Here are measurements of the profiles of a couple avalanche tongues at Great Sand Dunes National Monument.
Profiles likely vary depending upon the wind conditions that emplaced the sand, height of dune, and perhaps sand texture.
Wind strength probably affects cornice length, and the profile of avalanche tongues will depend upon whether the dune is high enough to accommodate the full cornice; the slipface of a small dune could be entirely within the heavy grainfall zone that builds a cornice.
Fig 1. An induced avalanche tongue on an approximately 5m-high dune at Great Sand Dunes. Contrast-enhanced.
The avalanche in figure 1 was induced (by throwing a stone at the cornice inflection point) on a dune about 5m high at Great Sand Dunes, Colorado, USA. The central lobe of the tongue was followed by secondary flows on both sides.
Obtained using the shadow edge method, the cyan-shaded area of figure 2 below shows the cross-sectional profile of the above-surface portion of the toe of the avalanche tongue in figure 1. The image has been vertically compressed so that the cyan area appears with equal vertical and horizontal scaling.
Measurements of cross-sections are available from this spreadsheet (on the tab 'toe').
The profile of a single lobe avalanche in figure 2, below, has a width of 58.5 cm and area of 101 cm2.
Fig 2. Profile of avalanche toe in figure 1 (adjusted so that it has equal vertical and horizontal scaling). The photographer is standing at the base of the dune; the camera is looking downward, more or less perpendicular to the slipface, at the dune toe. Width: 58.5 cm, area 101 cm2.
Figure 3, below, shows the profile of a multi-lobe toe, having a width of 105.6 cm and a cross-sectional area of 142 cm2.
Fig 3. Profile of a single-lobe avalanche toe (adjusted so that it has equal vertical and horizontal scaling). Width: 105.6 cm, area 142 cm2.
Typically an avalanche begins near the inflection point of the lower slope of a cornice deposit, and then is fed by receding scarps that travel up to the top of the dune, ending when they erode the brink. Figure 4 shows the cross-sectional profile of one such brink trough, found on a dune about 8m high, at Great Sand Dunes. The photo is taken from the top of the dune looking down parallel to the slipface (and thus the trough is viewed in profile).
(This trough is unrelated to the toes measured above.)
The cyan-shaded trough area is 132 cm wide and has an area of 502 cm2. The measurements are in this spreadsheet (on the tab 'brinkTrough').
Fig 4. Profile of avalanche trough at the brink (adjusted so that it has equal vertical and horizontal scaling). The photographer is standing on the crest of the dune; the camera is looking downward more or less parallel to the slipface; a shovel and water bottle are visible on the interdune surface in the distance, maybe a dozen meters distant. Width: 132 cm, area 502 cm2.