What are the Geophysical Processes that Form Drumlins?Isabee Demski

Introduction Both scientists and common people have been fascinated with the glacial landforms named by the Irish country folk as droimin or little ridges (Clark, 2010, as cited by Bryce 1833). Drumlins were named and observed by the people who lived on and near them. Drumlins are oblong hills occurring across areas where glaciers once covered the continental landscape during global ice ages. These glaciers covered vast areas of land and created structures that present-day glaciers, calving into the sea or located in mountain ravines, do not duplicate. This makes explaining drumlin formation from direct observation challenging. Drumlins have been observed individually and as a pattern of the post-glacial landscape. Various geologists have attempted to create models explaining drumlins using a variety of possible formation processes. Currently forming drumlins have, however been exposed by the retreat of a surge type glacier in Iceland. Observation of an active surge type glacier allows geologists to compare models to an active current regime, feeding enthusiasm for a much studied landform (Mark D. Johnson et a 2012l). In studying a recently revealed drumlin field in Iceland, Mark D. Johnson, et al. were able to conclude that drumlins are built up and formed by a combination of sub-glacial depositional and erosional processes. The observation of active drumlin field structures gives observational data that supports both of the two theories prevalent in glacial bed form studies. The physically based instability theory as well as the meltwater flood theory (Stokes et al, 2013) (NO, JOHNSON'S DATA DISAGREES WITH THE MELTWATER THEORY) both deal with the depositional and erosional processes observed in the field dynamics of drumlin field reviled at the margin of the Mulajorkull Glacier in Iceland by Johnson et al. According to Clark, both peasantry and scholars have made observations about drumlin sedimentology and have been curious about drumlin formation for centuries. This study examines the physics behind the processes that contribute to drumlin formation and compares these models to actual drumlin fields.

The Drumlin Formation Process is a Self-organizing and Dynamic System Smalley and other geologists have studied how flow could cause drumlins to form around an obstruction theorized about the energy required for till mobilization. Soil mechanics were studied and glacial residues have been observed and many conjectures have been made about the glacial landscape. Smally used what he called the golf ball model to explain that the formation of drumlins facilitates glacial flow. Drumlins form in a layer between the ice and the ground. He compared the effect of the dimpled surface of a golf ball with the glacier-till boundary layer in its effects on the efficient fluid flow. Nature seeks the path of least resistance, causing the organization under the heavy moving ice to form a pattern that allows for locally accelerated flow rate. In their paper The Golf-Ball Model and the Purpose of Drumlin Formation (Smalley, et al, 2000), claim that a dynamic system self organizes towards the edge of the ice sheets because stress and strength curves cross and favor the deformation that causes drumlin formation. According to Smally, and reiterated by Clark, many drumlin fields have a pattern like a mold of a golf ball rolled over the landscape. This analogy is used to suggest that the physics of the bed glacier interface naturally form to reduce friction and drag and promote faster ice flow. Smalley also states that this reduction of drag reduces boundary layer detachment. This system geometry has attracted mathematically inclined individuals like Hook, R. L., and Medford, Araron to develop the thermo-mechanical Instability Theory to replace or supplement the melt water flood and obstacle accumulation models that do not account for the regularity of drumlin fields that inspired the golf ball analogy. Smalley and his team use Turings ideas of chemical morphogenesis to study the possibility of self-organization in the geomorphology in concepts of landscape organization (Ibid). They concluded that an interactive system would develop a form of equilibrium, from which it could depart into a drumlin formation (ibid). According to Smalley et al, A Turing instability is defined as the point where the system is driven far enough from equilibrium for a patterned response to appear. Drumlin fields have an observed pattern in spite of the complexity of individual drumlin character as studied and

illustrated by Stokes et al. in 2013. Smalley I. S. et al also states that as the flow pattern developed the flow it would cause local erosion and deposition that would further pattern the drumlin field. This flow pattern could promote self-organization and cause a stress field to develop around the forming drumlins that could be seen as a relatively simple two dimensional packing (Smalley I. S. et al, 2000). He suggests further study of soil and clast packing and that drumlins help the ice, till interface to remain attached longer and flow would therefore be easier in the sub- glacial zone. This two dimensional model is pursued in Hooks thermo-mechanical instability theory of drumlin formation. He created planner models that included pressure melting because field evidence suggests the presence of water in drumlin formation. His models showed geothermal heat would be more focused on the trough and less heat would be focused on the crest of the deformations in the till that would become drumlins. He suggested that positive feedback from continual energy and temperature adjustments would cause drumlins to grow in relationship to each other in a wave pattern.

