Mixing in density- and viscosity-stratified flows

Allen, P. A.; Dorrell, R. M.; Harlen, O. G.; Thomas, R. E.; McCaffrey, W. D.

Abstract

The lock-exchange problem is used extensively to study the flow dynamics of density-driven flows, such as gravity currents, and as a canonical problem to mixing in stratified flows. Opposite halves of a domain are filled with two fluids of different densities and held in place by a lock-gate. Upon release, the density difference drives the flow causing the fluids to slosh back and forth. In many scenarios, density stratification will also impose a viscosity stratification (e.g., if there are suspended sediments or the two fluids are distinct). However, numerical models often neglect variable viscosity. This paper characterizes the effect of both density and viscosity stratification in the lock-exchange configuration. The governing Navier-Stokes equations are solved using direct numerical simulation. Three regimes are identified in terms of the viscosity ratio μ 2 / μ 1 = (1 + γ) between the dense and less dense fluids: when γ ≪ 1, the flow dynamics are similar to the equal-viscosity case; for intermediate values (γ ∼ 1), viscosity inhibits interface-scale mixing leading to a global reduction in mixing and enhanced transfer between potential and kinetic energy. Increasing the excess viscosity ratio further (γ ≫ 1) results in significant viscous dissipation. Although many gravity or turbidity current models assume constant viscosity, our results demonstrate that viscosity stratification can only be neglected when γ ≪ 1. The initial turbidity current composition could enhance its ability to become self-sustaining or accelerating at intermediate excess viscosity ratios. Currents with initially high excess viscosity ratio may be unable to dilute and propagate long distances because of the decreased mixing rates and increased dissipation.

Citation

Allen, P. A., Dorrell, R. M., Harlen, O. G., Thomas, R. E., & McCaffrey, W. D. (2022). Mixing in density- and viscosity-stratified flows. Physics of Fluids, 34(9), Article 096605. https://doi.org/10.1063/5.0108337

• Journal Article Type: Article
• Acceptance Date: Aug 24, 2022
• Online Publication Date: Sep 20, 2022
• Publication Date: Sep 1, 2022
• Deposit Date: Dec 18, 2023
• Publicly Available Date: Dec 19, 2023
• Journal: Physics of Fluids
• Print ISSN: 1070-6631
• Electronic ISSN: 1089-7666
• Publisher: American Institute of Physics
• Peer Reviewed: Peer Reviewed
• Volume: 34
• Issue: 9
• Article Number: 096605
• DOI: https://doi.org/10.1063/5.0108337
• Keywords: Marine geology and geophysics; Numerical methods; Fluid mechanics; Computational fluid dynamics; Gravity currents; Fluid flows; Navier Stokes equations; Rheology and fluid dynamics; Viscosity; High performance computing
• Public URL: https://hull-repository.worktribe.com/output/4100999