Physical Oceanography, Vol. 16, No. 3, 2006
THERMOHYDRODYNAMICS OF THE OCEAN
DYNAMIC MODES OF PROPAGATION AND TRANSFORMATION
OF SUBSURFACE GRAVITATIONAL LENSES
A. S. Samodurov
We study the dynamic features of propagation of subsurface gravitational lenses and the condi-
tions of changes in the modes of control over their motion by various internal and external
forces. As these forces, we study the action of drag, molecular and turbulent viscosity due to the
presence of internal and external forces, and deceleration caused by the effects of double diffu-
sion. We also analyze the modes of propagation of small-scale gravitational lenses. The infor-
mation about these lenses taken from the literature is supplemented and generalized.
Subsurface gravitational lenses play an important role in the dynamics of the coastal regions of oceans and
seas. Formed as a result of the drainage of dry land and the discharge of rivers, they preserve the existing
contrast of their properties with the properties of surrounding water for long periods of time as a result of realiza-
tion of specific modes of the vertical and horizontal exchange of heat, salt, and other chemical admixtures in the
bulk of water. The frontal zones of the lenses serve as a basis for the development of various biological commu-
nities. In the present work, we make an attempt to describe the principal modes of propagation of small-scale
gravitational lenses encountered in nature.
A very simple and clear approach to the problem of the dynamics and evolution of small-scale gravitational
lenses was proposed by Benjamin . Following his work, we consider a stationary state of an air bubble of in-
finite volume in a layer bounded along the vertical by hard walls and filled with a moving fluid of density ρ
1). The viscous forces are neglected and the motion is regarded as two-dimensional. The velocity of the
incident flow far from the front is denoted by U and the velocity under the lens far from the front is denoted by
. As determining equations, we use the equation of continuity
UH = U
H – h
and the law of conservation of momentum
ρ UH gH+
= ρ UHh gHh
() ()−+ −
As a result, for the quantity U (this is actually the velocity of propagation of the front in immobile fluid),
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
3–14, May–June, 2006. Original article submitted February 18, 2005.
0928-5105/06/1603–0129 © 2006 Springer Science+Business Media, Inc. 129