Physical Oceanography, Vol. 19, No. 1, 2009
BOTTOM BOUNDARY LAYER IN THE BLACK SEA: FORMATION OF THE
A. S. Samodurov
We make an attempt to answer the following question: how a natural stationary system formed
by a layer and an interface “selects” a unique set of governing parameters from a great number of
possible collections under the conditions of double-diffusion layer convection (e.g., for the bot-
tom boundary layer in the Black Sea)? As the “rule of selection,” we use the principle of mini-
mum entropy production for systems close to the state of thermodynamic equilibrium. In the
process of solution of the problem, the system is regarded as a heat engine. The proposed ap-
proach is reduced to a simple procedure of application of the principle of minimum entropy pro-
duction to the analyzed case. The combined analysis of the theoretical results, the data of deep-
water field measurements in the Black Sea, and the results of laboratory experiments leads us to
the conclusion that, most likely, the stationary system “selects” its governing parameters accord-
ing to the Prigogine–Glansdorff principle. The density ratio (approximately equal to three for the
stationary case) proves to be the key parameter of the system.
The bottom boundary layer (BBL) located in the abyssal part of the Black Sea is an integral component of
the vertical structure of the sea and reflects the specific features of exchange processes running in the deep-water
part of the basin. The thermal structure of the BBL and the instability of temperature gradient in the lower
layer of the sea are explained by the presence of a bottom geothermal heat flux Q
[1, 2]. The presence of
stable density stratification is guaranteed by the vertical distribution of salinity which, in turn, is formed by the
salt waters of the Lower Bosporus Current . An especial role played by the geothermal flux in the formation
of the BBL in the Black Sea is partly explained by the fact that the dynamic processes participating in the forma-
tion of the bottom mixed layer in the open ocean, e.g., barotropic tides, are, in fact, absent in the sea.
The analyzed layer can be conventionally split into two parts: a lower quasiuniform layer formed by free
density convection and an upper stratified interface characterized by fairly large, as compared with the upper
layers of the liquid, drops of the potential temperature, salinity (Fig.
1), and potential density. The mean vertical
scale of the BBL d and the thickness of its stratified upper interface δ constitute about
and several tens
of meters, respectively. Hence, in constructing a model of the BBL, we assume that the thickness of interface δ
is negligibly small as compared with the thickness of the layer d.
The presence of sharp drops of salinity ΔS and potential temperature ΔT in the upper interface accompa-
nied by low values of the density ratio
(on the average, it is approximately equal to
enables us to assume that, in this case, the diffusive exchange is governed by the mechanism of double diffusion
under the conditions of layer convection. In the expression for the density ratio, S is the concentration of salt
(in SI units), T is the potential temperature, and β and α are, respectively, the corresponding coefficients of
contraction and expansion.
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol, Ukraine.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
16–25, January–February, 2009. Original article submitted August 1,
2007; revision submitted September 14, 2007.
0928-5105/09/1901–0013 © 2009 Springer Science+Business Media, Inc. 13