Open Access

ARTICLE

Sharp Interface Establishment through Slippery Fluid in Steady Exchange Flows under Stratification

Mustafa Turkyilmazoglu^1,2,*, Abdulaziz Alotaibi³

1 Department of Mathematics, Hacettepe University, Beytepe, Ankara, 06532, Türkiye
2 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan
3 Industrial Engineering Department, Faculty of Engineering, University of Tabuk, Tabuk, 71491, Saudi Arabia

* Corresponding Author: Mustafa Turkyilmazoglu. Email:

Computer Modeling in Engineering & Sciences 2025, 143(3), 2847-2865. https://doi.org/10.32604/cmes.2025.068031

Received 19 May 2025; Accepted 13 June 2025; Issue published 30 June 2025

Abstract

The variable salinity in stored reservoirs connected by a long channel attracts the attention of scientists worldwide, having applications in environmental and geophysical engineering. This study explores the impact of Navier slip conditions on exchange flows within a long channel connecting two large reservoirs of differing salinity. These horizontal density gradients drive the flow. We modify the recent one-dimensional theory, developed to avoid runaway stratification, to account for the presence of uniform slip walls. By adjusting the parameters of the horizontal density gradient based on the slip factor, we resolve analytically various flow regimes ranging from high diffusion to transitional high advection. These regimes are governed by physical parameters like channel aspect ratio, slip factor, Schmidt number, and gravitational Reynolds number. Our solutions align perfectly with ones in the no-slip limit. More importantly, under the conditions of no net flow across the channel and high Schmidt number (where stratification is concentrated near the channel’s mid-layer), we derive a closed-form solution for the slip parameter, aspect ratio, and gravitational Reynolds number that describes the interface’s behavior as a sharp interface separating two distinct zones. This interface, arising from hydrostatic wall gradients, ultimately detaches the low- and high-density regimes throughout the channel when the gravitational Reynolds number is inversely proportional to the aspect ratio for a fixed slip parameter. This phenomenon, observed previously in 2D numerical simulations with no-slip walls in the literature, is thus confirmed by our theoretical results. Our findings further demonstrate that wall slip leads to distinct and diverse flow regimes.

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Keywords

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