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Home , Potential density, Specific volume, Volume (thermodynamics)

Atmosphere and ocean differences Lesson 2 Atmosphere & ocean properties:  Fluids are physically different  Water is incompressible (atm is assumed equations of state and incompressible for many applications)  Ocean has no analogy for “latent ” source that atm has Review: differences b/t ocean &  Oceans are laterally bounded (by land)  Atm circulation largely forced by convection – heating atmosphere, equations of state from below for atmosphere & ocean  Ocean circulation forced by convection – heat loss from above – and by wind (no analogy in atm)

Density

Density ( ρ) is defined as the per unit : The equation of state - The functional relationship between the absolute , and for a ρ = mass Volume homogenous substance.

With units: g or kg General form: cm 3 m3 . Density is related to the specific volume, α, which is the . f (p,α,T ) = 0 volume per unit mass α = 1 ρ

3 m3 With units: cm or g kg

1 Ideal law – Moist law atmosphere The equation of state – For relatively small pressure values (on the order of (1 atm)), there exists an analytic relationship for the Due to Dalton’s law of partial , we can express an ideal equation of state: gas law for the molecular constituents of the atmosphere p = ρRT = ρ * R * p Rd T R = Where m And m is the molecular mass with units grams/ = × 2 Where Rd .2 8705 10 is the ideal for dry air kg ⋅o . Joules . And R* = .8 3143 ×10 3 is the ideal gas constant. o Kelvin ⋅ kg ⋅ mole T* is the virtual temperature and is defined as the temperature a parcel of dry air would have if its pressure and density were those of the parcel of This equation is only valid under the conditions that: moist air. If W is the mixing ratio in units of gm/kg then 1. Molecules exhibit no potential forces between each other. They only W interact through elastics collisions like billiard balls. T * ≈ T + 2. Molecules occupy no volume. They are all treated as “point” 6

Equation of state for the ocean General properties of ocean

Clearly, the requirements of the break down in Seawater is nearly incompressible (more than the ocean and therefore we are stuck with the general form of the equation of state: fresh water or air), thus seawater density depends (mostly) on & temperature f (p,α,T ) = 0 More dense Less dense In practice, we are interested in examining how the density . (specific volume) of the ocean varies with Pressure, Temperature and Salinity. Cold water Warm water

Density increases with a(n): Salty water Fresh(er) water - increase in Salinity and Pressure Density units in kg m -3 - decrease in Temperature

2 3.

(from Pinet, 1998)

What are factors that control the growth and structure of the Thermocline?

4 (NORTHERN HEMISPHERE)

(from Pinet, 1998)

SALINITY

General definition - The mass of salt per unit mass of seawater - measured in parts per thousand– It is very difficult to actually find the amount of salt or the amount of water at a given Temperature and pressure – Evaporation alone is not sufficient.

Practical Salinity : Salinity measured in accordance with the Practical Salinity Scale (conductivity scale as compared to a standard KCL solution) and has Practical Salinity units (PSUs).

4 (NORTHERN HEMISPHERE)

(from Pinet, 1998)

3 Major Constituents

high temperate subtropical

The concentrations of these 7. major constituents are conservative. They are (from Pinet, 1998) unaffected by most biological and chemical processes. What is the “halocline”? What factors control the growth and structure of the halocline?

11. (from Pinet, 1998)

(from the Navy Coastal Ocean Model)

Why is the Atlantic saltier (at the surface) than the other global oceans?

4 Effect of pressure on density

In-situ versus laboratory θθθ = T − ∫ Γdp Theoretical analysis of the ocean is important but is of little use o ∂T g − C without the experimental results to accompany it. Γ = = ≈ 1− 2 ×10 4 ∂ p Cp db There are many ways of obtaining the properties of Data off C ≈ 4 ×10 4 J /( kg oC) the ocean. These can broken into two main categories: Antarctica p

In-situ – measuring the quantities of interest at depth in the ocean. Γ is the adiabatic Often, the use of a CTD can be used for these type measurements. lapse rate Laboratory – Measuring the properties of interest by taking a sample

. at depth and bringing it to the surface. One must then account for variations in pressure and, to a lesser degree, temperature, in ~0.1º change at 1000 m transporting the fluid parcel. Many chemical properties of sea-water potential in-situ require this type of measurement. –

