This model represents the four-dimensional version of the advection-dispersion equation (1) for an estuary.
dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (1)
Where S: salinity (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume.
For a set value of Q, the equation becomes:
VdS/dt = QdS - (d(EA)/dx) dS (2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q)
We can rewrite (2) for the first estuarine box as:
Q(Sr-S1)=E(b)r,1(Sr-S1)-E(b)1,2(S1-S2) (3)
Where Sr: river salinity (=0), S1: mean estuary salinity for box 1; S2: mean estuary salinity for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2.
Because we're at the head of the estuary, E(b)r,1 is zero, wich means: no salt enters the river. Sr is also zero, because the river salinity is zero. Therefore:
Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:
VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q
At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:
Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)
Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity
E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.
By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:
QSe=E(b)e,s(Se-Ss) (Eq. 4)
At steady state
E(b)e,s = QSe/(Se-Ss) (Eq 5)
The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.
You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.
Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:
VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q
At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:
Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)
Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity
E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.
By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:
QSe=E(b)e,s(Se-Ss) (Eq. 4)
At steady state
E(b)e,s = QSe/(Se-Ss) (Eq 5)
The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.
You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.
Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:
VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q
At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:
Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)
Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity
E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.
By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:
QSe=E(b)e,s(Se-Ss) (Eq. 4)
At steady state
E(b)e,s = QSe/(Se-Ss) (Eq 5)
The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.
You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.
This model represents the four-dimensional version of the advection-dispersion equation (1) for an estuary.
dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (1)
Where S: salinity (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume.
For a set value of Q, the equation becomes:
VdS/dt = QdS - (d(EA)/dx) dS (2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q)
We can rewrite (2) for the first estuarine box as:
Q(Sr-S1)=E(b)r,1(Sr-S1)-E(b)1,2(S1-S2) (3)
Where Sr: river salinity (=0), S1: mean estuary salinity for box 1; S2: mean estuary salinity for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2.
Because we're at the head of the estuary, E(b)r,1 is zero, wich means: no salt enters the river. Sr is also zero, because the river salinity is zero. Therefore:
Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:
VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q
At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:
Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)
Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity
E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.
By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:
QSe=E(b)e,s(Se-Ss) (Eq. 4)
At steady state
E(b)e,s = QSe/(Se-Ss) (Eq 5)
The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.
You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.
Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:
VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q
At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:
Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)
Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity
E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.
By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:
QSe=E(b)e,s(Se-Ss) (Eq. 4)
At steady state
E(b)e,s = QSe/(Se-Ss) (Eq 5)
The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.
You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.
Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:
VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q
At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:
Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)
Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity
E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.
By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:
QSe=E(b)e,s(Se-Ss) (Eq. 4)
At steady state
E(b)e,s = QSe/(Se-Ss) (Eq 5)
The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.
You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.
Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:
VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q
At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:
Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)
Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity
E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.
By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:
QSe=E(b)e,s(Se-Ss) (Eq. 4)
At steady state
E(b)e,s = QSe/(Se-Ss) (Eq 5)
The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.
You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.
Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:
VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q
At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:
Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)
Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity
E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.
By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:
QSe=E(b)e,s(Se-Ss) (Eq. 4)
At steady state
E(b)e,s = QSe/(Se-Ss) (Eq 5)
The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.
You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.
Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:
VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q
At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:
Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)
Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity
E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.
By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:
QSe=E(b)e,s(Se-Ss) (Eq. 4)
At steady state
E(b)e,s = QSe/(Se-Ss) (Eq 5)
The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.
You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.
Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:
VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q
At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:
Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)
Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity
E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.
By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:
QSe=E(b)e,s(Se-Ss) (Eq. 4)
At steady state
E(b)e,s = QSe/(Se-Ss) (Eq 5)
The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.
You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.
This model represents the four-dimensional version of the advection-dispersion equation (1) for an estuary.
dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (1)
Where S: salinity (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume.
For a set value of Q, the equation becomes:
VdS/dt = QdS - (d(EA)/dx) dS (2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q)
We can rewrite (2) for the first estuarine box as:
Q(Sr-S1)=E(b)r,1(Sr-S1)-E(b)1,2(S1-S2) (3)
Where Sr: river salinity (=0), S1: mean estuary salinity for box 1; S2: mean estuary salinity for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2.
Because we're at the head of the estuary, E(b)r,1 is zero, wich means: no salt enters the river. Sr is also zero, because the river salinity is zero. Therefore:
This model represents the four-dimensional version of the advection-dispersion equation (1) for an estuary.
dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (1)
Where S: salinity (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume.
For a set value of Q, the equation becomes:
VdS/dt = QdS - (d(EA)/dx) dS (2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q)
We can rewrite (2) for the first estuarine box as:
Q(Sr-S1)=E(b)r,1(Sr-S1)-E(b)1,2(S1-S2) (3)
Where Sr: river salinity (=0), S1: mean estuary salinity for box 1; S2: mean estuary salinity for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2.
Because we're at the head of the estuary, E(b)r,1 is zero, wich means: no salt enters the river. Sr is also zero, because the river salinity is zero. Therefore:
This model represents the four-dimensional version of the advection-dispersion equation (1) for an estuary.
dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (1)
Where S: salinity (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume.
For a set value of Q, the equation becomes:
VdS/dt = QdS - (d(EA)/dx) dS (2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q)
We can rewrite (2) for the first estuarine box as:
Q(Sr-S1)=E(b)r,1(Sr-S1)-E(b)1,2(S1-S2) (3)
Where Sr: river salinity (=0), S1: mean estuary salinity for box 1; S2: mean estuary salinity for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2.
Because we're at the head of the estuary, E(b)r,1 is zero, wich means: no salt enters the river. Sr is also zero, because the river salinity is zero. Therefore:
[ This model represents the four-dimensional version of the advection-dispersion equation (1) for an estuary.
dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (1)
Where S: salinity (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume.
