# Tidal excursion

 Definition of Tidal excursion: the average distance travelled by tidal flow between low-water slack tide and high-water slack tide. This is the common definition for Tidal excursion, other definitions can be discussed in the article

## Notes

• The influence of river runoff on the travelled distance is not included in the tidal excursion.
• Slack tide is the time at which the tidal current (i.e. the tidal component of the current velocity) is smallest. Slack tide occurs twice during a tidal cycle. In coastal waters (flow influenced by friction and boundaries), one slack tide occurs closer to low water (low-water slack tide) and another slack tide occurs closer to high water (high-water slack tide).

The tidal excursion $L$ is given by the formula

$L = \int_{t_{LSW}}^{t_{HSW}} u(X(t),t) \; dt ,$

where $u(x,t)$ is the tidal component of the current velocity averaged over the channel cross-section, $X(t)$ is the position of a water parcel moving with velocity $u(X(t),t)$, starting from $x=0$ at $t=t_{LSW}$ (low-water slack tide, LSW), and arriving at $x=L$ at $t=t_{HSW}$ (high-water slack tide, HSW).

If $\quad u(t)=U \sin \omega t ,$

meaning that the current velocity does not depend on $x$ and that the tide is sinusoidal with period $T=2 \pi / \omega$, then

$\quad L=2 U / \omega$.