How to interpolate a 1D function along the desired axis of 2D function

General
1

Hi, I am facing a problem with the interpolation of the following function u_init
MWE Code for u_init

mesh = UnitIntervalMesh(256)
V = FunctionSpace(mesh, 'P', 1)
def u0_boundary(x, on_boundary):
    return on_boundary

bc = DirichletBC(V, Constant(0.0), u0_boundary)
u = TrialFunction(V)
v = TestFunction(V)
A = inner(nabla_grad(u), nabla_grad(v))*dx
RHS = v*dx
u_init = Function(V)
solve(A == RHS, u_init, bc)
plot(u_init)

I am getting the following plot of the u_init

velocity_profile_fenics
velocity_profile_fenics841×592 44 KB

I am using the following code for interpolating the 1D function u_init to a 2D function p

mesh1 = UnitSquareMesh(256, 256)
V1 = FunctionSpace(mesh1, "P", 1)
p = Function(V1)
p = interpolate(u_init, V1)
plot(p)

The plot of p is the following

fenics_plot
fenics_plot676×616 14.7 KB

But I need the interpolation of the same function u_init in the x direction and it should look like
fenics_plot_flip
fenics_plot_flip607×664 15.5 KB

What should I do? Please help.
I am using FEniCS 2019.