Meridian Touching Wave: Definition, Velocity Structure, and Hierarchical Relations

This paper defines the Meridian Touching Wave and its associated velocity quantities, organized into three hierarchical levels: the instantaneous level (Meridian Touching Wave), the periodic level (Meridian Touching Wave Packet), and the degenerate level (Meridian Envelope Interface). The Meridian Touching Wave is formed by the oscillation of the radial velocity D of the parent Envelope Interface. The bridge relation is KbV0 = KCj; after canceling K, the instantaneous resultant velocity of the Meridian Touching Wave is obtained as Cj = bV0 — a constant. At any instant, the Meridian Touching Wave satisfies Cj² = Vj² + Dj² + Sj². The Meridian Touching Wave forms a fixed-period dynamic process along the meridian — the Meridian Touching Wave Packet — whose period average yields three RMS velocity components Vu, Du, Su. Introducing the instantaneous center-radial resultant velocity Nj (Nj² = Dj² + Sj²) and the RMS center-radial resultant velocity Nu (Nu² = Du² + Su²), the resultant velocity is decomposed into tangential and center-radial parts. The definition Nu² = Du² + Su² holds uniformly for both the Meridian Touching Wave Packet and the Meridian Envelope Interface. The Meridian Touching Wave Packet is characterized by its frequency f_w (the reciprocal of the period T) and its wavelength λu = Vu / f_w (the tangential displacement per period). The Meridian Envelope Interface is a special case of the Meridian Touching Wave Packet — when Du = Su, it degenerates into an Envelope Interface with topological factor bj. Keywords: Meridian Touching Wave, Meridian Touching Wave Packet, Meridian Envelope Interface, frequency, wavelength, RMS, bridge relation