TY - JOUR

T1 - Regime transitions in stratified shear flows: the link between horizontal and inclined ducts

AU - Duran Matute, Matias

AU - Kaptein, Steven J.

AU - Clercx, Herman J.H.

PY - 2023/2/10

Y1 - 2023/2/10

N2 - We present the analytical solution for the two-dimensional velocity and density fields within an approximation for laminar stratified inclined duct (SID) flows where diffusion dominates over inertia in the along-channel momentum equation but is negligible in the density transport equation. We refer to this approximation as the hydrostatic/gravitational/viscous in momentum and advective in density (HGV-A) approximation due to the leading balances in the governing equations. The analytical solution is valid for laminar flows in a two-layer configuration in the limit of long ducts. The non-dimensional volume flux within the HGV-A approximation is given by Fr∗ = Reg/(AK), which is a control parameter with Reg the gravitational Reynolds number, A the aspect ratio of the duct and K a geometrical parameter that depends on the tilt of the duct and is obtained from the analytical solution. This analytical solution was validated against results from laboratory experiments, and allows us to gain new insight into the dynamics and properties of SID flows. Most importantly, constant values of Fr∗ describe, in both horizontal and inclined ducts, the transitions between increasingly turbulent flow regimes: from laminar flow, to interfacial waves, to intermittent turbulence and sustained turbulence.

AB - We present the analytical solution for the two-dimensional velocity and density fields within an approximation for laminar stratified inclined duct (SID) flows where diffusion dominates over inertia in the along-channel momentum equation but is negligible in the density transport equation. We refer to this approximation as the hydrostatic/gravitational/viscous in momentum and advective in density (HGV-A) approximation due to the leading balances in the governing equations. The analytical solution is valid for laminar flows in a two-layer configuration in the limit of long ducts. The non-dimensional volume flux within the HGV-A approximation is given by Fr∗ = Reg/(AK), which is a control parameter with Reg the gravitational Reynolds number, A the aspect ratio of the duct and K a geometrical parameter that depends on the tilt of the duct and is obtained from the analytical solution. This analytical solution was validated against results from laboratory experiments, and allows us to gain new insight into the dynamics and properties of SID flows. Most importantly, constant values of Fr∗ describe, in both horizontal and inclined ducts, the transitions between increasingly turbulent flow regimes: from laminar flow, to interfacial waves, to intermittent turbulence and sustained turbulence.

KW - gravity currents

KW - stratified flows

UR - http://www.scopus.com/inward/record.url?scp=85147092868&partnerID=8YFLogxK

U2 - 10.1017/jfm.2022.1077

DO - 10.1017/jfm.2022.1077

M3 - Article

SN - 0022-1120

VL - 956

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

M1 - A4

ER -