 Solution

With planar anchoring on the cylindrical side wall, uniform axial alignment $\mathbf{n}=\hat{\mathbf{z}}$ is a simple defect-free profile. The axial direction is tangent at every wall point, so it satisfies the lateral boundary everywhere without elastic distortion.

This assumes degenerate planar anchoring, or an azimuthal preference compatible with axial alignment. End constraints, selected circumferential anchoring or imposed twist can favor another state. planar anchoring alone does not require a circumferential vortex. The original axial-section sketch shows the uniform axial option.