Physical Oceanography, Vol. 16, No. 5, 2006
FOCUSING OF INTERNAL WAVES GENERATED BY THE NONUNIFORM
MOTION OF A REGION OF ATMOSPHERIC PRESSURES
V. F. Sannikov
In the linear statement of the problem, by using the long-wave approximation, we study the pos-
sibility of generation of significant disturbances in a continuously stratified fluid by the nonuni-
form motion of a region of atmospheric pressures. We consider the case where the disturbances
of the medium propagating from a part of the trajectory of motion of the generator simultaneous-
ly arrive at a selected point of the space (focus). The amplitude of disturbances in the focus is
evaluated for an arbitrary motion of the region of pressures, which may lead to the analyzed ef-
Traveling atmospheric formations constitute one of possible types of generators of internal waves in the
sea. The wave-forming action of cyclones manifests itself in the creation of the regions of disturbances of the at-
mospheric pressure, the fields of tangential wind stresses, and convective mixing whose source moves over the
sea surface . In the present work, we study the wave fields generated under the action of moving atmospheric
pressures. In , it is indicated that the response of the ocean to a traveling cyclone can be interpreted as a wake
of a moving storm. Numerous works are devoted to the investigation of the wave processes connected with
moving baric formations (see, e.g., ). The motion of anomalies of the atmospheric pressure is, as a rule, re-
garded as rectilinear and uniform with weak periodic variations of the intensity . It seems likely that the first
investigation of variable motion was carried out in , where the case of uniform motion of a generator of waves
along a circular path was analyzed. Note that it is quite difficult to take into account significant changes in the
parameters of motion typical of natural phenomena because this requires tremendous amounts of numerical cal-
In the present work, by using a simple hydrodynamic model, we consider one of possible mechanisms of
generation of significant local wave disturbances, namely, the phenomenon of focusing. This phenomenon is
observed in the case where the disturbances of the medium propagating from different points of a part of the tra-
jectory of motion of a generator (its active section) simultaneously reach a certain point of the space (focus).
Our investigation is carried out within the framework of the linear theory of waves by using the long-wave
approximation. Moreover, in order to construct an efficient algorithm of finding the space characteristics of
forced waves, we make the following simplifications:
— use the Boussinesq approximation and the “rigid-lid” boundary condition on the surface of the fluid
(this enables us to filter out the surface waves);
— neglect Earth’s rotation;
— consider a model distribution of atmospheric pressures.
Marine Hydrophysical Institute, Ukrainian Academy of Sciences, Sevastopol.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
22–29, September–October, 2006. Original article submitted April 13,
274 0928-5105/06/1605–0274 © 2006 Springer Science+Business Media, Inc.