METHOD FOR MODELLING A WATER CURRENT INDUCED BY A RIVER IN A GEOLOGICAL GRIDDED MODEL
A method of modelling a current induced by a river in a model comprising a plurality of cells, wherein the river-induced current is decomposed into a plurality of sub-currents corresponding to respective water depths, the method comprising, for each sub-current, steps of: —determining a width between lateral boundaries of a respective river jet of the sub-current, as a function of the distance from the river mouth, and —determining a direction and velocity of the sub-current in each cell located within the respective river jet, comprising: ∘determining a direction and velocity of the sub-current in each cell located at a centerline of the jet, as a function of the distance from the river mouth, and ∘inferring the direction and velocity of the sub-current in each other cell of the jet as a function of the distance between the cell and the centerline of the jet, and between the cell and the river mouth.
1 . A computer-implemented method of modelling a water current induced by a river in a geological gridded model comprising a plurality of cells wherein each cell is assigned a water depth, the river-induced current occurring within a river jet extending from a river mouth, and between two lateral boundaries, wherein the river-induced current is decomposed into a plurality of sub-currents corresponding to respective water depths, comprising at least:
a plume current, located at water surface, and
a bottom current, located at water bottom,
the method comprising, for each sub-current:
determining a width between lateral boundaries of a respective river jet of the sub-current, as a function of the distance from the river mouth, and
determining a direction and velocity of the sub-current in each cell located within the respective river jet, comprising:
determining a direction and velocity of the sub-current in each cell located at a centerline of the jet, as a function of the distance from the river mouth, and
inferring the direction and velocity of the sub-current in each other cell of the jet as a function of the distance between the cell and the centerline of the jet, and between the cell and the river mouth.
2 . A method according to claim 1 , further comprising determining a sedimentary charge distribution of the river mouth current according to the density of water brought by the river and the density of water in which flows the water of the river, the sedimentary charge distribution being selected among a group consisting of:
hypopycnal distribution,
homopycnal distribution,
hyperpycnal distribution.
3 . A method according to claim 2 , wherein, if the current has homopycnal distribution, the width of a river jet is computed as follows:
b
_
=
e
S
2
ξ
l
2
[
1
+
4
α
l
2
S
l
1
(
1
-
e
-
S
2
ξ
)
]
where
:
b
_
=
b
(
x
)
b
0
ξ
=
x
/
b
0
and S is a parameter computed from a friction factor, the width of the river mouth and the water depth at the river mouth,
α, l 1 and l 2 are fixed parameters,
b(x) is the half-width of the river jet at a distance x from the river mouth, and b 0 is the half-width of the river mouth.
4 . The method according to claim 2 , wherein, if the current has hypopycnal or hyperpycnal distribution, the width of a river jet is computed as follows:
{
b
_
=
e
s
2
ξ
l
2
[
1
+
4
α
l
2
S
l
1
(
1
-
e
-
S
2
ξ
)
]
if
x
≥
x
s
b
_
=
1
if
x
<
x
s
where
:
x
s
=
b
O
·
ξ
s
b
_
=
b
(
x
)
b
0
ξ
=
x
/
b
0
and S is a parameter computed from a friction factor, the width of the river mouth and the water depth at the river mouth,
ξ s is a parameter having a different value assigned to each subcurrent, wherein each value depends on the sedimentary charge distribution of the river-induced current,
α, l 1 and l 2 are fixed parameters,
b(x) is the half-width of the river jet at a distance x from the river mouth, and b 0 is the half-width of the river mouth.
5 . A method according to claim 1 , wherein the direction of the sub-current at the centerline of the jet is perpendicular to the direction along which extends the width of the river mouth and oriented away from the river mouth.
6 . A method according to claim 5 , wherein the direction of the sub-current in a cell in a respective river jet forms an angle with the centerline of the river jet which is a linear function of the distance between the cell and the centerline, such that the angle is 0 at the centerline and is equal to the angle between a lateral boundary of the river jet and the centerline at the lateral boundary.
