  Recently, spiral wave patterns (SWPs) have been detected in 3 minute
oscillations of sunspot umbrae, but the nature of this phenomenon has remained
elusive. We present a theoretical model that interprets the observed SWPs as
the superposition of two different azimuthal modes of slow magnetoacoustic
waves driven below the surface in an untwisted and non-rotating magnetic
cylinder. We apply this model to SWPs of the line-of-sight (LOS) velocity in a
pore observed by the Fast Imaging Solar Spectrograph installed at the 1.6 m
Goode Solar Telescope. One- and two-armed SWPs were identified in instantaneous
amplitudes of LOS Doppler velocity maps of 3 minute oscillations. The
associated oscillation periods are about 160 s, and the durations are about 5
minutes. In our theoretical model, the observed spiral structures are explained
by the superposition of non-zero azimuthal modes driven 1600 km below the
photosphere in the pore. The one-armed SWP is produced by the slow-body sausage
(m = 0) and kink (m = 1) modes, and the two-armed SWP is formed by the
slow-body sausage (m = 0) and fluting (m = 2) modes of the magnetic flux tube
forming the pore.
