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 [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 cross-section, [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] (low-water slack tide, LSW), and arriving at [math]x=L[/math] at [math]t=t_{HSW}[/math] (high-water 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].