Hook speculated that this patterning could arise from flow over a relatively flat bed, but not a

homogeneous one (Hook, R.L, Medford, A, 2013) and further explored the idea that instability of heavy ice flowing over deformable till would set up positive feedbacks that amplify the perturbation. Hooks mathematical models showed the results of the heat fluxes possibly occurring at the ice substrate interface and showed how drumlin topography could develop. He states that drumlins form from an instability arising from ice flow over deformable till. Hook emphasizes positive feedback and presents a model that shows pressure relative to the pressure melting point uses several mathematical formulas to prove how geothermal heat will be focused on the trough less than on the Crest of a developing wave of landscape deformation that becomes a drumlin. He makes it clear that it takes time for temperature transfer and that the bed perturbation grows as the ice moves over It (Hooke, R. L. Medford, A. 2013). Flow Instabilities and Theories of Drumlin formation related to Actual Landscapes Smalleys paper published in 2010 claims that drumlins were not just formed around obstacles, but developed to reduce flow stresses at the glacier base thus reducing shear stress. This also fits thermodynamic feedback models that are mathematically sound. This paper explaining instability theory inspired Geophysicists like Chris D. Clark to further observe and analyze drumlin types and their field relationships. It also encouraged the study of the more mathematical side of instability theory by researchers like Hooke and Medford. Clark concluded from his field observations and his studies searching for a mechanism that would generate the pattern observed in drumlin fields basic physics involving effective pressure and basal shear stress of glacier forms supports the Instability Theory as the model produces instabilities at the appropriate scale of subglacial bedforms (Clark, 2010). Although Hooks mathematical models are two dimensional, and Drumlins vary in structure, Clark gave support to the model and noted that just because a sedimentary structure is found within a Drumlin, it does not imply it was relevant to the process of drumlinization (Clark, 2010). Positive Feedback and Thermo-mechanical Instability

The high pore- water pressure mentioned by Clark, C. D. in his studies of flow instabilities and wave length spacing analysis reinforce the field evidence (that) suggests that drumlins form with water present (Hook, R. L., Medford, A., 2013). The stress differences observed to control the crevasses that develop in the active surge glacier in Iceland can be related to the frictional heating and flow drag that create a variation in the heat temperature distribution under the pressures of the overlying glacial models created by Hook, R.L, and Med ford in the Instability Model (ibid). This model shows that more geothermal heat will be focused on the trough and less on the crest of the wave like patterns of drumlin fields that give rise to heat- flux calculations for a topographic perturbation used by Hook, R. L. and Medford, A to Model the patterns of drumlin formations observed by Clark, C, R. in his paper about flow instabilities. Clark noted that the golf ball patterning in the Irish Midlands suggested a self-organizing behavior at the base of the ice sheet. Internal Structure of Drumlins

Stokes examined many papers on the structure of drumlins and distilled five main drumlin types and went on to show that they would fit into the instability theory model of drumlin formation. Till fabric and drumlin types were studied and presented schematically by Stokes, C.R. et al. Five types of drumlins were distilled from earlier literature. These types are named by Stokes as 1. Bedrock, 2.Part bedrock/part till 3.Mainly till 4.Part till/part sorted sediments 5.Mainly sorted (Stokes, C.R. et al 2013). Stokes is not sure whether the instability theory and its conceptual mathematical models explain all of these drumlin types. Stokes also states that we do not have a large enough sample size to judge whether observations to date are a representative sample of drumlin composition. Clark has since worked with Stokes and a group of mathematicians to show how the instability theory of drumlin formation fits with actual drumlins of varied composition and structure. Stokes would like to see the instability theory further developed to explain these varied compositions and structures of drumlins.

Stokes prefers the instability theory to the meltwater flood theory but speculates that perhaps a combination of processes could better explain deposition histories of drumlins Regional Patterns and Assumptions about Glacial Landforms In his Flow instability paper, Clark states that the bumpiness of the Irish Midlands causes the topography to look like the surface of a golf ball unrolled across Ireland. He believes that drumlins might be genetically related and form a continuum of other subglacial bedforms (Clark, 2010). He suggests that the golf ball like dimples reduce drag and that the visible patterning serves the purpose of promoting smoother ice flow. Wave forms develop both in the direction of flow and in the three dimensional extension of the formation pattern.

