Physical Oceanography, Vol.
MATHEMATICAL MODELING OF MARINE SYSTEMS
MODELING OF THE THREE-DIMENSIONAL STRUCTURE OF HYDROLOGICAL FIELDS
IN A KARST CAVITY UNDER THE ACTION OF SUBMARINE
DISCHARGE OF UNDERGROUND WATERS
N. B. Shapiro
We discuss the results of numerical simulation of the process of submarine discharge in a karst cavity. It
is assumed that fresh water percolates through cracks in the lateral boundaries of the cavity, and its tem-
perature is, generally speaking, not equal to the temperature of water in the grotto. The calculations are
carried out within the framework of a three-dimensional model on the
-coordinates in the hydrostatic
approximation by using the procedure of “convective adjustment” guaranteeing the existence of stable
density stratification with conservation of the amounts of heat and salt. The comparison with the data of
observations shows that the model gives a qualitatively correct description of the structure of the fields
of temperature, salinity, and current velocities formed as a result of submarine discharge in the cavity.
The possibilities of subsequent improvement of the model are discussed.
In the present work, we present the results of numerical experiments aimed at the reproduction of the ob-
served three-dimensional structures of the fields of temperature, salinity, and current velocity in a karst cavity
(grotto) located in the region of Cape Aiya on the South Coast of Crimea. Fresh water penetrates into the grotto
through cracks in its walls, i.e., we observe the phenomenon of submarine.
The observations  were carried out in the course of a special expedition in September 2007. The period
of measurements was characterized by the low level of the surge caused by the long-term action of the west
wind. Due to the presence of the low level of the surge (upwelling) during the day of measurements, the tem-
perature of water in the sea was ~
14º (the normal temperature of water for this period is equal to
the exit from the cavity (on the sea surface), the temperature of seawater attained
15º. The presented values of
temperature show that, in the analyzed case, fresh underground waters are warmer than seawater. The salinity of
water at the exit from the karst cavity under a thin surface layer with a salinity of
remained almost con-
stant in depth and equal to 18.2‰. In the absence of low level of the surge in the investigated water area in Sep-
tember, the indicated levels of salinity are typically observed at depths of 3050
The observed vertical structure of waters at the exit from the cavity and inside it reveals the presence of in-
tense submarine discharge of underground waters in the cavity. Its traces are mainly detected in the surface
layer with a thickness of at most 1
m both in the temperature and salinity fields and in the field of currents (in
this layer, water flow is directed from the cavity into the sea). According to the data of measurements, the
maximum velocity of the outward flow at the exit from the cavity equal to 4 cm/sec was attained on the sea sur-
face. The maximum velocity of the inward flow equal to 3
cm/sec was attained at depths of 1.5–2
m. We em-
phasize that we study currents averaged over time in order to exclude oscillations caused by the presence of
wind waves and swell.
Marine Hydrophysical Institute, Ukrainian National Academy of Sciences, Sevastopol, Ukraine.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
46–62, January–February, 2010. Original article submitted September 17,
2008; revision submitted October 13, 2008.
42 0928–5105/10/2001–0042 © 2010 Springer Science+Business Media, Inc.