Understanding Water Movement in Lakes and Streams

1. Lecture Goals • To present the external and internal physical processes that determine how water moves in lakes and streams. • To discuss some of the important consequences of water movement for other aspects of physical habitat in lakes and streams, and for species that inhabit these systems.

2. Types of flow • Laminar: layered and orderly • Turbulent: disordered

3. Types of flow

4. Types of flow

5. Types of flow

6. Laminar → Turbulent Transition • The greater the difference in fluid velocity, the greater the probability of turbulence. • The greater the differences in density, the greater the difference in velocity needed to get turbulence.

7. Laminar → Turbulent Transition • The Richardson Number (Ri) is used to predict when turbulence will occur at boundary layer in stratified water. • Ri = f(difference in density, velocity) • Ri > 0.25 = Stable flow • Ri <0.25 = Turbulent flow

8. Water Movement in Lakes • At surface • At metalimnion

9. Types of Water Movement in Lakes • Langmuir circulation • Metalimnetic tilting and entrainment • Seiches • Internal progressive waves

10. Langmuir Circulation

11. Langmuir Streaks Quake Lake, MT

12. Just because you saw it, doesn’t make it real… Langmuir Streaks Bigfoot

13. Metalimnetic Tilting and Entrainment (or Erosion)

14. Seiches

15. Seiches

16. Seiches • Lake Erie water displacement • 11/14/2003

17. Internal Progressive Waves

18. Water Movement Streams and Rivers • Discharge (Q) → How much water is moving at a particular time? • The Hydrograph → How does Q change over time? • Floods → Extreme Q-events!

19. Discharge • Q = WDU • Q = discharge, m3 / sec • W = width, m • D = depth, m • U = velocity, m / sec

20. The Hydrograph

21. USGS Real-Time Water Data http://nwis.waterdata.usgs.gov/mt/nwis/rt

23. Floods – Extreme Discharge Events

24. Floods – Extreme Discharge Events • Flood frequency (e.g., 50-yr, 100-yr) • What does it really mean?

25. Floods are RANDOM • Probability of occurrence does not depend on the past.

26. Recurrence Interval – DESCRIPTIVE • Time (e.g., years) between past occurrences of a random event. • T = (n + 1) / m • n = years of record • m = rank magnitude of flood, where 1 is highest, 2 is next highest, etc.

27. Recurrence Interval

28. Recurrence Interval Year Discharge rank (m) recurrence interval (n+1)/m 1976 57,406 10 1.1 1972 75,806 9 1.2 1970 81,806 8 1.4 1977 95,106 7 1.6 1974 99,706 6 1.83 1973 112,006 5 2.2 1979 112,006 4 2.8 1975 114,006 3 3.7 1971 123,006 2 5.5 1978 147,006 1 11

29. Flood Forecasting • Relies on the mathematics of probability • Flood probability (P) = Likelihood than an annual maximum flow will equal or exceed the value of a flood event of a given recurrence interval. • P = 1 / Recurrence interval (T)

30. Recurrence Interval Year Discharge rank (m) recurrence interval (n+1)/m 1976 57,406 10 1.1 1972 75,806 9 1.2 1970 81,806 8 1.4 1977 95,106 7 1.6 1974 99,706 6 1.83 1973 112,006 5 2.2 1979 112,006 4 2.8 1975 114,006 3 3.7 1971 123,006 2 5.5 1978 147,006 1 11 P = 1 / T = 0.55

31. 100-yr Flood • Discharge has exceeded that value on average once every 100 years in the past. • What is the minimum number of years of record needed to identify a 100-yr flood? • What is the probability of such a flood occurring next year? • If it occurs next year, how about the year after that? • What is the probability of a 100-yr flood occurring in the next 100 years?

32. Water Movement in Streams and Rivers Network Channel Reach

33. Water Movement in Streams and Rivers Network

34. Network-scale controls on water movement • Low-order: high gradient, low discharge, often geologically “constrained”.

35. Constrained

36. Network-scale controls on water movement • Low-order: high gradient, low discharge, often geologically “constrained”. • Mid-order: intermediate gradient, intermediate discharge, “beads on a string”. • High-order: low gradient, high discharge, often “unconstrained”.

37. Unconstrained

38. Network-scale controls on water movement • Low-order: high gradient, low discharge, often geologically “constrained”. • Mid-order: intermediate gradient, intermediate discharge, “beads on a string”. • High-order: low gradient, high discharge, often “unconstrained”.

39. Beads on a String

40. Channelized

41. How does mean velocity change moving downstream?

42. Water Movement in Streams and Rivers Network Channel

43. Channel-scale variation in water velocity and direction Erosion Entrainment Deposition

44. Variation in substrate size Erosion Entrainment Deposition

45. Variation in velocity  Variation in substrate size = Habitat diversity Longitudinal Lateral

46. Water Movement in Streams and Rivers Network Channel Reach

47. Water  Substrate = Reach Types Riffle Pool

48. Deep Depth Shallow Shallow Low Moderate High Velocity Low Moderate Gradient Moderate Circulating Flow Turbulent Laminar Peb/Sand Substrate Peb/Grav Grav/Cob Water  Substrate = Reach Types Cascade Riffle Run Pool Shallow Very High High Very Turbulent Cob/Boulder/Bedrock

49. Water  Substrate = Reach Types Cascade Riffle Run Pool

50. Deep Depth Shallow Shallow Low Moderate High Velocity Low Moderate Gradient Moderate Circulating Flow Turbulent Laminar Peb/Sand Substrate Peb/Grav Grav/Cob Water  Substrate = Reach Types Cascade Riffle Run Pool Shallow Very High High Very Turbulent Cob/Boulder/Bedrock