Fluctuation of autocorrelation of a signal due to signal's noise
If you view $V(t)$ as desired signal $kt$  affected by noise $R(t)$, the clearly as you keep increasing $k$, this has the effect of increasing signal energy. Hence if the noise power is kept constant then $V(t)$ tends towards being more deterministic (in a loose sense) with improving SNR, and autocorrelation hence is more deterministic with reduced fluctuations.