The keywords to search for this "scattering by a corner reflector" appear to have been "diffraction by a wedge". There's been quite a bit of research on exactly this kind of boundary. Particularly, ref. 1 provides explicit expressions for the solution of the problem that's set up as follows.

A two-dimensional wedge is situated in the space $0\le r<\infty$, $\alpha\le \theta\le 2\pi$, with $(r,\theta)$ being cylindrical coordinates (omitting $z$), as shown in the figure below (figure 1 from ref. 1). A plane wave is incident from the direction $\theta=\theta_0$ and scattered by the inner part of the wedge, which may be of any opening angle from $0$ to at least $4\pi$ (the case of hard-soft semi-infinite plane, see ref. 1 p. 277).

The solution of the wave equation, i.e. incident+scattered field, corresponding to $\alpha=120°$ is given in $\S 4$ as $G_{2\pi/q}(r,\theta,\theta_0;k)$ by equation $(23)$; in our case $q=3$. The expression (tweaked here for presentation) is

\begin{multline}
G_{2\pi/q}(r,\theta,\theta_0;k)=\sum_{m=0}^{q-1}\sum_{N\in\mathbb Z} \operatorname{H}[\pi-|\Delta\theta_m+4\pi N|]e^{ikr\cos(\Delta\theta_m)}+\\
+\frac{e^{i\pi/4}}{\sqrt\pi}\sum_{m=0}^{q-1} e^{ikr\cos(\Delta\theta_m)} \operatorname{sgn}\left[ \cos\left(\Delta\theta_m/2\right)\right]
\intop_{+\infty}^{\left| \cos\left(\Delta\theta_m/2\right) \right| \sqrt{2kr}} e^{-iv^2}\,\mathrm{d}v,
\end{multline}

where $\Delta\theta_m=\theta-\theta_0+4\pi m/q,$ $\operatorname{H}[\cdot]$ is the Heaviside step function, and $\operatorname{sgn}(\cdot)$ is the signum function. The summation over $N$ will pick only a handful of terms, because for others the Heaviside function will vanish. The integral in the second sum is expressible in terms of the Fresnel sine and cosine integrals:

$$\int\limits_{+\infty}^x \exp(-iv^2)\,\mathrm{d}v=
\frac{1-i}2 \sqrt{\frac\pi2} \left( (1+i)\operatorname{C}\left(\sqrt{\frac2\pi}x\right) + (1-i)\operatorname{S}\left(\sqrt{\frac2\pi}x\right)-1\right).$$

The cylindrical wave asked about in the OP originates from the second sum with these Fresnel-integral terms.

### References

- A. D. Rawlins,
*Plane-wave diffraction by a rational wedge*, Proc. R. Soc. A 411, 265-283 (1987).