DOI: 10.5061/dryad.80gb5mkqw
title: Wave-induced mixing in a numerical wave flume

description: 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.  
description: 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.
description: # Wave-induced mixing in a numerical wave flume
 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, 
 The dataset serves as a supplementary material to:
 ## 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<sup>st</sup> column - temperature
 (<sup>o</sup>C; 2<sup>nd</sup> 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<sup>st</sup>
 column - relative horizontal distance from the wavemaker (x/h);
 2<sup>nd</sup> column - relative water depth (z/h);
 3<sup>rd</sup> column - temperature
 (<sup>o</sup>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<sup>st</sup> column - relative horizontal distance from the
 wavemaker (x/h); 2<sup>nd</sup> column - relative water depth
 (z/h); 3<sup>rd</sup> column - temperature
 (<sup>o</sup>C); the columns for velocity (vel) files are:
 1<sup>st</sup> column - relative horizontal distance from the
 wavemaker (x/h); 2<sup>nd</sup> column - relative water depth
 (z/h); 3<sup>rd</sup> column - horizontal velocity component
 (m/s); 4<sup>th</sup> 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<sup>st</sup> column - horizontal velocity component (m/s);
 2<sup>nd</sup> 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.