Fig. 11

Nyquist diagram of the boundary layer transfer function in the frequency range − 103 ≤ σ/σbl ≤ 103 (σ being the tidal frequency and σbl the frequency characterizing the boundary layer introduced in Eq. (217)). The parametrized complex transfer function
(Eq. (215)) reduced by its value at σ = 0 is plotted as a function of the tidal frequency (σ) in the complex plane, where the horizontal axis corresponds to the real part of the function,
, and the vertical axis to the imaginary part
. The arrow indicates the direction of increasing σ. The gain of the transfert function is given by the distance of a point P of the curve to the origin O of coordinates
, and its phase by the angle of the vector OP to the horizontal axis. This plot shows that the response of the ground is always delayed with respect to the thermal forcing except at synchronization, where
and the gain is maximum. It also highlights the two identified regimes of the ground response: the lag tends to 0 (response in phase with the perturbation) and the gain increases at σ → 0, while the lag tends to ± π/ 4 and the gain to 0 at σ → ± ∞, the critical transition frequency being σbl.
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