function [u,udot,w,wdot] = linwavKin(d,z,H,k,x,t)
%linwavKin calculates the particle kinematics under a linear wave
%according to the linear velocity potential for INTERMEDIATE depth.
%Input:
% d=h - [m] water depth  (good to separate h from capital H if converting to other code language)
% z - [m] vector of vertical positions  (positive upwards, zero at still water level)
% H - [m] wave height, m
% k - [-] wave number, 2*pi/lambda
% x - [m] position along wavelength, can only take a single value in this code
% t - [s] wave phase period - can be single value or a vector set between 0:T s
% Outputs:
% u           - [m/s] horizontal particle velocity
% udot = dudt - [m/s^2] horizontal particle acceleration
% w           - [m/s] vertical particle velocity
% wdot = dwdt - [m/s^2] vertical particle acceleration
us = 0;  % [m/s] stream velocity zero in this code.
%%%%%%%%%%%%%

g=9.81; % [m/s^2] gravitational acceleration
omega=sqrt(g*k*tanh(k*d)); % [rad/s] angular wave frequency, 
zeta_a=H/2; % [m] wave amplitude

u = (omega*zeta_a * cosh(k*(z+d))/sinh(k*d)) .* sin(omega.*t-k.*x)+us;
w = omega*zeta_a*sinh(k*(z+d))/sinh(k*d) .* cos(omega.*t-k.*x);
udot = omega^2*zeta_a*cosh(k*(z+d))/sinh(k*d) .* cos(omega*t-k.*x);
wdot = -omega^2*zeta_a*sinh(k*(z+d))/sinh(k*d) .* sin(omega.*t-k.*x);

end