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We propose a computational framework for simulating the self-similar regime of turbulent Rayleigh–Taylor (RT) mixing layers in a statistically stationary manner. By leveraging the anticipated self-similar behaviour of RT mixing layers, a transformation of the vertical coordinate and velocities is applied to the Navier–Stokes equations (NSE), yielding modified equations that resemble the original NSE but include two sets of additional terms. Solving these equations, a statistically stationary RT (SRT) flow is achieved. Unlike temporally growing Rayleigh–Taylor (TRT) flow, SRT flow is independent of initial conditions and can be simulated over infinite simulation time without escalating resolution requirements, hence guaranteeing statistical convergence. Direct numerical simulations (DNS) are performed at an Atwood number of 0.5 and unity Schmidt number. By varying the ratio of the mixing layer height to the domain width, a minimal flow unit of aspect ratio 1.5 is found to approximate TRT turbulence in the self-similar mode-coupling regime. The SRT minimal flow unit has one-sixteenth the number of grid points required by the equivalent TRT simulation of the same Reynolds number and grid resolution. The resultant flow corresponds to a theoretical limit where self-similarity is observed in all fields and across the entire spatial domain – a late-time state that existing experiments and DNS of TRT flow have difficulties attaining. Simulations of the SRT minimal flow unit span TRT-equivalent Reynolds numbers (based on mixing layer height) ranging from 500 to 10 800. The SRT results are validated against TRT data from this study as well as from Cabot & Cook (Nat. Phys., vol. 2, 2006, pp. 562–568).
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This content will become publicly available on March 8, 2026
Grid independence studies applied to a field‐scale computational fluid dynamic (CFD) model using the detached eddy simulation (DES) technique along a reach of the Colorado River in Marble Canyon
Abstract Grid independence studies have emerged as essential methodological frameworks for comprehending the impact of domain resolution on simulating anisotropic turbulence at the river‐reach scale using large eddy simulation models. This study proposes a methodology to assess the loss of information in turbulent flow patterns when coarsening the computational domain, examined in a 1‐km transect of the Colorado River along Marble Canyon. Seven computational domain resolutions are explored to analyse the sensitivity of turbulent flow to spatial resolution changes, utilizing the turbulent kinetic energy (TKE) spectrum technique and spatiotemporal analysis of eddy structures via statistical metrics such as root mean square error (RMSE), Kullback‐Leibler (KL) divergence, Nash‐Sutcliffe model efficiency coefficient (NSE), wavelet power spectrum and grid convergence index (GCI). Based on physical principles and statistics, these metrics quantify information loss and assess domain resolutions. A computational fluid dynamic (CFD) model is developed by employing the detached eddy simulation (DES) technique, with boundary condition (BC) integrating the rough wall extension of the Spallart‐Allmaras model in cells near the bed. Evaluation of domain resolutions aims to identify grid cell sizes capturing flow behaviour and hydraulic characteristics, including primary and secondary flows, return currents, shear layers and primary and secondary eddies. The study observes an increase in data representation of the TKE spectrum with finer spatial domain resolution. Additionally, surface analysis, conducted via RMSE, KL and NSE metrics, identifies specific areas within the flow field showing high sensitivity to refining the grid cell sizes.
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- PAR ID:
- 10576212
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Earth Surface Processes and Landforms
- Volume:
- 50
- Issue:
- 3
- ISSN:
- 0197-9337
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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