Stratified inclined duct: two-layer hydraulics and instabilities

The stratified inclined duct (SID) sustains an exchange flow in a long, gently sloping duct as a model for continuously-forced density-stratified flows such as those found in estuaries. Experiments have shown that the emergence of interfacial waves and their transition to turbulence as the tilt angl...

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Bibliographic Details
Published inarXiv.org
Main Authors Atoufi, Amir, Zhu, Lu, Lefauve, Adrien, Taylor, John R, Kerswell, Rich R, Dalziel, Stuart B, Lawrence, Gregory A, Linden, P F
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 30.01.2023
Subjects
Attitude (inclination)
Base flow
Direct numerical simulation
Estuaries
Flow velocity
Fluid flow
Hydraulics
Interface stability
Laminar flow
Mathematical models
Shallow water equations
Stratified flow
Traveling waves
Turbulence
Wave breaking
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Summary:The stratified inclined duct (SID) sustains an exchange flow in a long, gently sloping duct as a model for continuously-forced density-stratified flows such as those found in estuaries. Experiments have shown that the emergence of interfacial waves and their transition to turbulence as the tilt angle is increased appears linked to a threshold in the exchange flow rate given by inviscid two-layer hydraulics. We uncover these hydraulic mechanisms with (i) recent direct numerical simulations (DNS) providing full flow data in the key flow regimes (Zhu & Atoufi et al., arXiv:2301.09773, 2023), (ii) averaging these DNS into two layers, (iii) an inviscid two-layer shallow water and instability theory to diagnose interfacial wave behaviour and provide physical insight. The laminar flow is subcritical and stable throughout the duct and hydraulically controlled at the ends of the duct. As the tilt is increased, the flow becomes everywhere supercritical and unstable to long waves. An internal undular jump featuring stationary waves first appears near the centre of the duct, then leads to larger-amplitude travelling waves, and to stronger jumps, wave breaking and intermittent turbulence at the largest tilt angle. Long waves described by the (nonlinear) shallow water equation are locally interpreted as linear waves on a two-layer parallel base flow described by the Taylor-Goldstein equation. This link helps us interpret long-wave instability and contrast it to short-wave (e.g. Kelvin-Helmholtz) instability. Our results suggest a transition to turbulence in SID through long-wave instability relying on vertical confinement by the top and bottom walls.
ISSN:2331-8422