# Wave-induced mixing in a numerical wave flume

## Cite this dataset

Paprota, Maciej (2024). Wave-induced mixing in a numerical wave flume [Dataset]. Dryad. https://doi.org/10.5061/dryad.80gb5mkqw

## Abstract

This dataset is a supplement to the article published in Earth System Dynamics. The article describes a semi-analytical solution to an advection–diffusion equation coupled with a nonlinear wavemaker model to investigate the effect of strong nonlinearity on wave-induced mixing. The numerical model is based on a pseudo-spectral solution of advection-diffusion equation and two theoretical approaches to the wavemaker problem - weakly-nonlinear analytical model and numerical model admitting higher nonlinearities. The results of numerical modeling of wave kinematics and associated mixing in a wave flume are provided.

The dataset comprises numerically predicted velocity and temperature fields. Matlab scripts are available, which display the data. Moreover, Matlab scipts for solution of advection-diffusion equation with a weakly-nonlinear input are provided (description of the model is presented in the journal paper). Please refer to a readme file for further details.

The data and the code may be freely used and modified.

## README: Wave-induced mixing in a numerical wave flume

https://doi.org/10.5061/dryad.80gb5mkqw

The dataset covers numerical results of wave-induced vertical mixing and Matlab scripts for solution of advection-diffusion equation with a weakly-nonlinear input.

Author: Maciej Paprota, Institute of Hydro-Engineering, Polish Academy of Sciences, Kościerska 7, 80-328 Gdańsk, Poland, mapap@ibwpan.gda.pl

The dataset serves as a supplementary material to:

https://esd.copernicus.org/preprints/esd-2022-27/

### Desription of the data and file structure

The *.dat files contain data used to prepare figures in the article linked to this dataset i.e.:

a) initial conditions for starting-up an advection-diffusion numerical model:

- ini_temp_profile.dat: initial temparature profile along the water depth;

the colums are:

1^{st} column - temperature (^{o}C;

2^{nd} column - relative water depth (z/h);

- ini_temp_space.dat: initial temperature spatial distribution in a wave flume;

h - water depth; x - horizontal coordinate; z - vertical coordinate;

the columns are:

1^{st} column - relative horizontal distance from the wavemaker (x/h);

2^{nd} column - relative water depth (z/h);

3^{rd} column - temperature (^{o}C);

You can use the script temp_ini_plots.m (on Zenodo) to plot the data and see more details on the data structure.

b) temperature and velocity fields in a wave flume:

\weakly_temp_kh[water_depth conditions]_Hh[wave_steepness].dat: temperature field for weakly-nonlinear model

\weakly_vel_kh[water_depth conditions]_Hh[wave_steepness].dat: velocity field for weakly-nonlinear model

\LMTV_temp_kh[water_depth conditions]_Hh[wave_steepness].dat: temperature field for fully-nonlinear model based on Lagrangian mean transport velocity

\LMTV_vel_kh[water_depth conditions]_Hh[wave_steepness].dat: Lagrangian mean transport velocity field for fully-nonlinear model

\EMTV_vel_kh[water_depth conditions]_Hh[wave_steepness].dat: Eulerian mean transport velocity field for fully-nonlinear model

the columns for temperature (temp) files are:

1^{st} column - relative horizontal distance from the wavemaker (x/h);

2^{nd} column - relative water depth (z/h);

3^{rd} column - temperature (^{o}C);

the columns for velocity (vel) files are:

1^{st} column - relative horizontal distance from the wavemaker (x/h);

2^{nd} column - relative water depth (z/h);

3^{rd} column - horizontal velocity component (m/s);

4^{th} column - vertical velocity component (m/s);

- u_profile_kh[water_depth conditions]: vertical velocity profile (along the depth) from a weakly-nonlinear theory;

the colums are:

1^{st} column - horizontal velocity component (m/s);

2^{nd} column - relative water depth (z/h);

[water_depth conditions] = 05, 10, 20 refer to kh = 0.5, 1.0, 2.0, respectively,

[wave_steepness] = 005, 010, 020 refeer to Hh = 0.05, 0.10, 0.20, respectively, where

k - wave number; h water depth; H - wave height;

You can use the scripts vel_field_plots.m, vel_field_diff_plots.m and temp_field_plots.m (on Zenodo) to plot the data and see more details on the data strructure.

c) MatLab scripts for plotting the *.dat files (on Zenodo):

- temp_field_ini_plots.m - plots initial values of temperature (profile and space);

- temp_field_plots.m - plots calculated temperature fields;

- vel_field_diff_plots.m - plots calculated differences between velocity fields;

- vel_field_plots.m - plots calculated velocity fields;

d) Matlab scripts of an advection-diffusion modelling of wave-induced vertical mixing:

- heat2D_RK4.m - main program and working example using weakly nonlinear theory as an input;

- remaining *.m scripts are functions used in the main program.

For more information inspect the scripts, where a large number of comments provides a guidance how the code works with relevant references to equations.

No other locations of the dataset are available.

## Methods

This dataset is an outcome of numerical models presented in the associated journal paper. The data were processed using scripts which are provided as a supplement to the data. Please refer to the readme file for further details.