1 / 60

Lecture 10

Lecture 10. Static Stability. General Concept. An equilibrium state can be stable or unstable Stable equilibrium: A displacement induces a restoring force i.e., system tends to move back to its original state

knut
Download Presentation

Lecture 10

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. Lecture 10 Static Stability

  2. General Concept • An equilibrium state can be stable or unstable • Stable equilibrium: A displacement induces a restoring force • i.e., system tends to move back to its original state • Unstable equilibrium: A displacement induces a force that tends to drive the system even further away from its original state

  3. A More Realistic Scenario Equilibrium

  4. Small Displacement

  5. Small Displacement

  6. Small Displacement

  7. Small Displacement

  8. Small Displacement

  9. Small Displacement

  10. Small Displacement

  11. Small Displacement

  12. Small Displacement

  13. Small Displacement

  14. Small Displacement Stable.

  15. Large Displacement

  16. Large Displacement

  17. Large Displacement

  18. Large Displacement

  19. Large Displacement

  20. Large Displacement Unstable.

  21. Idea of Previous Slides • There may be a critical displacement magnitude • displacement < critical  stable • displacement > critical unstable • (More about this shortly)

  22. Atmospheric Stability Unsaturated Air

  23. Consider a vertical parcel displacement, z • Assume displacement is (dry) adiabatic • Change in parcel temperature = -d z • Denote lapse rate of environment by 

  24. T=T0 - dz T = T0 - z Temp of displaced parcel  temp of environment z T = T0 T = T0 Environment Parcel

  25. Two Cases • Parcel temp. > environment temp.  parcel less dense than environment  parcel is buoyant • Parcel temp. < environment temp.  parcel denser than environment  parcel is negatively buoyant

  26. Lapse Rates • Tparcel = T0 - dz • Tenv = T0 - z • Tparcel > Tenv if T0 - dz > T0 - z   > d • Tparcel < Tenv if T0 - dz < T0 - z   < d

  27. Stability •  > d  resultant force is positive  parcel acceleration is upward (away from original position)  equilibrium is unstable •  < d  resultant force is negative  parcel acceleration is downward (toward original position)  equilibrium is stable

  28. Graphical Depiction Temp of rising parcel z Stable lapse rate Unstable lapse rate Temperature

  29. Saturated Air • Recall: Vertically displaced parcel cools/warms at smaller rate • Call this the moist-adiabatic rate, m • Previous analysis same with d replaced by m • Equilibrium stable if  < m • Equilibrium unstable if  > m

  30. General Result • Suppose we don’t know whether a layer of the atmosphere is saturated or not •  > d   > m  equilibrium is unstable, regardless • Equilibrium is absolutely unstable •  < m   < d  equilibrium is stable, regardless • Equilibriumis absolutely stable

  31. Continued • Suppose m <  < d • Layer is stable if unsaturated, but unstable if saturated • Equilibrium is conditionallyunstable

  32. Absolutely stable Conditionally unstable Absolutely unstable  d m

  33. Application • If a layer is unstable and clouds form, they will likely be cumuliform • If a layer is stable and clouds form, they will likely be stratiform

  34. Example: Mid-Level Clouds • Suppose that clouds form in the middle troposphere • Unstable  altocumulus • Stable  altostratus

  35. Altocumulus

  36. Altostratus

  37. Deep Convection • Previous discussion not sufficient to explain thunderstorm development • Thunderstorms start in lower atmosphere, but extend high into the troposphere

  38. Physics Review: Energy Object at height h h

  39. Physics Review: Energy Remove support: Object falls h

  40. Physics Review: Energy Let z(t) = height a time t z(t)

  41. It Can Be Shown … potential energy kinetic energy (v = speed) As object falls, potential energy is converted to kinetic energy.

  42. Available Potential Energy • Object may have potential energy, but it may not be dynamically possible to release it

  43. Technically, PE = mgh, but lower energy state is inaccessible. The energy is unavailable. h

  44. Energy Barriers To get from a to b, energy must be supplied to surmount the barrier. Energy needed: mghb hb a h b

  45. Energy Barriers Now, ball can roll down hill. a h b

  46. Energy Barriers Amount of PE converted to KE: mg(h + hb) Net release of energy: mg(h + hb) – mghb = mgh hb a h b

  47. CAPE, CIN • CAPE: Convective Available Potential Energy • (Positive area) • CIN: Convective Inhibition • (Negative area at bottom of sounding)

  48. Sounding Dry adiabat Saturated adiabat Positive area Negative area LCL

  49. CAPE, CIN • CIN is the energy barrier • CAPE is the energy that is potentially available if the energy barrier can be surmounted

More Related