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 The Persian Gulf is considered the third largest gulf in the world, following the Gulf of Mexico and Hudson Bay. The Strait of Hormuz is the most important passage for the entry and exit of oil to the world and one of the most significant routes for the transit of non-oil goods from Southeast Asia to the Middle East. It's also one of the most strategic regions in the world. The Persian Gulf and the Gulf of Oman are critical strategic and commercial centers for Iran, housing a variety of biological species as well as oil and gas resources (Raeisi et al, 2020). 

The Persian Gulf is a semi- enclosed water basin with an average depth of 35 meters. The Gulf of Oman, located in the northwest Indian Ocean near the Arabian Sea, is L-shaped. The Persian Gulf, a semi-enclosed and shallow marine area, is one of the world's most important and strategic waterways in terms of military, economic, and political significance. This gulf is connected to the Gulf of Oman and the Indian Ocean via the Strait of Hormuz. The Strait of Hormuz is located approximately at 26 degrees 30 minutes north and 56 degrees 30 minutes east. Its importance is highlighted by the fact that an ocean-going vessel passes through the strait every six minutes (Alhajri, 1991). The width of the Strait of Hormuz is 56 km, with average and maximum depths of 90 and 110 meters, respectively. The weather conditions in this gulf include northwesterly winds with seasonal variations, also seen in the Gulf of Oman. The water temperature in the Persian Gulf at the Strait of Hormuz varies between 32-34 degrees Celsius in summer and 18-20 degrees Celsius in winter. Due to the high rate of surface water evaporation compared to the influx of fresh water from precipitation and rivers, the Persian Gulf is considered an inverse estuary (Reynolds, 1993).

 The Persian Gulf extends northwest-southeast between 25 to 30 degrees north latitude and 48 to 56 degrees east longitude. The Gulf of Oman is located between 26 to 32 degrees north latitude and 56 to 62 degrees east longitude (Figure 1). The maximum depth of the Persian Gulf is 90 meters, while depths greater than 100 meters are observed in the Strait of Hormuz." 

Figure 1: Map of the Persian Gulf, Strait of Hormuz, Gulf of Oman, and the Arabian Sea (Pous et al., 2003). 

The shallow depth in the Persian Gulf and the high rate of evaporation, along with the limited water exchange in the Strait of Hormuz, create a thermohaline circulation and a body of saline water in the southern Persian Gulf. The water exchange in the Strait of Hormuz resembles an inverted estuary with the surface waters of the Indian Ocean. The thermohaline characteristics of the water masses in the Persian Gulf decrease downstream from the Persian Gulf to the Gulf of Oman. The thermohaline characteristics of the waters in the Persian Gulf and the surface waters of the Indian Ocean exhibit significant seasonal variations, which can be observed by plotting temperature, salinity, and relative density contours and comparing them. The average mass transfer of thermohaline currents in the Strait of Hormuz is estimated at 0.1 to 0.2 Sverdrup, with a velocity ranging between 0.2 to 0.3 meters per second using flow data. Temperature is a crucial physical parameter in the region and one of the factors affecting the thermohaline currents in the Strait of Hormuz, eventually generating wind and causing currents. Temperature studies in the region can also aid in studies of flow and circulation in the Gulf. The main factor for temperature fluctuations on Earth is the angle of solar radiation with different regions. The increase in water temperature inversely affects density. The movement and rotation of water masses in the Persian Gulf and Strait of Hormuz are directly influenced by temperature. Therefore, by examining surface and depth temperatures, the impact on currents can be observed. 

