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A class of metasurfaces for underwater sound absorption, based on a design principle that maximizes thermoviscous loss, is presented. When a sound meets a solid surface, it leaves a footprint in the form of thermoviscous boundary layers in which energy loss takes place. Considered to be a nuisance, this acoustic to vorticity/entropy mode conversion and the subsequent loss are often ignored in the existing designs of acoustic metamaterials and metasurfaces. The metasurface created is made of a series of topographic meta-atoms, i.e., intaglios and reliefs engraved directly on the solid object to be concealed. The metasurface is acoustically sticky in that it rather facilitates the conversion of the incident sound to vorticity and entropy modes, hence the thermoviscous loss, leading to the desired anechoic property. A prototype metasurface machined on a brass object is tested for its anechoicity, and shows a multitude of absorption peaks as large as unity in the 2–5 MHz range. Computations also indicate that a topographic metasurface is robust to hydrostatic pressure variation, a quality much sought-after in underwater applications. [ABSTRACT FROM AUTHOR]