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This paper seeks and examines N-symmetric vortical solutions of the two-layer geostrophic model for the special case when the vortices (or eddies) have vanishing summed strength (circulation anomaly). This study is an extension [Sokolovskiy et al. Phys. Fluids 2020, 32, 09660], where the general formulation for arbitrary N was given, but the analysis was only carried out for N=2. Here, families of stationary solutions are obtained and their properties, including asymptotic ones, are investigated in detail. From the point of view of geophysical applications, the results may help interpret the propagation of thermal anomalies in the oceans.

The three-layer version of the contour dynamics/surgery method is used to study the interaction mechanisms of a large-scale surface vortex with a smaller vortex/vortices of the middle layer (prototypes of intrathermocline vortices in the ocean) belonging to the middle layer of a three-layer rotating fluid. The lower layer is assumed to be dynamically passive. The piecewise constant vertical density distribution approximates the average long-term profile for the North Atlantic, where intrathermocline eddies are observed most often at depths of 300–1600 m. Numerical experiments were carried out with different initial configurations of vortices, to evaluate several effects. Firstly, the stability of the vortex compound was evaluated. Most often, it remains compact, but when unstable, it can break as vertically coupled vortex dipoles (called hetons). Secondly, we studied the interaction between a vertically tilted cyclone and lenses. Then, the lenses first undergo anticlockwise rotation determined by the surface cyclone. The lenses can induce alignment or coupling with cyclonic vorticity above them. Only very weak lenses are destroyed by the shear stress exerted by the surface cyclone. Thirdly, under the influence of lens dipoles, the surface cyclone can be torn apart. In particular, the shedding of rapidly moving vortex pairs at the surface reflects the presence of lens dipoles below. More slowly moving small eddies can also be torn away from the main surface cyclone. In this case, they do not appear to be coupled with middle layer vortices. They are the result of large shear-induced deformation. Common and differing features of the vortex interaction, modeled in the framework of the theory of point and finite-core vortices, are noted.

The theory of point vortices is used to explain the interaction of a surface vortex with subsurface vortices in the framework of a three-layer quasigeostrophic model. Theory and numerical experiments are used to calculate the interaction between one surface and one subsurface vortex. Then, the configuration with one surface vortex and two subsurface vortices of equal and opposite vorticities (a subsurface vortex dipole) is considered. Numerical experiments show that the self-propelling dipole can either be captured by the surface vortex, move in its vicinity, or finally be completely ejected on an unbounded trajectory. Asymmetric dipoles make loop-like motions and remain in the vicinity of the surface vortex. This model can help interpret the motions of Lagrangian floats at various depths in the ocean.

In order to evaluate the role of substituents at 3-C and 17-C in the cytotoxic and cytoprotective actions of DHEA and 5-AED molecules, their derivatives were synthesized by esterification using the corresponding acid anhydrides or acid chlorides. As a result, seven compounds were obtained: four DHEA derivatives (DHEA 3-propionate, DHEA 3-butanoate, DHEA 3-acetate, DHEA 3-methylsulfonate) and three 5-AED derivatives (5-AED 3-butanoate, 5-AED 3,17-dipropionate, 5-AED 3,17-dibutanoate). All of these compounds showed micromolar cytotoxic activity toward HeLa and K562 human cancer cells. The maximum cytostatic effect during long-term incubation for five days with HeLa and K562 cells was demonstrated by the propionic esters of the steroids: DHEA 3-propionate and 5-AED 3,17-dipropionate. These compounds stimulated the growth of normal Wi-38 cells by 30–50%, which indicates their cytoprotective properties toward noncancerous cells. The synthesized steroid derivatives exhibited antioxidant activity by reducing the production of reactive oxygen species (ROS) by peripheral blood mononuclear cells from healthy volunteers, as demonstrated in a luminol-stimulated chemiluminescence assay. The highest antioxidant effects were shown for the propionate ester of the steroid DHEA. DHEA 3-propionate inhibited luminol-stimulated chemiluminescence by 73% compared to the control, DHEA, which inhibited it only by 15%. These data show the promise of propionic substituents at 3-C and 17-C in steroid molecules for the creation of immunostimulatory and cytoprotective substances with antioxidant properties.