ISSN 0021-8944, Journal of Applied Mechanics and Technical Physics, 2018, Vol. 59, No. 1, pp. 22–31.
Pleiades Publishing, Ltd., 2018.
Original Russian Text
V.G. Kozlov, S.V. Subbotin.
IN A ROTATING SPHERICAL CAVITY
UDC 532.5.01; 532.51; 532.526
V. G. Kozlov and S. V. Subbotin
Abstract: Steady ﬂow generated by oscillations of an inner solid core in a ﬂuid-ﬁlled rotating
spherical cavity is experimentally studied. The core with density less than the ﬂuid density is
located near the center of the cavity and is acted upon by a centrifugal force. The gravity ﬁeld
directed perpendicular to the rotation axis leads to a stationary displacement of the core from the
rotation axis. As a result, in the frame of reference attached to the cavity, the core performs circular
oscillation with frequency equal to the rotation frequency, and its center moves along a circular
trajectory in the equatorial plane around the center of the cavity. For the diﬀerential rotation of
the core to be absent, one of the poles of the core is connected to the nearest pole of the cavity
with a torsionally elastic, ﬂexible ﬁshing line. It is found that the oscillation of the core generates
axisymmetric azimuthal ﬂuid ﬂow in the cavity which has the form of nested liquid columns rotating
with diﬀerent angular velocities. Comparison with the case of a free oscillating core which performs
mean diﬀerential rotation suggests the existence of two mechanisms of ﬂow generation (due to the
diﬀerential rotation of the core in the Ekman layer and due to the oscillation of the core in the
oscillating boundary layers).
Keywords: rotation, inner core, oscillation, steady ﬂow, diﬀerential rotation, inertial waves.
The study of ﬂows in rotating cavities is an important geophysical problem related to the problem of ﬂuid
motion in the atmospheres and cores of planets [1, 2]. The problem of ﬂuid ﬂow in a spherical layer between two
concentric spheres rotating about a common axis with diﬀerent angular velocities is classical . In [4–6], the
internal sphere (core) is located on the axis of the cavity and the diﬀerential rotation of the core is given from the
The vibrational mechanism of generation of mean rotation of a free inner core was discovered and investigated
in [7, 8]. If the core oscillates relative to the cavity, mean stresses arise in the oscillating boundary layers which lead
to diﬀerential rotation of the core. Depending on the oscillation frequency, both lagging and advancing rotation of
the core is generated, accompanied by intense steady ﬂuid ﬂow .
It is of interest to study the oscillatory ﬂuid motion generating steady ﬂow in rotating cavities . Fluid
oscillation caused by tidal deformations (periodic change in shape)  or librations (periodic change in rotation
velocity)  of a cavity, and precession  have been considered.
The structure of the ﬂow generated by a free core oscillating in a rotating spherical cavity has been in-
vestigated . It has been shown that quasi-two-dimensional azimuthal ﬂuid motion is generated in the cavity;
before instability, the axisymmetric ﬂow structure has the form of coaxial cylindrical surfaces rotating with diﬀerent
Perm State Humanitarian Pedagogical University, Perm, 614000 Russia; email@example.com; sub-
firstname.lastname@example.org. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 59, No. 1, pp. 28–38,
January–February, 2018. Original article submitted October 20,1, 2016; revision submitted November 22, 2016.
2018 by Pleiades Publishing, Ltd.