Plotting Quiver with Contour

Hello,

I need help with plotting using Quiver function such that the arrows of this function follows the contour lines. The equations in the following code are right since I have a got the desired contour plot. PLease note that 𝑢=𝜕𝜓/𝜕𝑦,𝑣=−𝜕𝜓𝜕𝑥. I have attached a picture as an example. Thanks

clc
clear all
syms x y 
L = 10000;
H = 6000;
sig = 0.03;
alp = 0;
r1 = (-alp+sqrt(alp^2+4*pi^2/H^2))/2;
r2 = (-alp-sqrt(alp^2+4*pi^2/H^2))/2;
x = linspace(0,L,100);
y = linspace(0,H,100);
[X,Y] = meshgrid(x,y); 
p = (sig*H^2/pi^2).*sin(pi*Y/H).*(((exp(r2*L)-1).*exp(r1*X)+(1-exp(r1*L)).*exp(r2*X))/(exp(r2*L)-exp(r1*L))-1);
U = (sig*H/pi).*cos(pi*Y/H).*(((exp(r2*L)-1).*exp(r1*X)+(1-exp(r1*L)).*exp(r2*X))/(exp(r2*L)-exp(r1*L))-1);
V = -1.*(sig*H^2/pi^2).*sin(pi*Y/H).*(((r1.*exp(r2*L)-1).*exp(r1*X)+r2.*(1-exp(r1*L)).*exp(r2*X))/(exp(r2*L)-exp(r1*L))-1);
contour(X,Y,p)
hold on
quiver(X,Y,U,V)
hold off
xlabel('X');
ylabel('Y');
title('sig = 0.03, alp = 0');