The magnetotail-like magnetoplasma configuration is examined for the stability to the transversal mode by means of linear 2.5- and nonlinear 3-dimensional MHD simulations. The exact two-dimensional Kan-like solution of the Vlasov-Maxwell equations is utilized for background equilibrium bent current sheets. Both linear and nonlinear simulations reveal the same features: the bent current sheet is unstable to perturbations with the wave vector pointing in the out-of-plane direction; the unstable mode is localized in the summer hemisphere; in-plane plasma flow is rotating from the earthward/tailward direction in the near-Earth region to the vertical direction in the tail. Rotation of the plasma velocity and variation of the background plasma parameters in longitudinal (Earth-Sun) direction allow considering the observed plasma motions as a transient mode from the so-called double-gradient (in distant tail) to the conventional ballooning (close to the Earth) instability. It is found that the mode localization is controlled by second derivatives of the total pressure in longitudinal and normal (north-south) directions. This feature is rendered by a newly developed quasi-two-dimensional analytical model of the transversal mode in the bent current sheet.