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Cytoplasmic streaming plays a particularly important role in large cells, where the timescales of diffusion are too slow for the mixing and transport of cellular material. The motion of molecular motors on cytoskeletal elements has been known to drive streaming in a variety of biological systems. Previous theoretical studies established that in the Drosophila oocyte, cytoplasmic streaming arises as an instability where normally anchored cortical microtubules (MTs) under compressive loads of molecular motors collectively deform and generate fluid flows. During streaming, the MTs form a globally aligned pattern with two nematic defects. In this paper, we focus on understanding the dynamics of the MT bed that gives rise to streaming in Drosophila oocytes. Using live-imaging and dimensionality reduction techniques, we find a waving regime of MT movement that has yet to be described and quantitatively characterized. We propose an explanation of these waving dynamics in light of our current biophysical model of streaming and we use numerical simulations to find waving behavior at the boundary of two previously characterized regimes. We conclude using both experiments and simulations to suggest that this oscillatory modulation has a function in the mixing of yolk granules, the major source of protein in the early embryo.