We study recent observations of propagating fluctuations in a prominence foot with Hinode Solar Optical Telescope (SOT) high-resolution observations in Ca~II and H alpha emission which we identify as nonlinear fast magnetosnic waves. Here we analyze further the observations of propagating waves and flows with Interface Region Imaging Spectrograph (IRIS) Mg~II slit jaw images, in addition to Hinode/SOT Ca~II images. We find that the waves have typical periods in the range of 5 - 11 minutes and wavelengths in the plane of the sky (POS) of about 2000 km, while the flows in narrow threads have typical speed in the POS of ~16-46 km/s. We also detect apparent kink oscillations in the threads with flowing material, and apply coronal seismology to estimate the magnetic field strength in the range 5-17 G. Using 2.5D MHD we model the combined effects of nonlinear waves and flows on the observed dynamics of the prominence material, and reproduce the propagating and refracting fast magnetosonic waves, as well as standing kink-mode waves in flowing material along the magnetic field. The modeling results are in good qualitative agreements with the observations of the various waves and flows in the prominence foot, further confirming coronal seismology analysis and improving the understanding of the fine scale dynamics of the prominence material.
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