Local:Equilibrium Tide Theory

From AMCGMedia

Jump to: navigation, search

Return to Tidal Modelling

The 'equilibrium tide' is the theoretical tide produced on a water world where the ocean depth is deep enough that the tidal bulge can keep up with the relative position of the Moon.

The following equations are used to calculate the equilibrium tide response of the three main species of tidal constituent:

ηeq(λ,θ,t) = sin2θKicos(σit + χi + 2λ) + sin2θKjcos(σjt + χj + λ) + (3sin2θ − 2)Kkcos(σkt + χk)
ijk

where ηeq = equilibrium tidal potential (m), λ = east longitude (radians),θ = colatitude (\left( \frac{\pi}{2}\right) -latitude), radians), χ = astronomical argument (radians), σ = frequency of tidal constituent (s-1), t = universal standard time (s), and K = equilibrium amplitude of tidal constituent (m).Subscript i represents the semidiurnal constituents (e.g., M2), subscript j the diurnal constituents (e.g., K1) and subscript k the long period constituents (e.g., Mf)

Equilibrium tidal amplitudes are as follows:

 M2AMP = 0.242334
 S2AMP = 0.112841
 N2AMP = 0.046398
 K2AMP = 0.030704
 K1AMP = 0.141565
 O1AMP = 0.100514
 P1AMP = 0.046843
 Q1AMP = 0.019256
 MfAMP = 0.041742
 MmAMP = 0.022026
 SsaAMP = 0.019446

Equilibrium tidal frequencies are as follows:

 M2FREQ = 1.40519E-04
 S2FREQ = 1.45444E-04
 N2FREQ = 1.37880E-04
 K2FREQ = 1.45842E-04
 K1FREQ = 0.72921E-04
 O1FREQ = 0.67598E-04
 P1FREQ = 0.72523E-04
 Q1FREQ = 0.64959E-04
 MfFREQ = 0.053234E-04
 MmFREQ = 0.026392E-04
 SsaFREQ = 0.003982E-04

Return to Tidal Modelling

This page was last modified on 1 March 2013, at 16:29. This page has been accessed 4,975 times.