| An idealized 1D river plume in the sea can be presented as the upper layer of zero salinity and
thickness h, lying above a saline water column, so that the density jump between the two
layers is ΔÏ. Since the Ekman transport (i.e. vertically integrated drift velocity) is directed
right-hand relatively to the wind direction and its value u*2-f (where u*2 is the squared
friction velocity, defined as the wind stress divided by the water density Ï0, and f is the
Coriolis parameter) does not depend on the presence of river plume, while the density
stratification works to confine the Ekman transport mainly within the river plume layer, one
may expect that the river plume causes an increase of both the scalar value of the sea surface
drift velocity and the clockwise turn angle of the velocity vector. To develop more
detailed, quantitative description of the effect of river plume on the sea surface
Ekman drift velocity, dimensional analysis along with numerical simulation has been
applied.
In a case of no river plume, the sea surface Ekman drift velocity components,(u0,v0)(or
the velocity scalar and angle (U0,φ0)), depend on, apart from u* and f, two parameters of
the length dimension — the roughness parameter z0 and some averaging landscale za
specifying the features of the drift velocity measurements/simulations. The dimensional
analysis implies functional forms as follows
U0 = u*F0 (LE -z0, za-z0), φ0 = Φ0(LE-z0, za-z0)
(1)
where LE = 0.4u*-f is the Ekman length and F0 and Φ0 are some functions of two
non-dimensional variables.
Implying that the dependencies (1) are known and focusing on the net effect of river
plume on the Ekman drift in the sea, we can suggest for the sea surface velocity scalar and
angle (U,φ) following functional forms
U = U0 -
F (E)-
(Fr2-E )α, φ = φ0 -
Φ (E)-
(Fr2-E )β
(2)
where E = LE-h and Fr = u*-(g*h)1-2 are the non-dimensional Ekman and Froude
numbers, accordingly, g* = g -
ΔÏ-Ï0 is the reduced gravity, F(x) andΦ(x) are some
functions of a variable x, α and β are the exponents of power functions (to be determined).
The sense of choosing of (Fr2-E) for the second non-dimensional parameter is to make it free
of any h–dependence, and thereby to confine the h–dependence within the first
non-dimensional parameter E. It is evident from simple physical reasons that U - U0,
φ - φ0 at h - 0,-, which corresponds to asymptotics of F(E ), Φ(E) - 1 at E - 0,-
and implies maxima of F(E) and Φ(E) at some intermediate values of E where
F, Φ > 1.
To estimate non-dimensional dependencies (2), numerical simulations of the Ekman drift
at different value of the wind stress in the presence of a river plume of different thickness and
density jump were performed by means of a 1D version of the Princeton Ocean
Model (POM) with a 2.5 moment turbulence closure sub-model embedded (Mellor
& Yamada 1982). The prognostic runs of the 1D POM at constant value of the
friction velocity were used to obtain time series of current velocity in the surface
layer with inertial oscillations filtered out, and to calculate the maximum value of
the velocity scalar achieved in the course of river plume erosion and thickening
caused by turbulent mixing. The numerical simulations showed that the maximum
value of F(E )and Φ(E) in (2) is achieved at E=15–18 and E=8–10 accordingly,
and the exponent for the power function of (Fr2-E)αis estimated at α = -1-4. |