  Observations by recent space missions reported the detection of Rossby waves
(r-modes) in light curves of many stars (mostly A, B, and F spectral types)
with outer radiative envelope. This paper aims to study the theoretical
dynamics of Rossby-type waves in such stars. Hydrodynamic equations in a
rotating frame were split into horizontal and vertical parts connected by a
separation constant (or an equivalent depth). Vertical equations were solved
analytically for a linear temperature profile and the equivalent depth was
derived through free surface boundary condition. It is found that the vertical
modes are concentrated in the near-surface layer with a thickness of several
tens of surface density scale height. Then with the equivalent width,
horizontal structure equations were solved, and the corresponding dispersion
relation for Rossby, Rossby-gravity, and inertia-gravity waves was obtained.
The solutions were found to be confined around the equator leading to the
equatorially trapped waves. It was shown that the wave frequency depends on the
vertical temperature gradient as well as on stellar rotation. Therefore,
observations of wave frequency in light curves of stars with known parameters
(radius, surface gravity, rotation period) could be used to estimate the
temperature gradient in stellar outer layers. Consequently, the Rossby mode may
be considered as an additional tool in asteroseismology apart from acoustic and
gravity modes.