The measured average salinity at the mouth of the Strait of Hormuz is approximately 36.5 to 37 psu. Moving away from the strait and into the Persian Gulf, salinity increases significantly, reaching about 41-41.5 psu in the coastal waters of Saudi Arabia. However, moving in the opposite direction and advancing into the waters of the Gulf of Oman, salinity decreases to 35 psu. According to hydrographic reports, the salinity of the Persian Gulf in winter is higher than in summer, possibly due to high water evaporation in winter due to cold air adjacent to the sea water and the flow of fresh water from the Arvand River, which reaches its minimum level from September to November each year. The salinity of the water in the southern part of the strait at the entrance of the Persian Gulf to the strait in the United Arab Emirates reaches 44.3 psu, likely due to limited circulation in the Gulf and high evaporation rates in the region. The RV Atlantis (1977) conducted a marine survey of the Persian Gulf. According to this study, Indian Ocean water with a salinity of 36.6 psu and a temperature of 22 degrees Celsius enters the Gulf through the strait and flows northwards. Along this path, salinity increases to 40.5 psu in the middle of the Gulf, then decreases again to 36 psu near the coasts of Iraq and Kuwait, due to the presence of the Arvand River in this area (Brewer and Dyrssen, 1985). The water circulation model in the Persian Gulf indicates that the main factor for the outflow of water from the Gulf through the Strait of Hormuz is density, while wind is the primary factor for the inflow of Indian Ocean water into the Gulf. The density difference on both sides of the strait causes the saline and dense waters of the Persian Gulf to move toward the Gulf of Oman, completing the circulation in the Persian Gulf. In winter, the density difference between the Gulf of Oman and the Persian Gulf is due to the lower salinity of the water entering the Persian Gulf from the Gulf of Oman. Along the Iranian coast, coastal currents form due to the density difference between rivers and the waters of the Persian Gulf. Density studies in the northern part of the Strait of Hormuz show that in winter, the water has a single-layer structure in the north of the strait, while it has a double-layer structure in the south of the strait.

 In summer, the northern Strait of Hormuz splits into two separate layers, while in the south, the water retains its winter double-layer structure. The density differences between the northern and southern parts of the strait show that the flow movement in the northern strait aligns with the depth contours, meaning that current lines do not intersect depth contours. In the southern part, the depth contours intersect the current lines moving from the Gulf to the strait. This phenomenon in the southern strait is due to the increased density caused by higher salinity and the movement of dense Persian Gulf water to the depths. Meanwhile, in the northern strait, the waters on both sides have similar densities, and perhaps the incoming waters from the Indian Ocean are slightly less dense than the existing regional waters. 

The Persian Gulf is a source of one of the world's saline water masses, thus studying it through various methods like satellite, field, and numerical studies is important. Water circulation studies are key for other studies including water masses, as in some basins like the Persian Gulf, water mass formation occurs during its circulation. Prasad et al. (2010) demonstrated this water circulation and mass formation effectively. 

The inflows and outflows currents of the Persian Gulf 

The inflows and outflows of the Persian Gulf were described by Matsumaya et al. (1998) using an ADCP (from December 16, 1993, to January 2, 1994) in the southern Strait of Hormuz, showing the vertical current structure and its variations as a combination of tidal and low-frequency currents. The tidal currents are mainly due to barotropic tides, with diurnal tidal currents dominating over semidiurnal ones. Inflow from the surface layer and outflow from the deep layer of the Persian Gulf was observed. In their longest field study (December 1996 to March 1998), John et al. (2003) described the physical and hydrodynamic characteristics of the water using a mooring system in the southern Strait of Hormuz. They observed a stable outflow of dense Persian Gulf water from 40 meters depth to the seabed at a velocity of approximately 20 cm s^(-1). Surface water flow direction varied with location and time. Pous et al. (2004) measured physical properties, current profiles, water level fluctuations, and surface current characteristics in the eastern (entrance) Strait of Hormuz (October and early November 1999), examining outflowing and inflowing Persian Gulf water and different water masses. Inflowing water enters from the Iranian side of the strait, while dense Persian Gulf water exits from the southern part and the deep layer of the strait.

 Recent studies by Azizpour et al. (2016) during field measurements (November 2012 and January 2013) with four subsurface mooring systems characterized the tides in the Strait of Hormuz as a standing wave, combining semidiurnal to diurnal tides. Hunter (1982) analyzed data from the UK Meteorological Center’s floating vessel in 1981, showing a surface current at a speed of 0.1 m/s from the eastern strait into the Persian Gulf along the Iranian coast. Seasonal variations of this inflow current from the Gulf of Oman into the Strait of Hormuz were stronger in summer (about 0.2 m/s) and weaker in winter and autumn, with the inflow estimated between 0.1 to 0.2 m/s along the Iranian coast by observing ship deviations.

