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Fluid dynamics in intrinsically curved geometries is encountered in manyphysical systems in nature, ranging from microscopic bio-membranes all the wayup to general relativity at cosmological scales. Despite the diversity ofapplications, all of these systems share a common feature: the free motion ofparticles is affected by inertial forces originating from the curvature of theembedding space. Here we reveal a fundamental process underlying fluid dynamicsin curved space: the free motion of fluids, in the complete absence of solidwalls or obstacles, exhibits loss of energy due exclusively to the intrinsiccurvature of space. We find that local sources of curvature generate viscousstresses as a result of the inertial forces. The curvature-induced viscousforces are shown to cause hitherto unnoticed and yet appreciable energydissipation, which might play a significant role for a variety of physicalsystems involving fluid dynamics in curved spaces.

Energy dissipation in flows through curved spaces