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Modern and traditional analyses of two-dimensional (2D) and three-dimensional (3D) aerodynamic shapes reveal a flow-based sensitivity to specific deformations that can be represented generally by affine transformations (rotation, scaling, shearing, and translation). We present a novel representation of shapes that decouples affine-style deformations over a submanifold and a product submanifold principally of the Grassmannian. As an analytic generative model, the separable representation, informed by a database of physically relevant airfoils, offers: (i) a rich set of novel 2D airfoil deformations not previously captured in the data, (ii) an improved low-dimensional parameter domain for inferential statistics informing design\/manufacturing, and (iii) consistent 3D blade representation and perturbation over a sequence of nominal 2D shapes.<\/jats:p>","DOI":"10.1093\/jcde\/qwac140","type":"journal-article","created":{"date-parts":[[2023,2,1]],"date-time":"2023-02-01T18:34:29Z","timestamp":1675276469000},"page":"468-487","source":"Crossref","is-referenced-by-count":8,"title":["Separable shape tensors for aerodynamic design"],"prefix":"10.1093","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1244-1623","authenticated-orcid":false,"given":"Zachary J","family":"Grey","sequence":"first","affiliation":[{"name":"National Institute of Standards and Technology, Applied and Computational Mathematics 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