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We perform three-dimensional numerical simulations to investigate the sedimentation of a single sphere in the absence and presence of a simple cross-shear flow in a yield stress fluid with weak inertia. In our simulations, the settling flow is considered to be the primary flow, whereas the linear cross-shear flow is a secondary flow with amplitude 10 % of the primary flow. To study the effects of elasticity and plasticity of the carrying fluid on the sphere drag as well as the flow dynamics, the fluid is modelled using the elastoviscoplastic constitutive laws proposed by Saramito ( J. Non-Newtonian Fluid Mech. , vol. 158 (1–3), 2009, pp. 154–161). The extra non-Newtonian stress tensor is fully coupled with the flow equation and the solid particle is represented by an immersed boundary method. Our results show that the fore–aft asymmetry in the velocity is less pronounced and the negative wake disappears when a linear cross-shear flow is applied. We find that the drag on a sphere settling in a sheared yield stress fluid is reduced significantly compared to an otherwise quiescent fluid. More importantly, the sphere drag in the presence of a secondary cross-shear flow cannot be derived from the pure sedimentation drag law owing to the nonlinear coupling between the simple shear flow and the uniform flow. Finally, we show that the drag on the sphere settling in a sheared yield stress fluid is reduced at higher material elasticity mainly due to the form and viscous drag reduction.
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Analytic reparametrizations of translation toral flows with countable Lebesgue spectrum
We give an example of a real analytic reparametrization of a minimal translation flow on $$\mathbb{T}^{5}$$ that has a Lebesgue spectrum with infinite multiplicity. As a consequence, we see that the dynamics on a non-Diophantine invariant torus of an almost integrable Hamiltonian system can be spectrally equivalent to a Bernoulli flow.
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- Award ID(s):
- 2101464
- PAR ID:
- 10538200
- Publisher / Repository:
- AIMS
- Date Published:
- Journal Name:
- Discrete and Continuous Dynamical Systems
- Volume:
- 43
- Issue:
- 10
- ISSN:
- 1078-0947
- Page Range / eLocation ID:
- 3706 to 3727
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3934/dcds.2023063
