Erase vectors within a certain area on quiver plots

I am trying to make a quiver plot showing the flow of water around a hump who's center is located at the origin with a radius of 1cm. When I create the quiver plot, it creates vectors with bases inside this semicircular area. Is there any way to set parameters to remove these certain vectors from the plot?

Thanks.

Here is my code and the plot outputted:

clear;clc;
U = 5;
a = .01;
X = -.03:.003:.03;
Y = 0:.003:.03;
[x,y] = meshgrid(X,Y);
u = U + ((U*a^2)./((x.^2 + y.^2).^2)).*(y.^2 - x.^2);
v = ((U*a^2)./((x.^2 + y.^2).^2)).*(-2.*x.*y);
% if y < a^2 - x.^2
%     u = 0; v = 0;
% end
theta = linspace(0, pi, 1000);
x_circ = a*cos(theta);
y_circ = a*sin(theta);
figure;
    quiver(x, y, u, v, 4.5)
    hold on 
    plot(x_circ,y_circ)
    fill(x_circ,y_circ,"r")
axis equal
xlim([-.03 .03]);
ylim([0 .03]);

Here is the plot without the hump being filled. Obviously, these vectors should not exist since there is a solid object to cause the flow to move around it

Answer 1

[Simon Chan]

Find all points inside the semi-circle and set NaN to those points on vector u and v.

clear;clc;
U = 5;
a = .01;
X = -.03:.003:.03;
Y = 0:.003:.03;
[x,y] = meshgrid(X,Y);
u = U + ((U*a^2)./((x.^2 + y.^2).^2)).*(y.^2 - x.^2);
v = ((U*a^2)./((x.^2 + y.^2).^2)).*(-2.*x.*y);
% if y < a^2 - x.^2
%     u = 0; v = 0;
% end
theta = linspace(0, pi, 1000);
x_circ = a*cos(theta);
y_circ = a*sin(theta);
y_circ(end) = 0;                            % Make sure the end point goes to 0
[in,~] = inpolygon(x,y,x_circ,y_circ);      % Find points inside the semi-circile
u(in)=NaN;                                  % Set value inside the semi-circle to NaN
v(in)=NaN;
figure;
    quiver(x, y, u, v)                      % Auto scale
    hold on 
    plot(x_circ,y_circ)
    %fill(x_circ,y_circ,"r")
axis equal
xlim([-.03 .03]);
ylim([0 .03]);