In magnetohydrodynamics (MHD), the liquid is assumed to be an ideal liquid if it is nonviscous and infinitely conductive. Tile finiteness of the coefficient of conductivity is the dissipative factor associated with wave attenuation. In oscillation studies, two limiting cases of long and short waves are generally considered with tim use of the model of an infinitely deep liquid having a free surface as a short-wave approximation. The investigations of the effect of viscosity on free surface waves, which were begun by Lamb [1] at tim end of the 19th century, have acquired a complete mathematical form [2]. The theory of MHD waves in a conducting liquid is still far from a complete theory. A number of studies have been focused on this subject (see, e.g. [3][4][5][6][7]) where the spectrum of free oscillations of dissipative MHD waves in the canonical regions was not treated in detail. In the present paper, this spectrum for an infinitely deep liquid is studied by analytical and numerical methods. The discrete and continuous oscillation spectra of a heavy liquid of finite conduction subjected to an external tlorizontal nmgnetic field are considered.1. Formulation of the Problem. We consider a nonviscous conducting liquid that occupies the lower halfospace. There is a vacuum above the liquid. We introduce a Cartesian coordinate system such that the Oxy plane coincides with the undisturbed horizontal surface of the liquid, and the z axis is directed downward. Let the gravity (0.0, g) and a constant nmgnetic field (H0, 0, 0) be applied to the liquid. We investigate two-dimensional natural oscillations of the liquid in the xz plane. The liquid motion and the electromagnetic field are described by the equations given, for example, in [8]. We divide the space into two regions:1. Liquid (z ~> 0). Let V(Vx,O, V:) be the velocity vector, p be the density, c~ be the electrical conduction, and h(hx, 0, h:) and e(0, ey, 0) be, respectively, the disturbances in the magnetic-and electricfield intensities caused by the liquid motion. Assuming that the oscillations are small, we write the linearized momentum and induction equations [8] in dimensionless form
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