1 / 22

Importance of Rotation to Ocean Currents: Geostrophy

Importance of Rotation to Ocean Currents: Geostrophy. Lecture 11. OEAS-604. October 31, 2011. Outline: Review of Scaling Inertial Oscillations Geostrophic Balance Thermal Wind. Reynolds averaged X-momentum Equation:. Scaled form of X-momentum:.

lucas-craig
Download Presentation

Importance of Rotation to Ocean Currents: Geostrophy

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Importance of Rotation to Ocean Currents: Geostrophy Lecture 11 OEAS-604 October 31, 2011 • Outline: • Review of Scaling • Inertial Oscillations • Geostrophic Balance • Thermal Wind

  2. Reynolds averaged X-momentum Equation: Scaled form of X-momentum:

  3. How do you Scale Friction when flow can be either Laminar or Turbulent? Stress due to viscosity: Stress due to turbulence:

  4. Scaling Friction Turbulence is chaotic or unstable eddying motion in a fluid. Momentum Flux can be parameterized with Eddy Viscosity (Az) Where eddy viscosity is the product of a velocity scale (UT) times a length scale (LT).

  5. Density Stratification Impacts Effectiveness of Turbulent Mixing The restoring force of the buoyancy associated with density stratification limits the vertical length scale of turbulence (LT) and the turbulent velocities (UT) Takes more energy to lift fluid in a stratified environment.

  6. Scaling Friction Both the length scale and velocity scale of turbulence changes a lot for different environments. So unlike the viscosity of water which is constant (property of the fluid), the Eddy Viscosity changes considerably (property of flow) Eddy Viscosity can vary by many orders of magnitudes: Az ~ 10-5 to 10-2 m2/s

  7. Flow becomes turbulent because of “shear instabilities” Velocity Profile fast TIME slow In turbulent flow, instabilities grow and then collapse, resulting in irreversible mixing. Velocity shear: Gradient in velocity (u)

  8. When will turbulence develop? When instabilities in the flow driven by shear (velocity gradients) are greater than the stabilizing force of buoyancy. A measure of weather there will be turbulence or not is the gradient Richardson number: Stratification opposes instabilities Velocity gradient favors instabilities Turbulence likely: No active turbulence Ri < 0.25 Ri > 0.25

  9. Bottom Line: In a lot of flows in the ocean, particularly far from the boundaries, friction is not important. Pressure Gradient is almost always important

  10. What happens if neither friction nor pressure gradient is important? Governing equations (1) Ignore terms that are assumed unimportant (2) This results in two coupled, first order differential equations: Take derivative Plug into (1) rearrange Take derivative Plug into (2) rearrange

  11. This is motion in a circle with diameter = 2V/f and period T = 2pi/f The solution to this is: @ t=0, v=V; u=0 v @ t=pi/4, v=0; u=V where: u This is called an inertial current of inertial oscillation. Inertial currents are caused by rapid changes of wind at the sea surface. This initiates the motion, that then oscillates in a circle with a period of 2pi/f (inertial period).

  12. If there are no other forces acting on a water parcel other than the Coriolis force, once it is set in motion, it will perform endless circular motion with period T. v u Coriolis Parameter is a function of latitude so period of oscillation is maximum at equator and minimum at poles

  13. Because we are observing the currents of the ocean from a reference frame that is fixed on the rotating earth, we see the circular motions of the inertial oscillations. http://video.google.com/videosearch?client=safari&rls=en-us&q=coriolis%20derivation&oe=UTF-8&um=1&hl=en&ie=UTF-8&sa=N&tab=iv&start=0

  14. Previous Scaling Suggested That Acceleration Was Not Important in the Open Ocean. What gives? Inertial Oscillations result from processes that generally occur over short time scales, like short but intense winds. Over larger spatial scales acceleration is generally not important.

  15. For large scale open ocean flows, acceleration, friction and advection are generally small. This is called the “Geostrophic Balance” Pressure gradient is balanced by Coriolis.

  16. y-axis x-axis Consider a ball at the top of the hill. The ball starts to roll down hill under influence of gravity. This is just like a barotropic pressure gradient. However, the earth is rotating, so the ball is deflected to the right. Ball will no longer accelerate when the deflection by rotation is equal to the downhill force (pressure gradient)

  17. y-axis x-axis Mathematically this is written as:

  18. Geostrophic Flow in the Atmosphere

  19. The Gulf Stream Observed from Satellite Sea Surface Height

  20. Pressure Gradient Has Two Components Less dense water More dense water z y x x

  21. Viewed From Above More dense water Less dense water

  22. Barotropic Geostrophic Balance: Can there be vertical shear in the flow for barotropic geostrophic flow? Baroclinic Geostrophic Balance: Thermal Wind Relationship

More Related