Oguz, T. (2005) "Hydraulic adjustment of the Bosphorus exchange flow". Geophys. Res. Letters, 32, L06604, doi:10.1029/2005GL022353.
The anticipated quasi-steady hydraulic controls of the Bosphorus exchange flow system due to the sills near its two ends and the contraction in the middle have been qualitatively inferred by Oguz et al., (1990), Latif et al., (1991), Ozsoy et al., (1996), Di Iorio and Yuce, (1999), Ozsoy et al., (2001).
These observational studies have been complemented by a numerical modeling study (Oguz, 2005) using a three dimensional time dependent, continuously stratified flow structure. The goals of the modelling studies are
The model simulation shown in the figure below considers an idealized version of the strait geometry. The strait is considered in the form of 2 km wide rectangular channel with a 4 km long and 1 km wide constriction zone, gradually expanding on its both sides, placed at 12.5-16.5 km from the Marmara entrance. The idealized channel also accommodates 35-40 m deep southern sill located 3.0-4.0 km away from the Marmara entrance, and 60m deep northern sill at 2-3 km outside the northern entrance. Variations of the bottom topography between these sills are excluded by taking the flat bottom at 80 m depth.
The flows entering into the channel from both sides quickly establish a two-layer structure. The interface, identified by sigma-t range of 13-26 kg m-3, extends almost horizontally at the depth of 47±8 m on the upstream (northern) side of the constriction. Up on entering the constriction zone, the interface rises steeply and linearly by about 25 m, and then extends horizontally at the depth of 16±6 m up to the Marmara end of the channel. The currents in the surface layer are modified accordingly from their values less than 0.5 m s-1 to the north of the constriction to about 1.0 m s-1 near the southern exit of the constriction, and then to the range of 0.5-0.7 m s-1 towards the Marmara end of the channel.
The underflow enters into the strait from the Marmara side with salinity of ~38.5 psu, density >28 kg m-3 and speed of ~0.3 m s-1 below 20 m depth. Currents are then accelerated up to 0.7 m s-1, density is stratified between 26 and 28 kg m-3 within the southern sill and constriction zones. Thereafter, the underflow proceeds within the northern half of the strait with weaker currents of about 0.3-0.4 m s-1 up to the northern sill, where it undergoes significant transformations. It finally flows with currents in excess of 1.0 m s-1 over the sill and on its downstream side within a highly stratified narrow layer.
All these features are consistent with the observations. Thus, the simulation with such a highly idealized channel configuration was able to capture very well most of the main observed features of the Bosphorus exchange flow system.
The internal hydraulic adjustment of the exchange flow has been monitored approximately by computing the Richardson number Ri = [g(Δρ/ρ)•Δz] / Δu2 at every two meter bins over the water column. The condition of Ri<0.25 satisfied at points shown by triangles in the figure indicates transition of the flow to its supercritical state within the constriction. Few grid points beyond its southern exit, the value of Richardson number exceeds its critical limit indicating transition of the flow back to its subcritical conditions. The upper layer plays the major role on this particular hydraulic adjustment of the exchange flow system. Its impact on the lower layer is evident by stronger currents, stronger mixing, and a broader zone of weakly stratified water mass structure characterized by 27 and 28 kg m-3 sigma-t contours within the deepest 20 m layer of the water column.
Triangles representing Ri < 0.25 indicate another hydraulic control of the exchange flow system over the sill and supercritical conditions on its northern flank. The mixing associated with this hydraulic adjustment process causes some deformation and broadening of the interface as compared to its fairly stable structure in the northern half of the strait. Sharp rise of the isopycnals at grid point 22-23 and their subsequent deepening at grid points 25-26 indicate establishment of the subcritical state through internal hydraulic jump between two adjacent control sections.
The third hydraulic adjustment takes place when the lower layer flow is sandwiched between the northern sill and the deep upper layer at grid points 67-69. As in the case of the southern sill, the dense water mass of the Mediterranean origin flows supercritically for 3 km along the northern periphery of the sill, and then reverts to the subcritical state through undergoing an internal hydraulic jump. The contribution of the upper layer is negligible for this hydraulic control.
The idealized-case simulation is repeated by introducing
(i) a more detailed representation of the constriction zone,
(ii) the “L-shape” bends on both sides of the constriction zone,
(iii) details of the topography excluded for the region between the sills in the previous simulation.
Except slight weakening of currents as compared with the straight channel case, the northern bend does not introduce any appreciable impact on the Bosphorus dynamics. The interface structure, the upper and lower layer flow properties, and the internal hydraulic properties of the exchange flow system between the southern sill and the constriction zone resemble very closely those reported in the previous idealized case.
The only major change in the flow structure occurs near the southern end of the strait. The interfacial layer rises gradually and is exposed to another jump around grid points 8-10, which lie on the downstream side of the sharp convex bending of the channel. As suggested by triangles in the figure, this jump reflects hydraulic adjustment of the flow, and transition of the upper layer flow to its supercritical state as it leaves the strait with typical currents of about 1.0 m s-1 within the uppermost 10 m layer. The lack of these features in the absence of the bend (see the previous figure) shows a contribution of the centrifugal force arising from the channel curvature to the internal hydraulic adjustment of its flow structure near the southern end of the Bosphorus. No matter how weak, the constriction zone first tilts the interface closer to the surface so that the surface-intensified upper layer flow is able to exert a more strong hydraulic control at the southern exit. As in the previous simulation, the underflow experiences a well-defined control by the sill located near the northern end of the strait.
In conclusion, the upper and lower layer flows exiting from the strait at both ends are characterized by u~1 m s-1, h~10 m, g'~0.1 m s-2, and therefore the Bosphorus two layer exchange flow system possesses the maximal exchange conditions. The way in which the shallow interface at the southern exit is connected to a deeper interface of the Bosphorus-Marmara junction region in fact reflects an outcome of the maximal exchange.