~0.3º change at 3000 m One must be careful though since neglect of pressure may mislead the observer into indications of an instability when actually does not exist. Γ can also be obtained from Unesco North Atlantic Deep Water (with higher potential density) over Technical Papers in Marine Science # 44 by Antarctic Bottom Water (with lesser potential density) Fofonoff and Millard, Unesco 1983

Ocean density representation Ocean density representation Given that we know density depends on salinity, temperature and pressure, we can approximate density as a linear function of its state variables using a Density is actually a non-linear function of T,S and p so we must use different techniques to get an accurate representation of density over Taylor series. If we expand about reference values, To, So and po we obtain a wide range of state variable values ρ( ) ≈ ρ ( −α ( − )+ β ( − ) + ( − )) T, S, p o 1 T T To S S So K p po The international equation of state for seawater is a widely accepted Where empirical technique to obtain accurate values of density to order 10 -5. ∂ρ α = − 1 - coefficient T ρ ∂ . T . The international equation of state for seawater is not static (fixed), ∂ρ and note that the Intergovernmental Oceanographic Commission has β = 1 S - Haline contraction coefficient approved a modification, TEOS-10 http://www.teos-10.org/ ρ ∂S 1 ∂ρ K = = An amazingly detailed (179 pg) brief is hosted by the Australian government ρ ∂ - Isothermal coefficient p (Commonwealth Scientific and Industrial Research Organisation) at: http://www.marine.csiro.au/~jackett/TEOS-10/TEOS-10_Manual_08Jan2010.pdf The above representation is only useful locally (with little change in the domain or parameters)

5 International equation of state International equation of state for seawater for seawater The international equation of state for seawater calculates density by finding the secant bulk modulus, K, which is the slope of a segment on Solving for density in the previous equation we obtain a graph of density versus fractional rate of change of volume. α ρ Its value is K = o p = p ρ ( ) α −α ρ − ρ o S,T, po o o ρ()S,T, p = p 1− K()S,T, p

p . . K and ρ =0 are then empirically fit to different values of salinity, α ρ ο K = o p = p ρ α −α ρ − ρ temperature and pressure. The accepted expansion of K and ο are . . o o

α − α α −α p = ,0 o = 0 o o α α o o

International equation of state Representing the density of for seawater seawater K(S,T, p) = There are other more recent techniques for finding the density of ρ( ) = 19652 21. S,T 0, seawater. −2 +148 .4206 T − .2 327105 T 2 999 .842594 + .6 793952 ×10 T − − + .1 360477 ×10 2 T 3 − .5 155288 ×10 5 T 4 − .9 095290 ×10 −3T 2 + .1 001685 ×10 −4 T 3 Some recent approaches are by McDougall et al (2002) or Feistel −3 + .3 239908 p + .1 43713 ×10 Tp − − (2003) − .1 120083 ×10 6 T 4 + .6 536332 ×10 9 T 5 + .1 16092 ×10 −4 T 2 p − .5 77905 ×10 −7 T 3 p + × −1 − × −3 + .8 50935 ×10 −5 p 2 − .6 12293 ×10 −6 Tp 2 .8 24493 10 S .4 0899 10 TS McDougall T.J., Jackett D. R., Wright D. G., Feistel R., 2002, Accurate −8 2 2 −5 2 −7 3 . + .5 2787 ×10 T p + .7 6438 ×10 T S − .8 2467 ×10 T S . and computationally efficient formulae for and + − − − density. J. Atmos. Ocean. Tech., 20 , 730-741 54 .6746 S .0 603459 TS + .5 3875 ×10 9 T 4 S − .5 72466 ×10 3 S 2/3 + × −2 2 − × −5 3 .1 09987 10 T S .6 1670 10 T S −4 2/3 −6 2 2/3 − − + .1 0227 ×10 TS − .1 6546 ×10 T S + .7 944 ×10 2 S 2/3 + .1 6483 ×10 2 TS /3 2 Feistel R., 2003. A new extended thermodynamic potential of −4 2 − .5 3009 ×10 −4 T 2 S /3 2 + .2 2838 ×10 −3 pS + 4.8314 ×10 S seawater. Prog. , 36 , 249-347. − .1 0981 ×10 −5 TpS − .1 6078 ×10 −6 T 2 pS + .1 91075 ×10 −4 pS 2/3 − .9 9348 ×10 −7 p 2 S + .2 0816 ×10 −8 Tp 2 S + .9 1697 ×10 −10 T 2 p 2 S

6 Tables

A good java program that allows use to find the thermodynamic properties of the ocean is found . . .

here

.

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