7 . A method according to claim 1 , wherein if the current has hypopycnal or hyperpycnal distribution, the velocity of a sub-current in a cell located at a distance x from the river mouth, and along the centerline of the respective jet of the sub-current, is as follows:
{
u
(
x
)
=
u
0
if
x
<
x
s
u
_
(
x
)
=
e
-
S
2
ξ
[
1
+
4
α
l
2
S
l
1
(
1
-
e
-
S
2
ξ
)
]
if
x
≥
x
s
and
x
s
=
b
O
·
ξ
s
u
_
(
x
)
=
u
(
x
)
u
0
ξ
=
x
/
b
0
where S is a parameter computed from a friction factor, the width of the river mouth and the water depth at the river mouth
α, l 1 and l 2 are fixed parameters,
ξ s is a parameter having a different value assigned to each subcurrent, wherein each value depends on the sedimentary charge distribution of the river-induced current,
u(x) is the velocity of the sub-current at the distance x from the river mouth, u 0 is the velocity of the sub-current at the river mouth.
8 . A method according to claim 1 , wherein, if the current has homopycnal distribution, the velocity of a sub-current in a cell located at a distance x from the river mouth, and along the centerline of the respective jet of the sub-current, is as follows:
u
_
(
x
)
=
e
-
S
2
ξ
[
1
+
4
α
l
2
S
l
1
(
1
-
e
-
S
2
ξ
)
]
u
_
(
x
)
=
u
(
x
)
u
0
ξ
=
x
/
b
0
where S is a parameter computed from a friction factor, the width of the river mouth and the water depth at the river mouth
α, l 1 and l 2 are fixed parameters,
u(x) is the velocity of the sub-current at the distance x from the river mouth, u 0 is the velocity of the sub-current at the river mouth.
9 . A method according to claim 7 , wherein the velocity u 0 at the river mouth is the same for all sub-currents and along all the width of the river mouth.
10 . A method according to claim 7 , wherein the velocity of a sub-current in a cell located off the centerline, and, for currents having hypopycnal or hyperpycnal sedimentary charge distribution, at a distance x from the river mouth greater than x s , is a linear function of the distance between the cell and the centerline of the river jet, decreasing from a maximum value at the centerline until reaching a value of 0 at the lateral boundaries of the river jet.
11 . A method according to claim 7 , wherein the current has hypopycnal or hyperpycnal sedimentary charge distribution, and the velocity of a sub-current in a cell located off the centerline and at a distance x from the river mouth lower than x s is:
equal to the velocity at the centerline of the river jet if the cell is located at a distance from the centerline lower than L lim , defined such that:
L
lim
=
b
0
.
x
s
-
x
x
s
a linear function of the distance between the cell and the centerline if the cell is located at a distance from the centerline greater than L lim , from a maximum value at a distance equal to L lim , to a value of 0 at the lateral boundaries of the river jet.
12 . A computer implemented method for modelling the formation of a sedimentary area, comprising-:
receiving a geological gridded model of the area, comprising a plurality of cells,
assigning a water depth to each cell of the geological gridded model,
modelling a water current induced by a river in the geological gridded model according to claim 1 ,
modelling the introduction of at least one particle brought by the river in the geological gridded model,
simulating the transport of each introduced particle by the modelled river-induced current, and
updating the geological gridded model of the area according to the transport of the particle.
13 . The computer implemented method according to claim 12 , wherein the modelling a water current induced by a river in the geological gridded model includes: determining a sedimentary charge distribution of the river mouth current according to the density of water brought by the river and the density of water in which flows the water of the river, the sedimentary charge distribution being selected among a group consisting of:
hypopycnal distribution,
homopycnal distribution,
hyperpycnal distribution,
the method further comprising:
defining an amount of particles brought by the river, wherein the sedimentary charge distribution determines a repartition of the amount of particles among the subcurrents, wherein the modelling the introduction of at least one particle in the geological gridded model comprises introducing the particle at the river mouth and determining a depth at which the particle is introduced, depending on the repartition determined by the sedimentary charge distribution.
14 . A computer program product, comprising code instructions for implementing the method according to claim 1 , when it is executed by a processor.
15 . A non-transitory computer readable storage medium, having stored thereon a computer program comprising program instructions, the computer program being loadable into a processor and adapted to cause the processor to carry out, when the computer program is run by the processor, the method according to claim 1 .
16 . A computing device comprising a processor configured to implement the method according to claim 1 .