Frontal Dynamics of Powder Snow Avalanches Cian Carroll, Barbara Turnbull and Michel Louge EGU General Assembly, Vienna, April 27, 2012 Sponsored by ACS Petroleum Research Fund Thanks to Christophe Ancey, Perry Bartelt, Othmar Buser, Jim McElwaine, Florence & Mohamed Naiim, Matthew Scase, Betty Sovilla Sovilla, et al, JGR (2010)

Field data rapid eruption Issler (2002) Sovilla et al (2006) time (s) height (m) time (s) static pressure (Pa) McElwaine & Turnbull JGR (2005) depression Sovilla, et al JGR (2006) slope width distance (m)

Consider avalanche head rapid eruption Issler (2002) Sovilla et al (2006) source avalanche rest frame avalanche head

Principal assumptions in the cloud source avalanche head Negligible basal shear stress Negligible air entrainment Inviscid Uniform mixture density

Rankine half-body potential flow Swelling Rankine, Proc. Roy. Soc. (1864) Slowing U’ U

Experiments and simulations on eruption currents

Static pressure in the cloud pressure p, air density , cloud density  ’ stagnation-source distance b’ fluidized depth h’ prediction data: McElwaine and Turnbull JGR (2005)

Porous snow pack interface pore pressure p Pore pressure gradients defeat cohesion rapid eruption Issler (2002) time (s) height (m)

Porous snow pack snowpack density  c, friction  e interface pore pressure p Pore pressure gradients defeat cohesion     2  yy xx   s  11 22 Mohr-Coulomb failure

Frontal Dynamics avalanche head

Mass balance

snowpack density  c, friction  e, inclination , entrained fraction of fluidized depth h’

Stability snowpack density  c, friction  e, inclination , entrained fraction of fluidized depth h’ Snowpack eruption feeds the cloud:Cloud pressure fluidizes snowpack:

Stability diagram unstable Ri stable  unstable stable Ri unstable  stable cloud height density entrained depth

Frontal Dynamics accelerationmomentumadded massweight + buoyancy

Acceleration gravitychannel width W distance (m)

Other predictions

Height vs distance cloud height Vallet, et al, CRST (2004)

Froude number vs distance cloud Froude number Vallet, et al, CRST (2004) Sovilla, Burlando & Bartelt JGR (2006)

Volume growth volume growth Measurements: Vallet, et al, CRST (2004) air entrainment in the tail total volume

Impact pressure ≠ static pressure Cloud arrest Impact increasing height An impact pressure decreasing with height does not necessarily imply density stratification.

Air entrainment

Air entrainment into the head source radius r c Ancey, JGR (2004)

Conclusions Our model of eruption currents is closed without material input from surface erosion or interface air entrainment. Porous snowpacks synergistically eject massive amounts of snow into the head of powder clouds. Suspension density swells the cloud and weakens its internal velocity field. Mass balance stability sets cloud growth. Changes in channel width affect acceleration. Experiments should record cloud density and pore pressure.

Thank you Cian Carroll Barbara Turnbull Betty Sovilla