For a set value of Q, the equation becomes:
VdS/dt = QdS - (d(EA)/dx) dS (2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q)
We can rewrite (2) for the first estuarine box as:
Q(Sr-S1)=E(b)r,1(Sr-S1)-E(b)1,2(S1-S2) (3)
Where Sr: river salinity (=0), S1: mean estuary salinity for box 1; S2: mean estuary salinity for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2.
Because we're at the head of the estuary, E(b)r,1 is zero, wich means: no salt enters the river. Sr is also zero, because the river salinity is zero. Therefore:
QS1=E(b)1,2(S1-S2) (4)
At steady state
E(b)1,2 = QS1/(S1-S2) (5) ]
Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:
VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q
At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:
Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)
Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity
E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.
By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:
QSe=E(b)e,s(Se-Ss) (Eq. 4)
At steady state
E(b)e,s = QSe/(Se-Ss) (Eq 5)
The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.
You can use the upper slider to turn off dispersion (set to zero). If the variable being simulated is (a) salinity, you will see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system; (b) POM, then the ocean (which typically has less POM) will not contribute a flushing effect and the concentration of POM in the tidal creek or estuary will be higher.
The middle slider allows you to simulate a variable river flow, and understand how dispersion compensates for changes in freshwater input.
Biology
Two biological functions are implemented in CREEK, both extremely simplified.
1. Primary production - a constant primary production rate is considered in gC m-3 d-1
2. Oyster filtration - a constant clearance rate (CR) is considered in L ind- 1 h-1, scaled to a certain stocking density S (ind m-3)
Units are normalized, and food depletion is CR * S * POM, in g POM m-3 d-1
The lower slider allows for adjustment of different densities.
The model provides three outputs: 1. POM concentration in mg L-1 2. Equivalent in chlorophyll (ug L-1) 3. Total oyster biomass in kg for the whole system
Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:
VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q
At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:
Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)
Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity
E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.
By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:
QSe=E(b)e,s(Se-Ss) (Eq. 4)
At steady state
E(b)e,s = QSe/(Se-Ss) (Eq 5)
The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.
You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.
Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:
VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q
At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:
Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)
Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity
E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.
By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:
QSe=E(b)e,s(Se-Ss) (Eq. 4)
At steady state
E(b)e,s = QSe/(Se-Ss) (Eq 5)
The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.
You can use the upper slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.
The lower slider allows you to simulate a variable river flow, and understand how dispersion compensates for changes in freshwater input.
Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:
VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q
At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:
Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)
Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity
E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.
By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:
QSe=E(b)e,s(Se-Ss) (Eq. 4)
At steady state
E(b)e,s = QSe/(Se-Ss) (Eq 5)
The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.
You can use the upper slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.
The lower slider allows you to simulate a variable river flow, and understand how dispersion compensates for changes in freshwater input.
[ This model represents the four-dimensional version of the advection-dispersion equation (1) for an estuary.
dN/dt = (1/A)d(QN)/dx - (1/A)d(EA)/dx(dN/dx) (1)
Where N: Nitrates (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume.
For a set value of Q, the equation becomes:
VdN/dt = QdN - (d(EA)/dx) dN (2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q)
We can rewrite (2) for the first estuarine box as:
Q(Nr-N1)=E(b)r,1(Nr-N1)-E(b)1,2(N1-N2) (3)
Where Sn: river nitrates(=5), N1: mean estuary Nitrates for box 1; N2: mean estuary nitrates for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2.
[ This model represents the four-dimensional version of the advection-dispersion equation (1) for an estuary.
dN/dt = (1/A)d(QN)/dx - (1/A)d(EA)/dx(dN/dx) (1)
Where N: Nitrates (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume.
For a set value of Q, the equation becomes:
VdN/dt = QdN - (d(EA)/dx) dN (2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q)
We can rewrite (2) for the first estuarine box as:
Q(Nr-N1)=E(b)r,1(Nr-N1)-E(b)1,2(N1-N2) (3)
Where Sn: river nitrates(=5), N1: mean estuary Nitrates for box 1; N2: mean estuary nitrates for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2.
[ This model represents the four-dimensional version of the advection-dispersion equation (1) for an estuary.
dN/dt = (1/A)d(QN)/dx - (1/A)d(EA)/dx(dN/dx) (1)
Where N: Nitrates (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume.
For a set value of Q, the equation becomes:
VdN/dt = QdN - (d(EA)/dx) dN (2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q)
We can rewrite (2) for the first estuarine box as:
Q(Nr-N1)=E(b)r,1(Nr-N1)-E(b)1,2(N1-N2) (3)
Where Sn: river nitrates(=5), N1: mean estuary Nitrates for box 1; N2: mean estuary nitrates for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2.
[ This model represents the four-dimensional version of the advection-dispersion equation (1) for an estuary.
dN/dt = (1/A)d(QN)/dx - (1/A)d(EA)/dx(dN/dx) (1)
Where N: Nitrates (kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).
For a given length delta x, Adx = V, the box volume.
For a set value of Q, the equation becomes:
VdN/dt = QdN - (d(EA)/dx) dN (2)
EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient (m3 s-1, i.e. a flow, equivalent to Q)
We can rewrite (2) for the first estuarine box as:
Q(Nr-N1)=E(b)r,1(Nr-N1)-E(b)1,2(N1-N2) (3)
Where Sn: river nitrates(=5), N1: mean estuary Nitrates for box 1; N2: mean estuary nitrates for box 2; E(b)r,1: dispersion coefficient between river and estuary box 1; and E(b)1,2: dispersion coefficient between the estuary boxes 1 and 2.
