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Mathematical modeling of Black Sea level change for the last 20000 years

July 25, 2014

A mathematical model of the Black Sea level change for the last 20,000 years is presented in this paper, based on the equations of viscous incompressible fluid motion according to Navier–Stokes, Sen-Venans, and the equation of water balance in the sea. The solution of the differential equations shows that the Black Sea level has been generally rising due to glacier melting and increase of freshwater balance in the late Pleistocene. Water which was flowing into the Black Sea did not have time to fully flow into the Marmara Sea because water was flowing through the long and very narrow canyon, which the Bosphorus strait was then. Water accumulating in the Black Sea increased the sea level, and increased the slope of the surface of river in the strait towards the Marmara Sea. When the level of the world ocean rose above river level, the strait began to form. Increasing depth caused excessive water to flow from the Black Sea. As a result of regression, the Black Sea level approached the Marmara Sea level, and the global oceanic transgression of the two seas began, continuing to the present.

When the depth of the strait was 12–15 m, the penetration of the Marmara Sea’s dense water into the Black Sea occurred. Water discharge in the counterflow was increasing when the ocean level was rising.

The calculations showed that secondary fluctuations of the Black and Marmara Seas levels greater than 50 cm were theoretically impossible during the Holocene, as the deep strait allowed the possibility of intensive flow toward either the Black or Marmara Sea. When the value of the freshwater balance is positive, the regression of the Black Sea level below Marmara Sea level is theoretically impossible.

Vertical movement of Earth crust can modify the shape of the eustatic sea level curves. A method allows calculation of the eustatic sea level course using the known local curves. The eustatic Mediterranean Sea level change and world ocean level change are calculated using nine local Mediterranean Sea level change curves. Tectonic components of the nine local curves were calculated. An assessment of the method’s accuracy was made.

Esin NV, Esin NI, in press: Mathematical modeling of Black Sea level change for the last 20000 years, Quaternary International, doi:10.1016/j.quaint.2014.05.026. Article (subscription required).

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