 Sonu (1979) predicted an inflow current extending 200 km into the Persian Gulf through the Strait of Hormuz, based on April 1977 data. Movements driven by water density changes and pressure gradients in the region were described by Schott (1918), Barlow (1932), the British Navy (1941), Emery (1956), Sugden (1963), Hartmann (1971), Szekielda (1972), Purser and Seibold (1973), and Grasshoff (1976). An outflow current from the Persian Gulf into the Gulf of Oman through the Strait of Hormuz was reported by Sewell (1934), Emery (1956), Duing and Koske (1967), Duing and Schwill (1976), Leveau and Szekielda (1968). Sugden (1963) proposed a surface inflow over the outflowing current along with a counterclockwise circulation within the Persian Gulf, influenced by seasonal monsoons. Hunter (1982) concluded that high evaporation in the northwest and north of the Persian Gulf causes dense water to sink and move towards the Strait of Hormuz with a rightward deflection by the Coriolis force, suggesting this current is compensated by another inflow from the Gulf of Oman into the Persian Gulf along the Iranian coast. Hunter’s numerical model (1983) predicted a strong surface inflow at 0.1 m/s along the Iranian coast, interpreting these results as a surface inflow in the northern Strait of Hormuz and a deep outflow in the southern strait. 

Hunter's results show a significant rotation of the current between the surface and the bottom. Al-Hajri (1990) proposed a model and concluded that density alone cannot be the cause of this circulation, and that wind force is an essential part of the circulation in the Persian Gulf. Johns and colleagues (2003) examined the inflows and outflows of the strait for an extended period from December 1996 to March 1998, showing that low-temperature and low-salinity water from the Gulf of Oman enters the Persian Gulf via the northern Strait of Hormuz. This circulating current brings waters from the Indian Ocean to the northeastern Persian Gulf, where high density and high salinity waters form. These waters then sink under the influence of the Persian Gulf's axial eddy circulation and exit through the deep parts of the Strait of Hormuz.

 Pous et al. (2003) reviewed the results of the GOGP99 cruise in the Strait of Hormuz, concluding that the surface water of the Indian Ocean, which is colder and less saline than regional waters, enters the Persian Gulf through the Iranian coast at depths of 30 to 60 meters. The most saline waters, exiting from the southern strait near the coasts of the UAE and Oman, are found at depths of 50 to 100 meters. For every 150 km the water moves from the Persian Gulf towards the Gulf of Oman, its temperature drops by 3°C and its salinity decreases by 1.5 psu. Pous et al. showed the exit currents' speeds to be less than 0.4 meters per second and estimated the geostrophic speed at a reference level of 30 meters to be 0.09 meters per second.

 Reynolds (1993) modeled water movements in the mesoscale Persian Gulf, with results indicating that surface currents in the Persian Gulf vary between 0.075 to 0.1875 meters per second. These results suggest that the circulation in the Persian Gulf is influenced by factors such as wind, evaporation, salinity differences, temperature differences, density effects, bottom friction, tides, and river discharge. It was confirmed that the slow surface currents entering the Persian Gulf move along the Iranian coast and rotate counterclockwise. 

Water masses of the Persian Gulf and the Gulf of Oman

 Water masses of the Persian Gulf and the Gulf of Oman were measured by Pous et al. in October and early November 1999 in the eastern Strait of Hormuz. They used measured data to review the Persian Gulf's outflow and inflow, as well as various water masses. They indicated that the inflowing water enters the Persian Gulf from the Iranian side of the Strait of Hormuz, while the dense Persian Gulf water exits from the southern and deep layers of the strait.

