Plotting a function changing over time with different Phi_0

I want to plot Z(t) vs t for different Phi_0( a 3D plot). A waterfall plot would be appropriate for this. Maybe we need Z_0 also. we may assign Z_0=0.15 and also Phi_0 from 0 to 2*pi. This is my code:

eps=100;

kappa=0.6;

Omega=1000;

gamma=10^(-5);

lambda=10000;

kd=6;

phi_0=3.14;

t=0:0.1:30;

Phi_dot=((lambda*z)-(((sqrt((1+z)./2)).*exp(1).^(-(kd*(sqrt(2*lambda*(1+z))))))).*(kappa*(sqrt((1-z)./(1+z)))-(sqrt((1+z)./(1-z)))))*(cos(phi_0))/2 + (eps.*cos(Omega.*t));

z_dot= -((((1+z)./2)).*exp(1).^-(kd*(sqrt(2*lambda*(1+z)))))*(1+kappa)*(sqrt(1-z^2))*(sin(phi_0))/2 + gamma.*(Phi_dot);