As datasets continue to increase in size and complexity, new techniques are required to visualize surface flow effectively. In this work, we introduce a novel technique for visualizing flow on arbitrary surface meshes. This new method utilizes the closest point method (CPM), an embedding technique for solving partial differential equations (PDE) on surfaces. The CPM operates by extending values off the surface into the grid and using standard three dimensional PDE stencils to solve embedded two dimensional surface problems. To adapt unsteady flow visualization for the CPM, unsteady flow line integral convolution (UFLIC) is applied in three dimensions to the embedded surface in the grid to visualize flow on an arbitrary surface. To address the increased size and complexity of datasets, we introduce the closest point sparse octree to efficiently represent an embedded surface. By constructing a closest point sparse octree, complex surfaces can be represented in a memory efficient manner. Further, various techniques, such as a Laplacian filter, can be applied more easily to the embedded surface because of the CPM. Finally, the memory efficiency of our new sparse octree approach allows grids to be constructed up to 8, 192³ in size on a GPU with 12GB of RAM.