Powder Snow Avalanches

Transcription

1 Powder Snow Avalanches Jim McElwaine Department of Earth Sciences Durham University

2 Acknowledgments Betty Sovilla Barbara Turnbull Kouichi Nishimura Christophe Ancey Dieter Issler Takahiro Ogura Eckart Meiburg

3 Plan of Talk Introduction to Avalanches Transition Experiments Direct Numerical Simulations Field Obervations Dynamic Models

4 Powder Avalanche on K2 Pierre Beghin

5 Head of Powder Snow Avalanche Cemagref

6 Slab Avalanche Fracture Line

7 Skier in Slab Avalanche Debris Cemagref

8 Patreksfjörður 1983, a Slush Flow Killed 3 People

9 Destroyed House at Saint Colomban Les Villars

10 Test Chute in Davos film

11 Destroyed Buildings at La Morte Cemagref

12 Damage by a flood wave at Súgandafjörður

13 CO 2 Avalanche on Mars from HiRise What is the connection between terrestrial and Martian avalanches? How must models be adapted for Mars? How important are avalanches in the geomorphology of Mars?

14 Current Avalanche Research Huge variety: speeds km/h densities 5 5 kg/m 3 masses kg Three dimensional terrain and structure Snow properties are complicated and ill-defined Unpredictable, destructive, unreproducible Current theories are phenomenological Genesis of powder snow avalanches not understood

15 Aim Understand formation of Suspension Currents Use steep slopes to give a low Richardson number for large density difference Transition to suspension Limited entrainment Steady flows Understand air interaction Comparison of field observations with experiments

16 Similarity Criteria Experiment Materials Re p Ri St ρ ρ a Re Powder snow avalanches Snow-air Ancey (24) sawdust water Bozhinskiy (1998) aluminium air Beghin (1981) Brine-water/ Beghin (1983) Sand-water Beghin (1983) suspension Nishimura (1998) Ping-pong balls McElwaine (21) air Hampton (1972) Kaolinite and <.5.1 water slurry Hermann (1987) Polystyrene powder water Hopfinger (1977) Brine Tochon-Danguy (1974) water Present Study Snow-air Present Study Polystyrene-air

17 Similarity Summary Exact similarity of Ri and ρ/ρ a Re and Re p not matched but qualitatively similar St is different sedimentation is important Slope angles are different. Appears unimportant at high Re

18 Experiments Funnel Tube Sieve Funnel Tube Sieve 1111 Hoist Air pressure sensor 3m 2m front view Angles 45 to 9 side view

19 Side View 8 Litre Avalanches 31.5 o slope 58.5 o slope 1 ml side 8 ml side 91. o slope

20 Non-dimensional Height h = h V 1/3 nondimensional final head height l 1. l 2. l 5. l slope angle ( o )

21 Polystyrene balls on 7 surface g

22 Ping-Pong Avalanches

23 Front Velocities at the K-Point 15 Velocity (ms -1 ) (log scale) v =1.8n 1/6 experiment Number of balls (log scale)

24 Non-Dimensional Velocity ũ = u V 1 6 g ~ u ~ u l θ ( o ) 1. l 2. l 5. l θ ( o )

25 Pressure Theory Comparison Pressure (pa) data dynamic fit hydrostatic fit Time (s) Air pressure in a small powder cloud

26 DNS simulations and Ping-Pong experiments Overpressure (Pa) experimental data p = 1/2 ρ a v 2 (R/r) 3 [2-(R/r) 3 ] v=1.2m/s, R=1.m, r=r-vt Time (s) Air pressure data from a ping-pong ball avalanches and comparison with theory Pressure Time Air pressure data from a direct numerical simulation of a gravity current

27 Front Instability, 5 l polystyrene, 51 slope

28 Conclusions Transition to suspension can be achieved in the laboratory Can deduce avalanche length, height, speed, and front angle from pressure data Good agreement between theory, experiments and field observations Pressure measurements can distinguish suspended from dense flows Coherent internal velocities can be twice front velocity Take care estimating forces!

29 Direct Numerical Simulations Meiburg Code 2d spectral with compact finite differences Diablo from John taylor 3d spectral with low order finite differences Simulation region 8 1 Release area 2.5 Slope angles 9 Boussinesq and non-boussinesq Test hypothesis: stagnation point is lowest point as Re

30 Time evolution, Re=32,, Slope=1 film front Height Position Angle nose lowest stagnation Time

31 Time evolution, Re=32,, Slope=6 film front Height Position Angle nose lowest stagnation Time

32 Re Comparison at slope 2k deg, s=3, t= 5.8 2knb deg, s=3, t= 5.8 4k deg, s=3, t= 5.8 4knb deg, s=3, t= 5.8 8k deg, s=3, t= 5.8 8knb deg, s=3, t= k deg, s=3, t= knb deg, s=3, t= k deg, s=3, t= knb deg, s=3, t= k deg, s=3, t= 5.8

33 Re Comparison at slope 2 2k 2deg, s=3, t= 5.8 2knb 2deg, s=3, t= 5.8 4k 2deg, s=3, t= 5.8 4knb 2deg, s=3, t= 5.8 8k 2deg, s=3, t= 5.8 8knb 2deg, s=3, t= k 2deg, s=3, t= knb 2deg, s=3, t= k 2deg, s=3, t= knb 2deg, s=3, t= 5.8

34 Re Comparison at slope 4 2k 4deg, s=3, t= 5.8 2knb 4deg, s=3, t= 5.8 4k 4deg, s=3, t= 5.8 4knb 4deg, s=3, t= 5.8 8k 4deg, s=3, t= 5.8 8knb 4deg, s=3, t= k 4deg, s=3, t= knb 4deg, s=3, t= k 4deg, s=3, t= knb 4deg, s=3, t= 5.8

