components of irregular oscillations of the flow, related to the northwestward propagation of anticyclones and cyclones through the channel. The weak transport signal in these modes is consistent with the eddies being advected by the mean flow. In contrast to other western boundary current regions, the passage of eddies provides the predominant explanation for the variability in the Yucatan Channel. However, the processes controlling transport variability remain unclear.
[1] Two-year-long time series of current and density structure measurements across the Yucatan Channel's main section allow the calculation of the time-dependent potential vorticity flux between the Gulf of Mexico and the Caribbean Sea, which is characterized by alternating periods of positive (cyclonic) and negative (anti-cyclonic) vorticity influx. Periods of negative cumulative vorticity influx are related to the Loop Current extending into the Gulf of Mexico, whereas periods of positive cumulative vorticity influx relate to a Loop Current retraction, sometimes coincident with the shedding of an anti-cyclonic eddy.INDEX TERMS: 4520
Recent measurements over the sill in the Yucatan Channel indicate that the deepest flows between the Caribbean Sea and the Gulf of Mexico, those that take place below the sill level at the Florida Straits, have zero mean net mass transport but carry significant amounts of heat and oxygen. The heat flux associated with the mean exchange exports approximately 150 GW from the deep Gulf toward the Caribbean and may be related to the formation of the Yucatan Undercurrent. The eddy heat transfer is also significantly different from zero and exports on average an additional 60 GW. This eddy transfer is attributable mostly to events that last from a few days to about 1.5 months, during which colder water from deeper levels in the Caribbean (beneath 2000 m) flows over the sill within a bottom boundary layer close to 200 m thick. The colder water is also very rich in oxygen, and the deep exchange sustains the near-bottom oxygen maximum in the Gulf of Mexico, whence that cold water must slide down the northern slope of the Yucatan Sill. Estimates of oxygen transport by diffusion from the deep water into the overlying intermediate water (∼50 m3 s−1) and the oxygen consumption reported in the literature (∼100 m3 s−1) are balanced by the rates of mean and eddy transfers over the sill (∼150 m3 s−1). The near-bottom mass transport [∼0.32 Sv (1 Sv ≡ 106 m3 s−1)] measured across the deepest portion of the central Yucatan Channel suggests a residence time for the deep waters of the Gulf of about 250 yr.
Five cross‐strait hydrographic sections repeated several times during the Gibraltar Experiment in 1985–1986 are used to examine the structure of the interface layer between the inflowing Atlantic waters and outflowing Mediterranean waters in the Strait of Gibraltar. The interface is 60–100 m thick, with a strong vertical salinity gradient identified by fitting individual salinity profiles to a piecewise‐linear, three‐layer model. The interface is deeper, thicker, fresher, and colder on the west end of the strait than in the Narrows, where there is a minimum in thickness and a maximum in salinity gradient. Farther east, the interface thickens again and continues to get saltier, warmer, and shallower. Property variations in all three layers are also cast in terms of the three principal water types involved in the exchange. The traditional Knudsen model of exchange is extended to three layers, assuming that the interface is a transport‐carrying third layer with uniform vertical shear. As much as half of the inflowing or outflowing transport occurs in the interface layer. Transport converges in both the upper and lower layers, implying, over the length of the strait, vertical exchange between layers that is comparable to about half the horizontal exchange. The richness of structure and complexity of interaction between the interface and the upper and lower layers argues against the use of two‐layer models to characterize exchange through the Strait of Gibraltar.
It has become common practice to measure ocean current velocities together with the hydrography by lowering an ADCP on typical CTD casts. The velocities and densities thus observed are considered to consist mostly of a background contribution in geostrophic balance, plus internal waves and tides. A method to infer the geostrophic component by inverting the linearized potential vorticity (P V) provides plausible geostrophic density and velocity distributions. The method extracts the geostrophic balance closest to the measurements by minimizing the energy involved in the difference, supposed to consist of P V-free anomalies. The boundary conditions and the retention of P V by the geostrophic estimates follow directly from the optimization, which is based on simple linear dynamics and avoids both the use of the thermal wind equation on the measured density, and the classical problem of a reference velocity. By construction, the transport in geostrophic balance equals the measured one. Tides are the largest source of error in the calculation. The method is applied to six ADCP/CTD surveys made across the Yucatan Channel in the springs of 1997 and 1998 and in the winter of 1998-1999. Although the time interval between sections is sometimes close to one inertial period, large variations on the order of 10 percent are found from one section to the next. Transports range from 20 to 31 Sv with a net average close to 25 Sv, consisting of 33 Sv of in ow into the Gulf of Mexico and 8 Sv of out ow into the Caribbean Sea. The highest velocities are 2.0 m sec 2 1 into the Gulf of Mexico near the surface on the western side of the channel, decreasing to 0.1 m sec 2 1 by 400 to 500 m depth. Beneath the core of the Yucatan Current a countercurrent,with speeds close to 0.2 m sec 2 1 and an average transport of 2 Sv, hugs the slopes of the channel from 500 to 1500 m depth. Our data show an additional 6 Sv of return ow within the same depth range over the abrupt slope near Cuba, which is likely to be the recirculating fraction of the Yucatan Current deep extention, unable to out ow through the Florida Straits. The most signi cant southerly ows do not occur in the deepest portion of the channel, but at depths around 1000 m.
The vertical structure of a recently detached Loop Current Eddy (LCE) is studied using in situ data collected with an underwater glider from August to November 2016. Altimetry and Argo data are analyzed to discuss the context of the eddy shedding and evolution as well as the origin and transformation of its thermohaline properties. The LCE appeared as a large body of nearly homogeneous water between 50 and 250 m confined between the seasonal and main thermoclines. A temperature anomaly relative to surrounding Gulf's water of up to 9.7 ∘ C was observed within the eddy core. The salinity structure had a double core pattern. The subsurface fresh core had a negative anomaly of 0.27 practical salinity unit, while the deeper saline core's positive anomaly reached 1.22 practical salinity unit. Both temperature and salinity maxima were stronger than previously reported. The saline core, of Caribbean origin, was well conserved during its journey from the Yucatan Basin to the Loop Current and at least 7 months after eddy detachment. The fresher homogeneous core resulted from surface diabatic transformations including surface heat fluxes and mixing within the top 200 m during the winter preceding eddy detachment. Heat and salt excess carried by the LCE were large and require important negative heat fluxes and positive fresh water input to be balanced. The geostrophic velocity structure had the form of a subsurface intensified vortex ring.
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