 Analyzing GOGP99 cruise data, it was found that the outflow current of the Persian Gulf's water mass from the Strait of Hormuz flows southeast, traveling along the sea bed in the Gulf of Oman. This southeast flow, after crossing the continental shelf break, shifts southwest and approaches the Omani coast, proceeding southeast along the coast with a speed of 0.2 meters per second. They also found that the temperature and salinity of the Persian Gulf's water mass decrease from 27°C and 39.75 psu in the Persian Gulf to 21°C and 37.1 psu in the northern Arabian Sea, but this reduction is not uniform. The Persian Gulf's water mass mixes intensely with adjacent water masses in a few places. By plotting temperature and salinity contours of the Strait of Hormuz and the Gulf of Oman, five main water masses were identified: the Seasonal Thermocline Water (TW) at depths of 25 meters with 30°C temperature and 37 psu salinity in summer; the Indian Ocean Surface Water (ISOW) at depths of 50 to 100 meters with 20-22°C temperature and 36-36.5 psu salinity; the Persian Gulf Water (PGW) in the Gulf of Oman at depths of 150 to 300 meters with 20-22°C temperature and 37.25-37.5 psu salinity; the Red Sea Water (RSW) at 800 meters depth with 10-12°C temperature and 35.5 psu salinity; and the North Indian Deep Water (NIDW) at 2000 to 4000 meters depth with 2°C temperature and 34.8 psu salinity.

 Siyof Jahromi (2013) simulated water flow exchanges between the Persian Gulf and the Gulf of Oman using the three-dimensional hydrodynamic model (ELCOM). This study modeled the entire water basin of the Persian Gulf and the Gulf of Oman, including their different waters. The model used tracers in the Strait of Hormuz to follow the water masses of each basin. The results revealed two fronts on both sides of the Strait of Hormuz and a third front in the Arabian Sea, uncovering mesoscale eddies in the Gulf of Oman and non-eddy formations in the Strait of Hormuz. 

The circulation and formation of eddies in the Persian Gulf and Gulf of Oman

 The circulation and formation of eddies in the Persian Gulf and Gulf of Oman were studied by Kampf and Sadrinasab (2004) using a three-dimensional coherence model. Their results showed that a significant seasonal and counterclockwise eddy forms over the entire Persian Gulf in spring and summer, transforming into mesoscale eddies in autumn and winter (Kaempf & Sadrinasab, 2004). 

Surface evaporation rates in the Persian Gulf waters are estimated by researchers to be 1.44 to 2.5 meters per year (Meshal & Hassan, 1986) (Privett, 1959). Meanwhile, river inflows are calculated at 0.15 to 0.46 meters per year, and rainfall at 0.07 to 0.1 meters per year, totaling much less than the evaporation rate. The shallow depth and high evaporation rate, along with limited water exchanges in the Strait of Hormuz, create a dense and saline water mass in the Persian Gulf, acting as an inverse estuary. The high surface evaporation rate in the Persian Gulf results in less saline and lighter Gulf of Oman water entering the Persian Gulf from the northern part of the Strait of Hormuz and flowing along the Iranian coast upstream into the Persian Gulf. Meanwhile, the dense and saline Persian Gulf water exits from the southern Strait of Hormuz into the Gulf of Oman (Kaempf & Sadrinasab., 2004).

 Considering the economic, political, and military significance of the Strait of Hormuz, understanding water circulation in this strait has long been of interest. In one of the recent studies by Johns and colleagues, an ADCP device was installed from December to March 1998 in the Strait of Hormuz, providing the first long term measurements of flow in the Persian Gulf region. These researchers focused on the water exchange between the Persian Gulf and the Gulf of Oman, summarized in Figure 2 They concluded that the outflow of water from the Strait of Hormuz occurs annually with a nearly constant rate throughout the year (Johns et al, 2003). 

Figure 2: Water circulation in the Persian Gulf and Strait of Hormuz by (Johns et al., 2003).

 They believe that the relatively less saline water from the Gulf of Oman enters the Strait of Hormuz from the surface and along the Iranian coast, moving towards the northern Persian Gulf (T1). Part of the incoming water exits with the outgoing waters from the middle layers of the Strait of Hormuz (T2). Heavier and saltier waters from the northwest and southeast Persian Gulf flow towards the Strait of Hormuz from the seabed and eventually exit through the deep layers along the coasts of Oman (T3).

