Fluid resonance in elastic-walled englacial transport networks

Abstract:

Englacial structures are an integral part of the glacial hydrological system, yet the geometry of fluid transport within ice sheets and glaciers remains largely unknown. In this study we explore how fluid resonance, initiated at the surface of a water-filled conduit, can define subsurface englacial geometries through excitation of characteristic eigenmodes of the system and could lead to their remote detection in high frequency water pressure time series. We define the dominant resonant modes of idealized englacial systems consisting of symmetric and asymmetric tabular cracks that intersect a central conduit at an arbitrary angle, and study which modes are excited following impulsive forcing at the conduit surface. We assume the conduit is straight and cylindrical, and that fractures are thin compared to the wavelengths of interest. Conduit and crack walls deform quasi-statically in response to fluid pressure variations, and we account for viscous dissipation in the conduit and cracks. For a single crack-conduit system, the fundamental mode involves gravity-driven fluid sloshing in and out of the elastic walled crack. Higher order modes include dispersive Krauklis waves generated within the crack and organ pipe tube wave modes localized in the conduit. If detectable, these mode classes constrain different geometrical aspects of subsurface cracks from pressure time series in the conduit. The coupled mode as the fundamental mode of the system is generally excited at a higher amplitude than Krauklis waves, making it the most appealing target for detection. We further examine the coupled mode in both fully developed flow and boundary layer limits and demonstrate that measurements of mode period and quality factor (energy loss over one wave cycle) is sufficient to predict fracture lengths in some settings. We finally interpret published data of fracture resonance from both alpine glaciers and the Greenland Ice sheet according to our model and discuss further applications in the englacial setting including englacial systems with multiple cracks and the possibility of monitoring subglacial lake drainage.