35 Stagnation Point Angle 25 Stagnation Angle Deviation k 4k 8k 16k 32k 64k Slope angle

36 Front Speed High angles evaporate Front Speed k 4k 8k 16k 32k 64k Slope angle

37 Hindered Sedimentation where particle flux φ t + q =, q = u s φ(1 αφ) D φ Sedimenting Boundary condition n (n q) = Resuspending boundary condition n q = Use modified schemes to exactly conserve mass 2D slip hindered sedimentation 2D no slip hindered sedimentation 3D slip hindered sedimentation 32k no sedimentation

38 Vallée de la Sionne Test Site film Artificial and Natural Releases 1 1,, kg 1 1 m s 1 instrumentation Video Laser Scanning Impact & air pressure Dopper & FMCW Radar Density Velocity profiles

39 Air Pressure Sensor design

40 Mast Mounting

41 Avalanche no. 628 Pressure (Pa) Time (s)

42 Avalanche no Pressure (Pa) Time (s)

43 Pressure Theory Comparison Pressure (pa) data dynamic fit hydrostatic fit Time (s) Air pressure in a small powder cloud

44 DNS simulations and Ping-Pong experiments Overpressure (Pa) experimental data p = 1/2 ρ a v 2 (R/r) 3 [2-(R/r) 3 ] v=1.2m/s, R=1.m, r=r-vt Time (s) Air pressure data from a ping-pong ball avalanches and comparison with theory Pressure Time Air pressure data from a direct numerical simulation of a gravity current

45 Phased Array FMCW Doppler Radar Left: Vallée de la Sionne test site. Upper middle: cross slope detail. Lower middle: topographic sketch. Upper right: Space-time showing multiple fronts and shocks. Lower right: Bunker and antenna

46 Kulikovskiy Sveshnikova Beghin (KSB) Three conservation equations volume buoyancy momentum dv dt db { dt } d [ ] B +(1+χ) Vρ a u dt = q s + q a = (ρ s ρ a )q s = Bg sinθ ρ s snow density ρ a air density g gravity θ slope angle q s snow flux q a air flux χ added mass

47 Geometric Closure 1/2 l y h θ ρ ρ a k = 2h/l V = πhl/2 χ = k u f = u dl dt aspect ratio u volume added mass front velocity s x u f δ t ρs h n

48 Flux Closure q s = u f h e q a = αu V { α(ri) = snow entrainment air entrainment e λri2 Ri 1 e λ Ri Ri > 1 Ri = ρ ρ a ρ a gh cosθ u 2 Analytic solutions when Ri and h e constant

49 Comparison with Velocity Data u f (m s -1 ) 6 4 u f (m s -1 ) x (m) s (m) Avalanche no. 2 Avalanche no u f (m s -1 ) x (m) Avalanche no. 628

50 Comparison with Ping-Pong Avalanches Velocity (m/s) Velocity (m/s) Velocity (m/s) ,5 balls measurements with curvature without curvature 21, balls 42, balls Flow distance (m) 84, balls 168, balls 32, balls Flow distance (m)

51 Comparison with Volume and Height Data h (m) x (m) 15 V (x1 4 m 2 ) x (m) Geometry closure is wrong

52 Plume Models O q s x u ρ a h ρ u f buoyancy flux q s at rear ρ a h u ρ u f x O q s buoyancy flux q s at front

53 Length Scales L 4 length scales x ut h e V 1 3 f h distance traveled entrained snow depth (Britter-Linden) cube root of fracture volume height g = 2g ρ ρ a ρ+ρ a t = t g L

54 Comparison With Position Data x/l Fr = u f g L t g L 2.2±.18

55 Avalanche Volume For Five Avalanches 15 1 V ( 1 6 m 3 ) t (s) V h 3 u 3 t 3

56 Discussion and Conclusions KSB model is good for front velocity, but bad for volume Plume approach is good for volume New plume model with time varying buoyancy in the head and KSB closure for velocity Issues sensitive dependence on depth of entrainable snow makes validation hard need point velocity and density to estimate destructive forces lateral spreading

57 Thanks!

58 Publications Turnbull, B. and J.N. McElwaine, 28. Experiments on the non-boussineq Flow of Self-Igniting Suspension Currents on a Steep Open Slope., J. Geophys. Res., 113(F13), doi:1.129/27jf753. Turnbull, B., J.N. McElwaine and Ancey, C., 27. The Kulikovskiy Sveshnikova Beghin Model of Powder Snow Avalanches: Development and Application, J. Geophys. Res., 112(F14), doi:1.129/26jf489. Turnbull, B., and J.N. McElwaine, 27. A Comparison of Powder Snow Avalanches at Vallée de la Sionne with Plume Theories, J. Glaciol., 53(3) J.N. McElwaine, and Turnbull, B.,26. Plume Theories Versus Compact Models for Powder Snow Avalanches, Sixth International Symposium on Stratified Flows, Perth, December 11-14, McElwaine, J.N., 25. Rotational flow in gravity current heads, Phil. Trans. R. Soc. Lond., 363, , 1.198/rsta McElwaine, J.N. and Turnbull, B., 25. Air Pressure Data from the Vallée de la Sionne Avalanches of 24, J. Geophys. Res., 11(F31), doi:1.129/24jf237. McElwaine, J.N. and Nishimura, K. 21. Particulate Gravity Currents, Blackwell Science, chap. Ping-pong Ball Avalanche Experiments, no. 31 in Special Publication of the International Association of Sedimentologists,