On planetary torque signals and sub-decadal frequencies in the discharges of large rivers

We explore the arguments presented in the past linking changes in the angular momentum \(modulus\), \(|{\bf L}|\), of the Sun's barycentric orbit, with the discharges of Po River in Europe and Paraná River in South America, looking for any evidence regarding to a possible underlying physical mechanism. We clarify the planetary effect on solar torque presenting new analyses and results; we also improve prior results on Paraná River's cycles finding significant spectral lines around 6.5 yr, 7.6 yr, 8.7 yr, and 10.4 yr. We show that the truly important dynamical parameter in this issue is the {\it vectorial} planetary torque. Moreover, following the variations of \({\bf L}\) respect to the Sun's spin axis of rotation (i.e., a LS relationship), we found virtually the same Paraná River discharge peaks: 6.3 yr, 7.7 yr, 8.6 yr and 9.9 yr. An analisys based on Magnitude Squared Coherence and Wavelet Coherence between Paraná River discharge and our LS relationship shows significant, although intermittently, coherence near 8-yr periodicities. Wavelet Coherence also shows big and significant regions of coherence inside 12-19 yr band. Our results ruled out classical tidal effects in this problem; but suggest that, if these rivers are trully related to solar barycentric motion, the physical origin of this connection might be related to a working solar spin-orbit interaction.