 Thoppil et al. (2010) studied the currents and eddies in the Persian Gulf using the HYCOM model, and they stated that the current towards the northwest Iranian coast is unstable due to baroclinic instability. They observed a series of cyclonic currents with diameters between 115-130 km and estimated the baroclinic Rossby radius of deformation to be between 25-30 km. Figure 3 shows a schematic diagram of these circulations presented by them (Thoppil et al., 2010).

 Figure 3 shows a schematic diagram of the circulation in the Persian Gulf (Thoppil et al., 2010).

 Yao et al. (2010) used the HYCOM model to examine the circulation and mass changes of water, the Persian Gulf, and its exchange with the Indian Ocean via the Strait of Hormuz. They observed an eddy about 100 km in size along the salinity front in summer and estimated the Rossby radius of deformation for the Persian Gulf to be 30 km (Yao et al., 2010). 

Pous et al. (2014) conducted a high-resolution study using the HYCOM numerical model on water circulation patterns in the Persian Gulf and the water exchanges in the Strait of Hormuz. They calculated the length of some mesoscale eddies to be 120 km (Pous et al., 2014).

 Bidokhti et al. (2004) examined the reasons and locations for the formation of eddies in the Persian Gulf. They used field data to determine the structure of temperature, salinity, conductivity, and density fields in the central Persian Gulf at various depths. They also identified the formation locations, heights, surface, or depth of the eddies, and their dynamic properties, such as potential and kinetic energy. Horizontal eddies were found to be about 120 km in diameter, with depths between 30-40 m. Moghadam and Bidokhti (2007) studied the formation of eddies in the Gulf of Oman due to density changes (caused by temperature and salinity changes). They sought the formation locations of eddies, whether they were surface or depth eddies, and their speed and horizontal diffusion coefficient in the Gulf of Oman. Pous et al. (2004) used field measurements from the GOGP99 marine survey conducted from October to early November 1999 in the Strait of Hormuz and the Gulf of Oman to identify the regional circulation of the Gulf of Oman (upper 300 m depth) using SADCP.

 Figure 4: shows the regional circulation of the Gulf of Oman using SADCP (Pous et al., 2004).

 Hégaret et al. (2015) studied the significant seasonal variations in mesoscale structures, water circulation, and the identification of water masses in the Gulf of Oman and the Arabian Sea under the influence of the monsoon. They examined their impact on water pathways in the Persian Gulf. Their study utilized field observations, satellite altimetry data, and the HYCOM model to analyze the interaction and merging of eddies. After studying various eddies in the Persian Gulf, they noted that the outflow currents from the Persian Gulf are influenced by mesoscale eddies, affecting the movement and distribution of these currents throughout the Gulf of Oman (Hégaret et al., 2015).

 Seasonal Structure of Inflowing and Outflowing Water Masses in the Persian Gulf:

 The structure of the outflowing Persian Gulf Water (PGW) is determined by its temperature and salinity in the Strait of Hormuz. Field studies specifically within the Strait of Hormuz are limited, and only a few have examined the physical and hydrodynamic properties of the water in this region. These include field measurements by Johns et al. (2003) and Pous et al. (2004), which were primarily focused on the southern part of the Strait of Hormuz.

 In some studies of the Persian Gulf and Gulf of Oman, the Strait of Hormuz was also examined (Johns et al., 2003). Other notable studies in this field include those by Emery et al. (1956), Reynolds (1993), and Brewer and Dyrssen (1985). Periodic RAPME surveys in the years 1991, 2000, 2001, and 2006 also conducted multifaceted measurements, including physical and chemical properties of the water masses in the region.

 Analyzing data from the UK Meteorological Centre's floating vessel in 1981 showed a current caused by the surface water mass of the Indian Ocean entering the Persian Gulf from the east of the strait at a speed of 0.1 meters per second along the Iranian coast. The results of this analysis for four seasons indicate that the inflow speed of the Indian Ocean surface water mass is stronger in summer (around 0.2 meters per second) and weaker in winter and autumn. A numerical model predicted a strong surface inflow at a speed of 0.1 meters per second along the Iranian coast, showing a surface inflow in the northern Strait of Hormuz and a deep outflow in the southern Strait of Hormuz. 

