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Tides in rotating barotropic fluid bodies: the contribution of inertial waves and the role of internal structure

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.