“…The interaction between a PW with frequency Δ and zonal wave number m, i.e., cos(Δ t + m − Φ n,s ), with a tide with frequency nΩ and zonal wave number s, cos(nΩt + s ), thus yields sum and difference secondary waves (hereafter SW + and SW − ), with frequencies nΩ ± Δ and zonal wave numbers s ± m. In the spectrum of a time series, long-period PW (Δ << nΩ) appears as two sideband peaks on either side of the main tidal peak at frequency nΩ. A well-documented example is modulation of the migrating (Sun-synchronous, westward propagating) semidiurnal tide (n = 2, s = 2) with the westward propagating quasi-2 day wave QTDW (n = 0.5, s = 3) [Cevolani and Kingsley, 1992;Beard et al, 1999;Manson et al, 1982;Harris and Vincent, 1993;Thayaparan et al, 1997aThayaparan et al, , 1997bPalo et al, 1999]. The SWs are a westward propagating 9.6 h wave with s = 5 and an eastward propagating 16 h wave with s = −1; the zonal wave numbers obviously cannot be differentiated using ground-based observations.…”