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In IEEE Std 952-1997 (Annex C) we find the answer to this. They have a fancy integral relation between Allan Variance ($\sigma^{2}$) and Power Spectral Density. If $K$ is the random walk coefficient of which you speak, they show that $$\sigma^{2}(\tau) = \frac{K^{2} \tau}{3}$$ So $$\sigma(\tau) = \frac{K \tau^{0.5}}{3^{0.5}}$$ The 0.5 power on \\$\...