Drumlins are increasingly used to infer bed conditions and flow dynamics of former glaciers and ice streams (Clark, 2010). Considering an active Drumlin Field Revealed in Iceland The emerging drumlins have given Johnson, M. D. et al a chance to study the morphmetrics of drumlins that are newly formed and compare those proportions to well studied Pleistocene drumlin

fields and found that the length and width ratios show these new drumlins to be typical in shape compared to drumlins formed during past glaciations. The till of the drumlins was studied where it has been exposed by water escape structures. It was concluded that periodic erosion and deposition left pebble fabrics that paralleled the axis of the drumlins. Johnson and his team also concluded that stress differences under and between crevasses would have initiated slight differences in erosion and deposition at the glacier bed, resulting in greater accumulation of till beneath the crevasses and less between creating the radial pattern of the drumlins that developed over successive growth surges and exposed by the glacial retreat between the 10 to 20 year surge occurrences. The active drumlin field emerging from the Mulajokull glacier in Iceland exhibit a fan shaped pattern around the surge lob of the glacier. Regions where the last glacial retreat has left drumlins show more extensive fields. The golf ball pattern is not evident in the fan shaped layout of the more than 50 drumlins (Johnson, 2012) revealed in the retreating fan shaped margin of the active drumlin field in Iceland. However, it was concluded by their field studies to be formed by a combination of depositional and erosional processes that fit the thermo-mechanical model of bed deformation. Drumlin field pattern development at the base of Icelands surge glacier is reinforced by the deposits being linearly organized in relationship to the crevasse pattern in the glacier. The pattern is fan shaped because the ice is moving out of a valley but still shows a regular pattern in the drumlin field geometry. These elliptically shaped hills are emerging out of the Mulajokul surge-type glacier in a fan shaped pattern such that each drumlin is located below a crevasse near the glacier margin. These crevasses are apparently form from the spreading of the glacier as it leaves the constraints of the valley walls. Conclusion The recent physical and mathematical models of drumlin genesis as well as the studies of the emerging drumlins in the active field in Iceland have both answered some questions about the reasons

that drumlins and drumlin fields have developed the way that they have and posited new questions about these fascinating structures. Although the math of the instability theory deals mostly with two dimensional models, the wave patterns and energy and pressure differences that would occur under a glacier are well accounted for. The Two dimensional models fit with the three dimensional structures of actual drumlin fields. The proportions of all drumlins are similar. This easily fits into the wave pattern models that explain the physics of sub-glacial bed deformation. The geometric pattern of actual drumlin fields as well as the proportions of individual drumlins provides a good fit for the need for facilitated glacial movement. The nature of the physical world is to seek the path of least resistance. The instability theory explains the feedback systems that would cause the sub-glacial formation of drumlin fields. The similarity of the proportions of drumlins and the regularity of the spacing of drumlins in fields supports the wave patterns described in the mathematical models used to support instability theory. Drumlins are formed at the bed glacier interface and not dropped from the retreating glacier or formed by moving water from the melt. Discussion Drumlins have been found by the models of the instability theory to be formed under the pressure of the glacier and not to be deposited as the glacier melts and retreats or till collected around obstacles. This is not the same as the early melt water hypothesis that compared drumlins to waves on a beach or wash out deposits. The models that have been developed and mathematically tested offer a basis for the further study of the geomorphology involved in these formations. The interest of scientists of several disciplines as well that of ordinary people is increased by the current field work as well as the new conceptual models of drumlin formation. Both field work and calculations will continue to build on the work that is being done at present and although drumlins and drumlin fields are still a bit of a mystery, this work helps to construct a more clear idea of the earth processes and physics that have formed the landscape that we live in.

References Clark, Chris D., 2010, Emergent drumlins and their Clones: from till dilantancy to flow instabilities, Journal of Glaciology, vol. 51, No. 2000, p1011-1025 Hooke, Roger LeB., Medford, A., 2013, Are Drumlins a product of a Thermo-mechanical Instability?, Quaternary Research, http://dx.doi.org/10.1016/j.yqres.2012.12.002 Johnson, M.D., Schomacker, A., Bendediktsson, O.I., Greiger, A.J., Ferguson, A., and Ingolfsson, O., 2010, Active drumlin field revealed at the Margin of Mulajokull, Iceland: S surge-type glacier, Geology: 38:943-946 Smalley, Ian J., Lu, Ping, Jefferson, I.F., 2000, The Golf Ball Model and the Purpose of Drumlin Formation, Studia Quaternaria, vol. 17: 29-33 Stokes, C. R., Fowler, A C., Clark, C.D., Hindmarsh, Richard C.A., Spagmolo, M., 2013, The Instability Theory of Drumlin Formation and its Explanation of their Varied Composition and Internal Structure, Quaternary Science Reviews, 62 p77-96