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A Mathematical Nature Walk
This chapter is in the book A Mathematical Nature Walk
Q.84:What shapes are river meanders?I love looking at river meanders when I’m in a window seat on a plane. I’venever been very successful at taking good photographs of them for at leastthree reasons: (i) I’m not the world’s best photographer, (ii) even if I’m seatedby a window, I’m often over a wing, and (iii) the amount of air between meand the ground causes much light to be scattered, so the scattered blue lightreduces the contrast between the river and its surroundings. And if I’mwalking in the vicinity of meanders and oxbow lakes, my perspective is verylimited because I’m not one hundred feet tall. Regardless of my complaintsabout this, the phenomenon is a fascinating one, so let’s start with some ob-servational details, obtained from a study of more than fifty rivers by LunaLeopold and coworkers. They are of interest in connection with the apparentregular ‘‘sinuosity’’ of rivers the world over. From their study of more than 50rivers, the following statements can be made:(i) No river, regardless of size, runs straight for more than 10 times itswidth.(ii) The radius of a bend is nearly always 2–3 times the width of the riverat that point.(iii) The wavelength (distance between analogous points of analogousbends) is 7–10 times the (average) width.The conclusion is that despite considerable, even dramatic, variations insize and in bed conditions, rivers are strikingly similar in their characteristics.Furthermore, it transpires that meanders are not ‘‘accidents’’ of nature, butaccording to one theory, they define the form in which a river does the leastwork in turning (as in proceeding from a pointAuphill to a pointBdown-hill), which in turn defines the most probable form a river can take.The namemeanderis from a winding stream in Turkey that was in ancientGreek times known as the Maiandros (today it is known as the Menderes). It

Q.84:What shapes are river meanders?I love looking at river meanders when I’m in a window seat on a plane. I’venever been very successful at taking good photographs of them for at leastthree reasons: (i) I’m not the world’s best photographer, (ii) even if I’m seatedby a window, I’m often over a wing, and (iii) the amount of air between meand the ground causes much light to be scattered, so the scattered blue lightreduces the contrast between the river and its surroundings. And if I’mwalking in the vicinity of meanders and oxbow lakes, my perspective is verylimited because I’m not one hundred feet tall. Regardless of my complaintsabout this, the phenomenon is a fascinating one, so let’s start with some ob-servational details, obtained from a study of more than fifty rivers by LunaLeopold and coworkers. They are of interest in connection with the apparentregular ‘‘sinuosity’’ of rivers the world over. From their study of more than 50rivers, the following statements can be made:(i) No river, regardless of size, runs straight for more than 10 times itswidth.(ii) The radius of a bend is nearly always 2–3 times the width of the riverat that point.(iii) The wavelength (distance between analogous points of analogousbends) is 7–10 times the (average) width.The conclusion is that despite considerable, even dramatic, variations insize and in bed conditions, rivers are strikingly similar in their characteristics.Furthermore, it transpires that meanders are not ‘‘accidents’’ of nature, butaccording to one theory, they define the form in which a river does the leastwork in turning (as in proceeding from a pointAuphill to a pointBdown-hill), which in turn defines the most probable form a river can take.The namemeanderis from a winding stream in Turkey that was in ancientGreek times known as the Maiandros (today it is known as the Menderes). It

Chapters in this book

  1. Frontmatter i
  2. Contents ix
  3. Preface xv
  4. Acknowledgments xix
  5. Introduction 1
  6. At the beginning . . . 11
  7. In the “playground” 13
  8. In the garden 24
  9. In the neighborhood 43
  10. In the shadows 58
  11. In the sky 64
  12. In the nest 122
  13. In (or on) the water 137
  14. In the forest 168
  15. In the national park 183
  16. In the night sky 194
  17. At the end... 217
  18. Appendix 1: A very short glossary of mathematical terms and functions 231
  19. Appendix 2: Answers to questions 1–15 234
  20. Appendix 3: Newton’s law of cooling 238
  21. Appendix 4: More mathematical patterns in nature 240
  22. References 243
  23. Index 247
  24. About the author 249
Readers are also interested in:
https://doi.org/10.1515/9781400832903-013

Chapters in this book

  1. Frontmatter i
  2. Contents ix
  3. Preface xv
  4. Acknowledgments xix
  5. Introduction 1
  6. At the beginning . . . 11
  7. In the “playground” 13
  8. In the garden 24
  9. In the neighborhood 43
  10. In the shadows 58
  11. In the sky 64
  12. In the nest 122
  13. In (or on) the water 137
  14. In the forest 168
  15. In the national park 183
  16. In the night sky 194
  17. At the end... 217
  18. Appendix 1: A very short glossary of mathematical terms and functions 231
  19. Appendix 2: Answers to questions 1–15 234
  20. Appendix 3: Newton’s law of cooling 238
  21. Appendix 4: More mathematical patterns in nature 240
  22. References 243
  23. Index 247
  24. About the author 249
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