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Rotational dynamics of the Earth, over geological timescales, have profoundly
affected local and global climatic evolution, probably contributing to the
evolution of life. To better retrieve the Earth's rotational history, and
motivated by the published hypothesis of a stabilized length of day during the
Precambrian, we examine the effect of thermal tides on the evolution of
planetary rotational motion. The hypothesized scenario is contingent upon
encountering a resonance in atmospheric Lamb waves, whereby an amplified
thermotidal torque cancels the opposing torque of the oceans and solid
interior, driving the Earth into a rotational equilibrium. With this scenario
in mind, we construct an ab initio model of thermal tides on rocky planets
describing a neutrally stratified atmosphere. The model takes into account
dissipative processes with Newtonian cooling and diffusive processes in the
planetary boundary layer. We retrieve from this model a closed-form solution
for the frequency-dependent tidal torque which captures the main spectral
features previously computed using 3D general circulation models. In
particular, under longwave heating, diffusive processes near the surface and
the delayed thermal response of the ground prove to be responsible for
attenuating, and possibly annihilating, the accelerating effect of the
thermotidal torque at the resonance. When applied to the Earth, our model
prediction suggests the occurrence of the Lamb resonance in the Phanerozoic,
but with an amplitude that is insufficient for the rotational equilibrium.
Interestingly, though our study was motivated by the Earth's history, the
generic tidal solution can be straightforwardly and efficiently applied in
exoplanetary settings.