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Stratification and Stability

Stratification and Stability. Lecture 2. OEAS-604. September 7, 2011. Outline: Review from Last Class Pressure and the Hydrostatic Balance CTDs Stability Mixing and Potential Energy T-S diagrams MATLAB. Key Points from Last Class:.

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Stratification and Stability

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  1. Stratification and Stability Lecture 2 OEAS-604 September 7, 2011 • Outline: • Review from Last Class • Pressure and the Hydrostatic Balance • CTDs • Stability • Mixing and Potential Energy • T-S diagrams • MATLAB

  2. Key Points from Last Class: • 1) Because of the unique molecular structure of water: • Water becomes less dense when it freezes • Water has unusually high boiling and melting points • Water has very high heat capacity, latent heat of fusion/vaporization • Water is a powerful solvent • Water conducts electricity • Water is slightly compressible 2) Directly measuring salinity is very difficult so oceanographers infer salinity from the conductivity of seawater. 3) Both temperature, salinity and pressure influence the density of seawater. 4) Like salinity, density is very difficult to measure directly, so we infer density from the equation of state ( funct [S,T,P] ). 5) Because of adiabatic effects, changes in pressure (i.e. depth) result in changes in temperature. 6) Adiabatic effects are accounted for using the density anomaly sigma_theta.

  3. Difference between In-situ and Potential Temperature In-situ Temperature Potential Temperature In-situ temperature appears unstable with colder water over warmer.

  4. Pressure and Depth in the Ocean Hydrostatic Pressure: Hydrostatic: Meaning water at rest. However, in many situations, even when water is not at rest, the effect of motion on the pressure can be neglected (this is called the hydrostatic approximation). Pressure is a force per unit area. So in SI units that is N/m2 or Pascals. Other common units include: pounds per square inch (psi); bars or millibars; or atmospheres. Standard atmospheric pressure at sea level: 1 atmosphere = 1.013 bars = 1013 mbars = 101.3 kPa = 15psi. Consider a column of water with uniform density (ρc): mass A z=0 acceleration Remember pressure (P) is a force per unit area, so: ρc h So at any height z: z=-h

  5. Hydrostatic Pressure (cont.): The pressure at any given depth is determined by the weight of the overlying water. This is impacted by the waters density. Consider the following 3 cases: 3) continually varying density 1) constant density: 2) 3 different densities z=0 A h1 ρ1 h ρc ρ h2 ρ2 ρ3 h3 z=-H Pressure at z = -H

  6. Oceanographic Tools A CTD — an acronym for Conductivity, Temperature, and Depth — is the primary tool for determining essential physical properties of sea water. It gives scientists a precise and comprehensive charting of the distribution and variation of water temperature, salinity, and density.

  7. Platforms for CTDs Moorings Floats Gliders

  8. Expendable Bathythermograph (XBT)

  9. http://floats.pmel.noaa.gov/ Argo is a global array of 3,000 free-drifting profiling floats that measures the temperature and salinity of the upper 2000 m of the ocean. This allows, for the first time, continuous monitoring of the temperature, salinity, and velocity of the upper ocean, with all data being relayed and made publicly available within hours after collection.

  10. Static Stability The static stability of the water column is controlled by the vertical distribution of density. Unstable: density distribution causes vertical motion Neutral: density has no influence on vertical motion Stable: density resists vertical motion ρ3 ρ1 ρ2 ρ2 ρ2 ρ1 ρ3

  11. Stability (E) Moving a parcel of water out of its equilibrium position requires work. Static stability might be considered as the “unwillingness of water to be moved vertically” The stronger the density gradient, and the further the excursion, the more work is required Stability is defined in terms of the rate of change of density with depth and is a measure of the amount of work required to move a particle vertically in the water column However, water parcel will expand a little less on the way up (and contract a little less on the way down) due to the compressibility of seawater, and the work done will cause the temperature to decrease as it moves upwards (or increase as it moves downwards)

  12. Brunt Vaisala Frequency (N) Another way of expressing stability is with the Brunt-Väisälä frequency (sometimes called buoyancy frequency) This is the oscillation of a water particle about its equilibrium depth. Units of frequency A particle of water forced upward will be heavier than the surrounding water and buoyant forces will push it downward and a particle forced downward will be lighter and buoyant forces will push it upward.

  13. Effects of Compressibility on Stability

  14. Potential Energy height mass Gravity (9.8 m/s2) z = 15 z = 0

  15. Which profile has the lowest potential energy

  16. Which profile has the lowest potential energy highest lower lowest • Since density is simply the mass per volume, the potential energy per volume can be expressed in terms of density. • While all three profiles have the same average density, the profile on the left has the greatest potential energy and the profile on the right has the lowest potential energy. • This can be calculated by vertically integrating the above equation or simply considering the vertical position of the center of mass. • The center of mass of the profile on the left is the highest and the center of mass of the profile on the left is the lowest.

  17. Vertical Mixing: Homogenizing the water column (increasing the potential energy) requires energy/work. Just like lifting a heavy box, vertical mixing raises the center of mass of a stratified water column. The heavier the box or the greater the distance it is lifted, the more energy is required. Mixing fluid across density surfaces (isopycnal surfaces) is called diapycnal mixing. Mixing fluid along lines of constant density (isopycnal mixing) requires little energy (100 million times less than diapycnal mixing)

  18. Temperature-Salinity Diagrams Contours of sigma-theta Helps normalize for both pressure effects and adiabatic effects

  19. No Class Next Monday Next Class: Wednesday, September 14th Topic: The Stratified Ocean and Global Distribution of T-S Reading: Knauss, Chapter 2 Before Next Class please download and install Matlab on you computer. If you have a computer, please bring it to class next Wednesday!!! Go To: http://www.mathworks.com/ You will need the following user name and password: Username = ckimbro@odu.edu Password = angel1234

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