Physical Oceanography, Vol. 13, No. 2, 2003
LAGRANGIAN TRANSPORT BY CURRENTS VARIABLE IN TIME IN THE
MODEL OF WIND-INDUCED CIRCULATION OF THE BLACK SEA
G. K. Korotaev
and G. A. Khomenko
UDC 551.465 (262.5)
We construct a simple model of seasonal variability of circulation in the Black Sea, which sat-
isfactorily explains the data of altimetric satellite observations. The model is used to describe the
nonstationary wind-induced currents in a round basin and study the trajectories of water particles
in the surface layer of the sea. It is shown that, for nonstationary currents, these trajectories can
be quite complicated. It is also assumed that Lagrangian mixing can be caused by the complex
trajectories of water particles.
In recent years, a great part of new information about the dynamics of sea basins is accumulated by analyz-
ing the satellite images or the data of observations over the drift of surface buoys. These observations are char-
acterized by high space and time resolutions and enable one to get qualitatively new pictures of processes in the
sea. Thus, in particular, the satellite images obtained in the optical and infrared spectral bands reveal various
threadlike structures formed in the coastal regions, over the continental slope, and near the boundaries of the cur-
rents. The trajectories of drifting buoys are often quite complicated and, as a result, the buoys can, e.g., re-
peatedly cross the midstream of the current. At first sight, the outlined complex structure of the field of surface
temperature (or sea color) and complex trajectories of the drifting buoys can be regarded as indications of the
complex dynamics and turbulence of sea currents. However, it should be emphasized that the drifting buoys and
satellite images characterize, to a significant extent, the Lagrangian transport. It is now well known that the
Lagrangian dynamics of water particles can be stochastic even if the velocity field is described by fairly simple
laws [1, 2]. As the most well-known example, we can mention stationary
ABC-currents characterized by chaotic
trajectories of the particles .
Numerous researchers formulate necessary and fairly general conditions under which the motion of water
particles may become chaotic. Thus, even in a two-dimensional flow, the motion of particles can be chaotic for a
simple law of nonstationary evolution of the velocity field [1, 2]. This should be taken into account both in anal-
yzing the phenomena with significant contribution of the Lagrangian transport and in their interpretation.
The aim of the present work is to give an illustration of possible behavior of water particles in the surface
layer of the sea in the case where the dynamics of currents is simple and obeys classical regularities. It should be
emphasized that a simple dynamics of this sort is realized in nature. As a prototype of our simplified model, we
use the dynamics of the Black Sea whose fairly detailed description can be obtained by analyzing the data of alti-
metric satellite measurements.
2. Seasonal Dynamics of Currents in the Black Sea
The uniform space distribution of the data of altimetric satellite measurements and their regularity turn
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol.
Université du Littoral Côte d'Opale, Dunkerque, France.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
14–26, March–April, 2003. Original article submitted October 22, 2001;
revision submitted January 3, 2002.
0928-5105/03/1302–0075 $25.00 © 2003 Plenum Publishing Corporation 75