Physical Oceanography, Vol.
THERMOHYDRODYNAMICS OF THE OCEAN
SOME GENERAL PROPERTIES OF TRANSVERSE MOTIONS
OF THE GEOSTROPHIC FRONT
S. F. Dotsenko,
and P. Brandt
Within the framework of the reduced-gravity model of the ocean taking into account the effect of
friction in the Rayleigh form, we study the two-dimensional problem of nonlinear motions of a
subsurface front of finite width. We consider the conservation laws and the character of motion
of the center-of-mass of the cross section of the front and their variations caused by the losses of
For fields with special structure, the problem is reduced to the solution of a system of
nonlinear ordinary differential equations. It is shown that the initially geostrophic frontal current
decays with time according to a power law. The deviations of the initial state of the front from
the state of geostrophic balance result in the generation of superinertial oscillations of the hy-
Frontal zones, i.e., regions with especially high space gradients of the characteristics of marine medium, are
quite common in the World Ocean. These formations are also characterized by pronounced variability as func-
tions of time. Even inside climatic frontal zones, we observe rapid structural transformations, motions of frontal
boundaries, meandering, formations of eddies, etc. Frontal zones “breathe,” i.e., permanently change their par-
ameters oscillating about certain average positions . As frontal zones of planetary scale, one can mention the
Gulf Stream, the Kuroshio Current, the zones of subtropical convergence, and the Antarctic Circumpolar Frontal
Zone. The fact that the influence of frontal zones on the dynamics of the ocean is significant reveals the neces-
sity of comprehensive analysis of the behavior of the characteristics of frontal zones and the mechanisms gov-
erning this behavior in time.
In the present work, we study the nonlinear dynamics of a frontal zone of finite width on the plane perpen-
dicular to the axis of the front. The analysis is performed within the framework of the reduced-gravity model of
dynamics of the ocean with regard for friction in the Rayleigh form. Our attention is focused on the time depen-
dences of the integral characteristics of the frontal zone and the kinematics of the center-of-mass of the cross
section of the front. For fields with special space structure, we study the decay of motions caused by the dissipa-
tion of energy and oscillations of the frontal zone induced by deviations of the fields from the geostrophic equi-
The integral conservation laws for a system of the shallow-water equations were discussed in . The
cases of nonlinear motion of a liquid in a closed basin and rectilinear channel (plane problem) were studied in 
and , respectively.
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol.
Hamburg University, Hamburg, Germany.
Kiel University, Kiel, Germany.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
3–14, July–August, 2003. Original article submitted May 20, 2002.
0928-5105/03/1304–0189 $25.00 © 2003 Plenum Publishing Corporation 189