Tidal excursion
From Coastal Wiki
Definition of Tidal excursion:
the average distance travelled by tidal flow between lowwater slack tide and highwater 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 (lowwater slack tide) and another slack tide occurs closer to high water (highwater slack tide).
The tidal excursion [math]L[/math] is given by the formula
[math]L = \int_{t_{LSW}}^{t_{HSW}} u(X(t),t) \; dt ,[/math]
where [math]u(x,t)[/math] is the tidal component of the current velocity averaged over the channel crosssection, [math]X(t)[/math] is the position of a water parcel moving with velocity [math]u(X(t),t)[/math], starting from [math]x=0[/math] at [math]t=t_{LSW}[/math] (lowwater slack tide, LSW), and arriving at [math]x=L[/math] at [math]t=t_{HSW}[/math] (highwater slack tide, HSW).
If [math]\quad u(t)=U \sin \omega t ,[/math]
meaning that the current velocity does not depend on [math]x[/math] and that the tide is sinusoidal with period [math]T=2 \pi / \omega[/math], then
[math]\quad L=2 U / \omega[/math].