The Plunging of Hyperpycnal Plumes on Tilted Bed by Three-Dimensional Large-Eddy Simulations

Felipe Nornberg Schuch
Jorge Hugo Silvestrini
School of Technology, Pontifical Catholic University of Rio Grande do Sul, Porto Alegre, Brazil.
felipe.schuch@edu.pucrs.br, jorgehs@pucrs.br

Eckart Meiburg
Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, USA
meiburg@engineering.ucsb.edu

Sylvain Laizet
Department of Aeronautics, Imperial College London, London, SW7 2AZ, UK
s.laizet@imperial.ac.uk

Abstract: Theoretical and experimental interest in the transport and deposition of sediments from rivers to oceans has increased rapidly over the last two decades. The marine ecosystem is strongly affected by mixing at river mouths, with for instance anthropogenic actions like pollutant spreading. Particle-laden flows entering a lighter ambient fluid (hyperpycnal flows) can plunge at a sufficient depth, and their deposits might preserve a remarkable record across a variety of climatic and tectonic settings. Numerical simulations play an essential role in this context since they provide information on all flow variables for any point of time and space. This work offers valuable Spatio-temporal information generated by turbulence-resolving 3D simulations of poly-disperse hyperpycnal plumes over a tilted bed. The simulations are performed with the high-order flow solver Xcompact3d, which solves the incompressible Navier-Stokes equations on a Cartesian mesh using high-order finite-difference schemes. Five cases are presented, with different values for flow discharge and sediment concentration at the inlet. A detailed comparison with experimental data and analytical models is already available in the literature. The main objective of this work is to present a new data-set that shows the entire three-dimensional Spatio-temporal evolution of the plunge phenomenon and all the relevant quantities of interest.

Keywords: Turbidity Current, Plunging Flow, Computational Fluid Dynamics, Large-Eddy Simulation, Xcompact3d.

• Publication (PDF): Download full-text
• Flow visualization: https://youtu.be/rUDY5UI0bG4
• Talk: https://youtu.be/n08U9l1Pgis
• Slides: https://prezi.com/view/2WGA1sVCm08ZNLpOlERO/

Simulations

Five poly-disperse simulations with 3 grain sizes based on the experimental set-up and the numerical configuration of:

• Lamb, M.P., McElroy, B., Kopriva, B., Shaw, J. and Mohrig, D., 2010. "Linking river-flood dynamics to hyperpycnal plume deposits: Experiments, theory, and geological implications". Geological Society of America Bulletin, Vol. 122, No. 9-10, pp. 1389–1400;

• Schuch, F.N., Pinto, L.C., Silvestrini, J.H. and Laizet, S., 2018. "Three-dimensional turbulence-resolving simulations of the plunge phenomenon in a tilted channel". Journal of Geophysical Research: Oceans, Vol. 123, pp. 1–13.

Cases	2	4	5	6	7
Inflow Discharge (m²/s)	0.0046	0.0025	0.0033	0.0043	0.0043
Volumetric particle concentration (%)	0.36	0.54	0.54	0.54	1.00
Reynolds Number	4,300	2,500	3,300	4,300	4,300
Initial densimetric Froude Number	17.81	8.45	11.16	14.54	11.68

Dataset

Data from the five simulations are included (cases 2, 4, 5, 6, and 7). The output files from Xcompact3d were converted to NetCDF aiming to be more friendly than raw binaries, they include data arrays together with metadata and the coordinates:

• n: Particle fractions, three were used for the poly-dispersed simulations;
• t: Time;
• x: Streamwise coordinate;
• y: Vertical coordinate;
• z: Spanwise coordinate;

Due to limitations at the storage size, the time sampling is smaller for larger arrays. There are four files for each simulated case:

• 3d-case-<num>.nc: Complete 3D snapshot at 12 different dimensionless times (250, 500, 750, 1,000, 1,250, 1,500, 1,750, 2,000, 3,000, 4,000, 5,000, 6,000), the arrays are:

  • ux (x,y,z,t): Streamwise velocity;
  • uy (x,y,z,t): Vertical velocity;
  • uz (x,y,z,t): Spanwise velocity;
  • phi (x,y,z,n,t): Concentration.

• xy-planes-case-<num>.nc: Spanwise-averaged quantities with a timestep of 5 dimensionless units:

  • ux (x,y,t): Streamwise velocity;
  • uy (x,y,t): Vertical velocity;
  • uz (x,y,t): Spanwise velocity;
  • phi (x,y,n,t): Concentration.

• xz-planes-case-<num>.nc: Depth-averaged quantities with a timestep of 5 dimensionless units:

  • ux (x,z,t): Streamwise velocity;
  • uy (x,z,t): Vertical velocity;
  • uz (x,z,t): Spanwise velocity;
  • phi (x,z,n,t): Concentration.

• LA-case-<num>.nc: The complete spatio-temporal analysis of the relevant quantities is possible in a layer-averaged context per width unit, it is based on three variables:

  • Layer-averaged Uh (x,t);
  • Layer-averaged U2h (x,t);
  • Layer-averaged UCh (x,n,t);

  that can be used to compute layer-averaged velocity U = U2h/Uh, flow depth H = (Uh)²/U2h, flow discharge Q = Uh, concentration C = UCh/Uh and local densimetric Froude number Fr. In addition to:

  • utau (x,t): Spanwise-averaged bed shear velocity;
  • dep (x,n,t): Spanwise-averaged deposition rate.

  All arrays with a timestep of 2.5 dimensionless units.

Each file can be loaded with the Python package xarray (see Why xarray), for instance:

dataset = xr.load_dataset("filename")

Examples

• 00-LA-and-Convert-to-NetCDF.ipynb - This Notebook is presented only for reference, it was used to compute the layer-averaged quantities and to convert the raw binary data from Xcompact3d to NetCDF. These files are available at Zenodo;

• 01-Computing-and-Plotting.ipynb - This Notebook shows how to read, compute and plot the variables presented in our work.

Setup

The examples above are only rendered online, if you choose to install and run them locally, follow these steps:

1. Clone the repository:

git clone https://github.com/fschuch/the-plunging-flow-by-3D-LES.git

2. Install the environment. This repository includes an environment.yaml file containing a list of the requirements to run the examples. To install them with conda run:

conda env create -f .binder/environment.yml
conda activate plunging-flow-analysis

3. Download the data files from Zenodo to the root folder of this repository.

4. Start a Jupyter session:

jupyter lab

Copyright and License

Copyright (c) 2020, Felipe N. Schuch. All content in this repository is under Creative Commons Attribution CC-BY 4.0, and all code is under BSD-3 clause.