Thank you everyone for the suggestions. I did some complementary test, with the same camera (my K-3) and microphone (Rode VideomicPro):
(a) the Rode shotgun mounted on the camera hotshoe and
(b) the Rod Shotgun placed 20 cm away from the K-3.
The tests were conducted at night with minimum background noise. All the camera settings were otherwise identical for all tests. (The lens was a MF lens.) For each test, the sound record was sub-sampled into sub-sets 2 s long, frequency analyses were conducted and the data were averaged for several successive periods. (In addition, the PSDs of left and right tracks were averaged.) The results are included in the attached plot together with the earlier tidal bore data.
The blue curve show Test (a) with the Rode shotgun mounted on the camera hotshoe. The red curve presents Test (b) with the Rod Shotgun placed 20 cm away from the K-3. We can see a marked difference in energy at low frequency (10-30 Hz), suggesting that the microphone mounted on the hotshoe pickup some low-frequency noise, very likely out of the camera. I cannot definitely confirm that the SR is the main cause of that noise, but it might be one effect.