  We study the azimuthal structure of the stellar disks of 18 face-on spiral
galaxies, using K-band photometry to trace the stellar surface mass density.
Assuming the disks are co-planar, we characterize their deviation from
axisymmetry by the fractional amplitudes, A_i and phases of the azimuthal
Fourier components at radii R about the photometric galaxy center. We find that
most disks exhibit a wealth of non-axisymmetric structures, specifically: (1)
that about one third of them are substantially lopsided (A_1/A_0>= 0.20) at 2.5
disk exponential scale length, (2) that almost one half of them have strong
two-armed spirals with an arm/interarm surface-brightness contrasts of order
unity, and (3) that typical disks have some intrinsic ellipticity. We estimate
that in the disk plane the characteristic ellipticity of the underlying
potential is 0.045+-0.03. However, the spiral pattern couples significantly to
the estimate of the intrinsic ellipticity, and our measurement may represent an
upper limit on the ``true" potential triaxiality. We estimate the radial
streaming motions of the disk stars, $v_R$, which are produced by these
distortions. By averaging over our sample of galaxies and all azimuthal angles,
we find v_R=7km/s due to lopsided distortions and 6km/s due to intrinsic
ellipticity. These non-circular motions are expected to contribute about
0.15mags scatter to measurements of the Tully-Fisher relation.
