\subsection{Impact of the Shell}
To estimate the impact of the shell on the cloud, we first compare the energy in the shell with the gravitational binding energy. With an effective radius of 5 pc (from the approximated geometrical mean of the cloud extent), we calculate the gravitational binding energy to be $3.97\times10^{47}$ erg, which is 30 times larger than the kinetic energy in the shell. Clearly, the shell does not have the energy to unbind the entire cloud.

One way to assess whether or not the embedded stellar wind is powerful enough to drive the turbulence is by comparing the energy injection rate ($\dot E_W$) of the shell to the turbulence dissipation rate ($L_{turb}$). The intuitive way to estimate the energy injection rate of the shell is to assume a timescale during which the wind from the embedded B-stars has been accumulating the kinetic energy that we observe within the shell. Following Arce et al. (2011), we assume $\tau_W$ $\sim$ $1\times10^6$ yr. We then have $\dot E_W = E_{shell}/\tau_W \sim 3.4\times10^{33}$ erg/s. Another way to assess this is following Eq. 3.7 in \citet{McKee_1989}:

\begin{equation}
\dot E_W = 0.5\,(\dot M_W\,v_W)\,v_{rms}\;\;\;\text{,}
\end{equation}

where $v_{rms}$ is the rms velocity of the turbulence in the cloud. $\dot M_W$ and $v_W$ are the mass loss rate and the wind velocity respectively. The mass loss rate of the shell can be estimated from the shell momentum we calculated in \S5.1 by assuming $\tau_W$ and a wind velocity $v_W$.

\begin{equation}
\dot M_W = \frac{P_{shell}}{\tau_W\,v_W}
\end{equation}

Assuming $\tau_W$ $\sim$ $6\times10^6$ yr and $v_W$ $\sim$ 200 km/s, we get a mass loss rate $\dot M_W$ $\sim$ $2.3\times10^{-5}$ M$_{\sun}$/yr. With the rms velocity of the turbulence $\sim$ 1.68 km/s, we get an energy injection rate of $\sim$ $10^{33}$ erg/s.

The turbulence dissipation rate depends on the dissipation time, which is related to the free-fall time and is often written as $t_{diss} = \eta\,t_{ff}$. In \citet{McKee_1989} and McLow (1999), numerical simulations give $\eta$ in the range of 1 to 10. Assuming $\eta$ = 5 and a volume density of $10^3$ cm$^{-3}$, we have $t_{diss}$ $\sim$ $5\times10^6$ yr. We can then calculate the turbulence dissipation rate:

\begin{equation}
L_{turb} = \frac{E_{turb}}{t_{diss}}
\end{equation}

This gives $L_{turb}$ $\sim$ $10^{33}$ erg/s, which is on the same order of magnitude as the energy injection rate of the shell. These estimates indicate that the spherical wind from B-stars ($\rho$ Oph) has the potential for driving the turbulence in the Ophiuchus cloud. This result agrees with \citet{Arce_2011}.