Data for: Connectivity and larval dispersal pathways of Panulirus argus in the Gulf of Mexico: a numerical study

% Matlab script
% Developed by Julio Antonio Lara-Hernandez ([e-mail])
% and Jorge Zavala-Hidalgo ([e-mail]).
% Ocean-atmosphere interaction group, Center of Atmospheric Sciences,
% National Autonomous University of Mexico (UNAM), Mexico.
%
% This script shows that a Turbulent-Difussion velocity (v') can be
% equivalently constructed from random numbers of (1) uniform or (2) normal
% distributions. It also shows that by setting a = b/sqrt(dt), the effect of
% Turbulent-Difussion remains the same regardless the selected time-step (dt):
%
% (1) v' = Va * Ru
% Where: v' = Turbulent-Difussion velocity
% Va = Advective velocity (e.g. velocity of an ocean current)
% Ru = Random number of uniform distribution from -a to a
% a = b/sqrt(dt)
% b = User-defined parameter modulating the degree of Turbulen-Difussion
% dt = Time-step defined by the user
%
% (2) v' = Rn
% Where: Rn = Random number of normal (Gaussian) distribution with a mean
% equal to zero and a standard deviation std_Rn = Va*a/sqrt(3)
%
% In the resulting graphs after running the script, the central curve
% indicates the mean, the upper curve is the mean+std, and the lower curve
% is the mean-std. The overlapping of the curves from both approaches
% indicates that they are equivalent. Reproducing the same curves by
% considering different time-steps shows that setting a equal to b/sqrt(dt)
% works to achieve the same effect of Turbulent-Difussion regardless the
% selected time-step.