  Spiral arms are observed in numerous protoplanetary discs. These spiral arms
can be excited by companions, either on bound or unbound orbits. We simulate a
scenario where an unbound perturber, i.e. a flyby, excites spiral arms during a
periastron passage. We run three-dimensional hydrodynamical simulations of a
parabolic flyby encountering a gaseous protoplanetary disc. The perturber mass
ranges from $10\, \rm M_J$ to $1\, \rm M_{\odot}$. The perturber excites a
two-armed spiral structure, with a more prominent spiral feature for higher
mass perturbers. The two arms evolve over time, eventually winding up,
consistent with previous works. We focus on analysing the pattern speed and
pitch angle of these spirals during the whole process. The initial pattern
speed of the two arms are close to the angular velocity of the perturber at
periastron, and then it decreases over time. The pitch angle also decreases
over time as the spiral winds up. The spirals disappear after several local
orbital times. An inclined prograde orbit flyby induces similar disc
substructures as a coplanar flyby. A solar-mass flyby event causes increased
eccentricity growth in the protoplanetary disc, leading to an eccentric disc
structure which dampens over time. The spirals' morphology and the disc
eccentricity can be used to search for potential unbound stars or planets
around discs where a flyby is suspected. Future disc observations at high
resolution and dedicated surveys will help to constrain the frequency of such
stellar encounters in nearby star-forming regions.
