Hi ALvaro,
The code below sets P=Q=0 to make the spacial dependence more clear.
Rather than meshgridding the 1d velocity vectors U1 and V1 to make U2 and V2 (I renamed them), you should define them directly as functions of the meshgridded matrix coordinates X and Y. Figure 2 satisfies the original equations and is much different than the original result of Figure(1).
There is also a question of overall sign reversal in the approach you used, but sign reversing back does not solve the problem. The real issue is not the sign but the method for calculating U and V.
a = .1;
b = .2;
P = 0;
Q = 0;
x1=-5;
x2=5;
y1=-5;
y2=5;
N = 20;
x = linspace(x1,x2,N);
y = linspace(y1,y2,N);
[X,Y]= meshgrid(x,y);
U1 = -P +a.*y; % sign reversed?
V1 = -Q +b.*x; % sign reversed?
[U2,V2]=meshgrid(U1,V1);
figure(1)
quiver (X,Y,U2,V2);
U3 = P -a.*Y;
V3 = Q -b.*X;
figure(2)
quiver (X,Y,U3,V3);
