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Energy dissipation of Oldroyd-B fluids in plane Couette flow
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DOI：10.1017/jfm.2026.11731.png)
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Abstract
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This paper establishes a rigorous upper bound on the infinite-time-averaged energy dissipation rate of Oldroyd-B fluids in plane Couette flow. The bound depends only on system parameters – the Reynolds number; Weissenberg number and viscosity ratio – and applies to all steady and unsteady solutions within a certain region in parameter space. The bound is proven by extending the ‘background-flow method’ to the case where the system energy is no longer a quadratic functional of the underlying flow fields; and is obtained by using a non-polynomial auxiliary functional related to the free polymeric energy. Within the range of the flow parameters in which the steady solution is known to be globally stable; the dissipation rate of the steady flow is recovered; and in the Newtonian limit the result reduces to the best-known bound for Newtonian Couette flow. Our analysis also identifies a range of parameters for which the total energy of the viscoelastic flow must be bounded; thus ruling out the possibility of energy blow-ups in these situations.
Keywords:
turbulent flows
non-Newtonian flows
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IF:
3.9
Papers:
2.0W
Citations:
9.4W
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