Topographic instability of flow in a rotating fluid

Abstract

Abstract.Here are presented the results of experimental and theoretical studies on a stability of zonal geostrophic flows in the rotating layer of the shallow water. In the experiments, a special apparatus by Abastumani Astrophysical Observatory Georgian Academy of Science was used. This apparatus represents a paraboloid of rotation, which can be set in a regulable rotation around the vertical axis. Maximal diameter of the paraboloid is 1.2 m, radius of curvature in the pole is 0.698 m. In the paraboloid, water spreads on walls as a layer uniform on height under the period of rotation 1.677 s. Against a background of the rotating fluid, the zonal flows are formed by the source-sink system. It consists of two concentric circular perforations on the paraboloid bottom (width is 0.3 cm, radiuses are 8.4 and 57.3 cm, respectively); water can be pumped through them with various velocities and in all directions. It has been established that under constant vertical depth of the rotating fluid the zonal flows are stable. There are given the measurements of the radial profiles for the water level and velocity in the stationary regime. It has been found that zonal flows may lose stability under the presence of the radial gradient of full depth formed by a change of angular velocity of paraboloid rotation. An instability origin results in the loss of flow axial symmetry and in the appearance of self-excited oscillations in the zonal flow. At the given angular velocity of rotation, instability is observed only in the definite range of intensities of the source-sink system.The theoretical estimations are performed in the framework of the equations of the shallow water theory, including the terms describing the bottom friction. It has been shown that the instability of zonal flows found experimentally has a topographical nature and is related with non-monotone dependence of the potential vorticity on radius.Correspondence to: M. V. Kalashnik (lingel@obninsk.com)

Theoretical and experimental investigation of the structure of azimuthal source–sink flow in a rotating shallow water layer

“…Emphasize that all experiments were carried out at the constant fluid depth in the absence of radial motions. As it was shown in our recent work [16], gradient of full depth can destabilize the source-sink flows. Occurrence of the instability is associated with non-monotonic radial distribution of the potential vorticity.…”

“…This apparatus consists of a parabolic vessel which can be variably rotated about the vertical axis (see Fig. 1 in [16]). The maximum diameter of the paraboloid is d = 1.2 m, and the radius of curvature at the pole is R = 1/κ = 0.698 m. The parabolic vessel with water is rotated at the angular velocity = √ gκ = 3.75 s −1 , which corresponds to a constant fluid depth (period of rotation T = 1.677 s).…”