  We discuss the linear response to low-frequency tidal forcing of fluid bodies
that are slowly and uniformly rotating, are neutrally stratified and may
contain a solid or fluid core. This problem may be regarded as a simplified
model of astrophysical tides in convective regions of stars and giant planets.
The response can be separated into non-wavelike and wavelike parts, where the
former is related instantaneously to the tidal potential and the latter may
involve resonances or other singularities. The imaginary part of the potential
Love number of the body, which is directly related to the rates of energy and
angular momentum exchange in the tidal interaction and to the rate of
dissipation of energy, may have a complicated dependence on the tidal
frequency. However, a certain frequency-average of this quantity is independent
of the dissipative properties of the fluid and can be determined by means of an
impulse calculation. The result is a strongly increasing function of the size
of the core when the tidal potential is a sectoral harmonic, especially when
the body is not strongly centrally condensed. However, the same is not true for
tesseral harmonics, which receive a richer response and may therefore be
important in determining tidal evolution even though they are usually
subdominant in the expansion of the tidal potential. We also discuss
analytically the low-frequency response of a slowly rotating homogeneous fluid
body to tidal potentials proportional to spherical harmonics of degrees less
than five. Tesseral harmonics of degrees greater than two, such as are present
in the case of a spin-orbit misalignment, can resonate with inertial modes of
the full sphere, leading to an enhanced tidal interaction.
