Wellner is a sedimentologist and stratigrapher who works primarily in high latitudes, including Antarctica as well as Norway and Alaska, on questions related to sediment facies, stratigraphic architecture, glacial history, and sea-level change. She and her students also study modern sediments on the Texas coast. She has been on the faculty at the University of Houston, Department of Earth and Atmospheric Sciences, since 2006 where she teaches stratigraphy, sequence stratigraphy, modern depositional environments, marine geology, and oceanography. Wellner has completed over fifteen ocean-going cruises collecting geophysical data and sediment cores, including twelve in Antarctica.