Modeling Concepts - Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use and Development - page 276

estimate for the period of the complex seiche resulting from the superposition of
the N -node longitudinal and the M -node transverse barotropic seiches:

− 05 .

2
2

2
2

2 M

a

N
b

MN
barotrop

( )

T = + (6.49)

gH

where g 9.81 [m s −2 ], H [m] is the depth of the basin, and a and b [m] are the

width and length of the basin, respectively. The maximum period corresponding to
a one-node longitudinal or transversal seiche is obtained by setting M

≈

= 0 or N = 0 ,

respectively. The lowest nodes generally represent the seiche adequately. 22
Seiches can exist as barotropic surface seiches, involving motions of the whole
water masses that reach their maximum amplitude at or near the free surface, or as
baroclinic internal seiches associated with the density stratification, with currents
reaching their maximum amplitude at or near the pycnocline. 22
For a two-layer basin, the period of an internal longitudinal one-node seiche
may be estimated by 24

− 1 − 1

2 ⋅⋅ bH H

g

+

up

down

() 1

T = (6.50)

barocl

⋅ − ( 1 ρρ / )

up down

where H up , H down , and ρ up , ρ down are the thickness and density of the upper and the

lower layer, respectively.
The phase speed of a barotropic seiche is c , where g is gravity and H is

the water depth. For internal (baroclinic) seiches, the phase speed is reduced by one or
two orders of magnitude because g is replaced by the reduced gravity g

= gH ⋅

′ = g ⋅ ( ∆ρ / ρ ),

where is the density difference between the upper and

lower layers. For example, in elongated basins of 10 to 100 km in length, the period
of oscillation of a barotropic seiche will be on the order of minutes or hours, while that
of baroclinic seiches will be tens of hours or days. These different time scales are also
associated with the effects of the Coriolis force, which modify the corresponding gravity
waves into Kelvin or Poincaré waves, respectively. 22
For example, in the Vistula Lagoon ( a

ρ is the average density and ∆ρ

2.7 m) the natural
period of oscillations are 9.8 and 1.0 h for the barotropic longitudinal and transversal
seiches, respectively.
The simple seiche theory 23 does not provide information on the seiche amplitude.
It totally depends on the amount of energy supplied to the basin by the wind action.
However, if the maximum amplitude ( h ) is known, for example, from the measure-
ments, the corresponding current at the seiche node points (where the amplitude is
zero and the current is maximum) may be estimated by the formula

= 91 km, b = 9 km, H =

h
H

V = gH ⋅ (6.51)

4 ⋅

A seiche will develop in a lagoon when the period over which the wind stops
is smaller than half the period of its fundamental (or one-node) mode. In this case,