Johns and colleagues examined the inflow and outflow water masses in the Strait of Hormuz for an extended period from December 1996 to March 1998, showing that low-temperature and low-salinity water from the Gulf of Oman enters the Persian Gulf via the northern Strait of Hormuz. Pous and colleagues reviewed the results of the GOGP99 survey in the Strait of Hormuz and concluded that the surface water mass of the Indian Ocean, which is colder and less saline than regional waters, enters the Persian Gulf through the Iranian coast at depths of 30 to 60 meters. The saltiest waters, exiting from the southern strait near the coasts of the UAE and Oman, are found at depths of 50 to 100 meters. Pous and colleagues showed the exit currents' speeds to be less than 0.4 meters per second and estimated the geostrophic speed at a reference level of 30 meters to be 0.09 meters per second.

 Reyis AlSadat and Banazadeh (2001) developed a model for water circulation in the Persian Gulf. Their study confirmed that the calm surface water mass entering the Persian Gulf moves along the Iranian coast and rotates counterclockwise. The inflow from the Gulf of Oman into the Strait of Hormuz is deflected towards the north of the strait along the Iranian coast due to the Coriolis force. This surface current moves towards the Persian Gulf due to the lower density of the waters in this area compared to the surrounding waters in the Persian Gulf, with a surface speed reaching 10 to 20 centimeters per second (Reynolds, 1993).

 Evaporation and radiation cause an increase in temperature and salinity, forming a thermohaline current in this region. The increase in density leads to the deepening and formation of the dense water mass of the Persian Gulf and its thermohaline current, moving towards the Strait of Hormuz. The densest water, with over 1033 kg per cubic meter, is found around the coasts of Bahrain. These deep currents reach speeds of 5 to 10 cm per second within the Persian Gulf but accelerate to about 20 to 30 cm per second while passing through the Strait of Hormuz (Swift and Bower, 2003).

 In autumn, the incoming water mass in the Strait of Hormuz exhibits dynamic instability. During this season, entering the cold season and the cooling of waters in the southern parts of the strait, denser water forms locally with densities exceeding 1030 kg per cubic meter. Mid-scale eddies form at depths of 20 meters along the density front. The dense water from the shallow regions of the southern Persian Gulf gradually moves towards the deep dense current and eventually covers the Strait of Hormuz and the Persian Gulf (Bower et al., 2000). 

In winter, surface circulation due to water movement disintegrates into mid-scale eddies. This process is observed throughout the Strait of Hormuz, particularly in the Persian Gulf. Winter cooling creates a denser water mass in the shallow southern regions of the Persian Gulf with densities over 1032 kg per cubic meter, which moves with the deep outflow towards the Strait of Hormuz. This increase in density is observed from late January to May. There is a three-month delay between the formation of the dense water mass in shallow waters and its observation in the Strait of Hormuz (Chao et al., 1992).

 In spring, the density differences across the strait reach their maximum. In this season, inflow currents begin to form and move towards the Persian Gulf, even entering the shallow areas of the southern Strait of Hormuz. Importantly, surface waters of the Persian Gulf and the Strait of Hormuz are saltier in winter than in summer. Increased surface inflow to the Persian Gulf from the Gulf of Oman may explain the lower salinity of surface waters in the northern Strait of Hormuz and the Persian Gulf (Matsuyama et al., 1994). 

The seasonal circulation of the Persian Gulf is associated with the formation of dense deep water in the southern Gulf during autumn and winter, which appears in the strait in late winter and early spring. It can be concluded that the formation of dense deep water in the Persian Gulf may be due to the cooling of surface saline waters in autumn and the beginning of winter. The outflow of water from the Persian Gulf is relatively stable throughout the year, with a transfer of 0.03 to 0.15 Sverdrup and an average salinity of 39.5 psu. The salinity of this outflow varies significantly across seasons, showing the most considerable changes in winter when the outflow salinity ranges from 39.5 to 40.8 psu (Matsuyama et al., 1998)