﻿200 
  Bucher 
  — 
  Origin 
  of 
  Ripples, 
  and 
  

  

  mum 
  of 
  resistance 
  along 
  the 
  contact 
  of 
  fluid 
  and 
  sedi- 
  

   ment, 
  04 
  It 
  is 
  held 
  that 
  any 
  other 
  form 
  of 
  contact 
  

   represents 
  an 
  unstable 
  condition 
  which 
  is 
  disturbed 
  by 
  the 
  

   slightest 
  cause. 
  The 
  fortuitous 
  changes 
  following 
  such 
  

   a 
  first 
  accidental 
  disturbance 
  are 
  thought 
  to 
  lead 
  finally 
  

   to 
  the 
  establishment 
  of 
  the 
  optimum 
  surface 
  form, 
  owing 
  

   to 
  the 
  fact 
  that 
  any 
  change 
  favorable 
  to 
  its 
  completion 
  is 
  

   liable 
  to 
  be 
  permanent 
  while 
  any 
  others 
  are 
  followed 
  by 
  

   further 
  rearrangements 
  until 
  all 
  parts 
  of 
  the 
  surface 
  

   have 
  reached 
  the 
  equilibrium. 
  This 
  interpretation 
  calls 
  

   for 
  an 
  analytical 
  study 
  of 
  great 
  complexity 
  which 
  I 
  am 
  

   unfortunately 
  unable 
  even 
  to 
  attempt. 
  It 
  also 
  calls, 
  

   however, 
  for 
  the 
  accumulation 
  of 
  a 
  store 
  of 
  reliable 
  

   quantitative 
  data 
  to 
  allow 
  of 
  the 
  application 
  of 
  a 
  general 
  

   analytical 
  solution 
  of 
  the 
  problem 
  to 
  specific 
  cases. 
  

  

  This 
  problem 
  in 
  its 
  most 
  general 
  form 
  may 
  be 
  formu- 
  

   lated 
  as 
  follows 
  : 
  What 
  is, 
  under 
  certain 
  favorable 
  condi- 
  

   tions, 
  the 
  shape 
  of 
  the 
  surface 
  of 
  contact 
  offering 
  a 
  

   minimum 
  of 
  friction 
  between 
  a 
  fluid 
  and 
  an 
  unconsoli- 
  

   dated 
  sediment? 
  

  

  Under 
  certain 
  conditions 
  outlined 
  in 
  a 
  previous 
  chap- 
  

   ter 
  this 
  optimum 
  surface 
  is 
  that 
  of 
  current-ripples 
  (and 
  

   oscillation-ripples). 
  It 
  is 
  characterized 
  by 
  the 
  vortical 
  

   layer 
  intercalated 
  between 
  fluid 
  (water 
  or 
  air) 
  and 
  sedi- 
  

   ment, 
  It 
  should 
  be 
  emphasized, 
  however, 
  that 
  the 
  vor- 
  

   tices 
  are 
  not 
  the 
  essential 
  element 
  in 
  the 
  formation 
  of 
  

   current 
  ripples. 
  They 
  are 
  suction 
  eddies, 
  such 
  as 
  develop 
  

   in 
  the 
  lee 
  of 
  any 
  obstacle 
  in 
  the 
  way 
  of 
  a 
  moving 
  fluid. 
  

   The 
  shifting 
  and 
  piling 
  up 
  of 
  grains 
  into 
  larger 
  obstacles 
  

   with 
  larger 
  eddies 
  in 
  their 
  lee 
  and 
  placed 
  at 
  regular 
  inter- 
  

   vals 
  is 
  directed 
  from 
  above 
  by 
  the 
  fluid 
  outside 
  the 
  zone 
  

   of 
  eddies. 
  The 
  vortices, 
  for 
  our 
  purpose, 
  may 
  be 
  con- 
  

   sidered 
  as 
  part 
  of 
  the 
  sediment, 
  not 
  of 
  the 
  fluid 
  above. 
  

   The 
  surface 
  of 
  equilibrium 
  for 
  the 
  free 
  fluid 
  above 
  the 
  

   ripples 
  plus 
  vortices 
  is 
  sinuous 
  in 
  profile. 
  A 
  similar 
  sur- 
  

   face 
  we 
  find 
  again 
  in 
  the 
  sand-waves, 
  established 
  directly 
  

   on 
  the 
  contact 
  of 
  fluid 
  and 
  sediment, 
  without 
  the 
  inter- 
  

   calation 
  of 
  vortices. 
  The 
  two 
  conditions 
  of 
  contact, 
  while 
  

  

  64 
  Snow 
  under 
  the 
  action 
  of 
  wind 
  shows 
  surface 
  forms 
  similar 
  to 
  those 
  

   of 
  sand. 
  The 
  "Sastrugi" 
  of 
  arctic 
  and 
  antarctic 
  regions 
  are 
  as 
  serious 
  

   obstacles 
  to 
  explorers 
  {e.g. 
  Nansen, 
  Nordenskjoeld) 
  as 
  the 
  sand 
  dunes 
  of 
  

   the 
  deserts, 
  That 
  the 
  phenomena 
  of 
  rippling 
  and 
  dune 
  formation 
  of 
  snow 
  

   and 
  snii'l 
  are 
  strictly 
  analogous," 
  was 
  emphasized 
  by 
  Tschirwinsky, 
  P. 
  M. 
  

   Zs. 
  Gletecherknnde, 
  vol. 
  2, 
  p. 
  103-112, 
  1907). 
  For 
  numerous 
  quantitative 
  

   data 
  concerning 
  snow 
  ripples 
  and 
  dunes 
  see 
  Cornish, 
  Geoffr. 
  Journal, 
  vols. 
  

   17, 
  18, 
  20. 
  ' 
  

  

  