34
3 Basics of Geophysical Fluid Dynamics
3.8.7 Density
Density, symbolised by the Greek letter ρ (“rho”), is the ratio of mass M over volume V :
ρ =
M
V
(3.12)
Density has units of kilograms per cubic metres (kg/m
3
). Density of seawater
is in a range of 1025–1028 kg/m
3
. Density variations are generally small (< 0.5%)
compared with the mean value. Freshwater has densities around 1000 kg/m
3
. The
density of seawater can be estimated by collecting a bucket of flui and measure its
weight over volume ratio.
3.8.8 The Equation of State for Seawater
Density of seawater depends on temperature, salinity and pressure. Pressure effects
can be eliminated by converting the in-situ (on-site) temperature to that a water
parcel would have when being moved adiabatically (without heat exchange with
ambient fluid to a certain reference pressure level.
Salinity is the mass concentration of dissolved salts in the water column. Seawater
has typical salinities of 34–35 g/kg. Note that, in modern oceanography, salinity
does not carry a unit, for it is define and measured in terms of a dimensionless
conductivity ratio. Numerical values of this practical salinity, however, are close to
salt mass concentrations in g/kg.
To first-orde approximation, it is often sufficien to calculate seawater density
from a simple linear equation of state:
ρ(T, S) = ρ o [1 − α(T − T o ) + β(S − S o )]
(3.13)
where mean density ρ o refers to seawater density at reference temperature T o and
reference salinity S o . The parameter α (“alpha”) is the thermal expansion coefficien
that attains a value of 2.5×10
−4◦
C
−1
at a temperature of 20
◦
C. The salinity coeffi
cient β (“beta”) has values of 8 × 10
−4
(no units). Oceanographers frequently use a
quantity called σ t (“sigma-t”). This is just the true density minus 1000 kg/m
3
.
3.9 Gravity and the Buoyancy Force
3.9.1 Archimedes’ Principle
Gravity is the gravitational pull toward the centre of Earth that a body would feel in
the absence of a surrounding medium; that is, in a vacuum. Gravity acts downward
3 Basics of Geophysical Fluid Dynamics
3.8.7 Density
Density, symbolised by the Greek letter ρ (“rho”), is the ratio of mass M over volume V :
ρ =
M
V
(3.12)
Density has units of kilograms per cubic metres (kg/m
3
). Density of seawater
is in a range of 1025–1028 kg/m
3
. Density variations are generally small (< 0.5%)
compared with the mean value. Freshwater has densities around 1000 kg/m
3
. The
density of seawater can be estimated by collecting a bucket of flui and measure its
weight over volume ratio.
3.8.8 The Equation of State for Seawater
Density of seawater depends on temperature, salinity and pressure. Pressure effects
can be eliminated by converting the in-situ (on-site) temperature to that a water
parcel would have when being moved adiabatically (without heat exchange with
ambient fluid to a certain reference pressure level.
Salinity is the mass concentration of dissolved salts in the water column. Seawater
has typical salinities of 34–35 g/kg. Note that, in modern oceanography, salinity
does not carry a unit, for it is define and measured in terms of a dimensionless
conductivity ratio. Numerical values of this practical salinity, however, are close to
salt mass concentrations in g/kg.
To first-orde approximation, it is often sufficien to calculate seawater density
from a simple linear equation of state:
ρ(T, S) = ρ o [1 − α(T − T o ) + β(S − S o )]
(3.13)
where mean density ρ o refers to seawater density at reference temperature T o and
reference salinity S o . The parameter α (“alpha”) is the thermal expansion coefficien
that attains a value of 2.5×10
−4◦
C
−1
at a temperature of 20
◦
C. The salinity coeffi
cient β (“beta”) has values of 8 × 10
−4
(no units). Oceanographers frequently use a
quantity called σ t (“sigma-t”). This is just the true density minus 1000 kg/m
3
.
3.9 Gravity and the Buoyancy Force
3.9.1 Archimedes’ Principle
Gravity is the gravitational pull toward the centre of Earth that a body would feel in
the absence of a surrounding medium; that is, in a vacuum. Gravity acts downward