• Numerical modeling of two-dimensional temperature dynamics across ice-wedge polygons

      Garayshin, Viacheslav Valer'evich; Гарайшин, Вячеслав Валерьевич; Romanovsky, Vladimir; Rybkin, Alexei; Nicolsky, Dmitry; Hinzman, Larry (2017-05)
      The ice wedges on the North Slope of Alaska have been forming for many millennia, when the ground cracked and the cracks were filled with snowmelt water. The infiltrated water then became frozen and turned into ice. When the annual and summer air temperatures become higher, the depth of the active layer increases. A deeper seasonal thawing may cause melting of ice wedges from their tops. Consequently, the ground starts to settle and a trough begins to form above the ice wedge. The forming trough creates a local temperature anomaly in the surrounding ground, and the permafrost located immediately under the trough starts degrading further. Once the trough is formed, the winter snow cover becomes deeper at the trough area further degrading the permafrost. In this thesis we present a computational approach to study the seasonal temperature dynamics of the ground surrounding an ice wedge and ground subsidence associated with ice wedge degradation. A thermo-mechanical model of the ice wedge based on principles of macroscopic thermodynamics and continuum mechanics was developed and will be presented. The model includes heat conduction and quasi-static mechanical equilibrium equations, a visco-elastic rheology for ground deformation, and an empirical formula which relates unfrozen water content to temperature. The complete system is reduced to a computationally convenient set of coupled equations for temperature, ground displacement and ground porosity in a two-dimensional domain. A finite element method and an implicit scheme in time were utilized to construct a non-linear system of equations, which was solved iteratively. The model employs temperature and moisture content data collected from a field experiment at the Next-Generation Ecosystem Experiments (NGEE) sites in Barrow, Alaska. The model describes seasonal dynamics of temperature and the long-term ground motion near the ice wedges and helps to explain destabilization of the ice wedges north of Alaska's Brooks Range.
    • Tsunami runup in U and V shaped bays

      Garayshin, Viacheslav Valer'evich; Гарайшин, Вячеслав Валерьевич; Rybkin, Alexei; Rhodes, John; Nicolsky, Dmitry (2013-08)
      Tsunami runup can be effectively modeled using the shallow water wave equations. In 1958 Carrier and Greenspan in their work "Water waves of finite amplitude on a sloping beach" used this system to model tsunami runup on a uniformly sloping plane beach. They linearized this problem using a hodograph type transformation and obtained the Klein-Gordon equation which could be explicitly solved by using the Fourier-Bessel transform. In 2011, Efim Pelinovsky and Ira Didenkulova in their work "Runup of Tsunami Waves in U-Shaped Bays" used a similar hodograph type transformation and linearized the tsunami problem for a sloping bay with parabolic cross-section. They solved the linear system by using the D'Alembert formula. This method was generalized to sloping bays with cross-sections parameterized by power functions. However, an explicit solution was obtained only for the case of a bay with a quadratic cross-section. In this paper we will show that the Klein-Gordon equation can be solved by a spectral method for any inclined bathymetry with power function for any positive power. The result can be used to estimate tsunami runup in such bays with minimal numerical computations. This fact is very important because in many cases our numerical model can be substituted for fullscale numerical models which are computationally expensive, and time consuming, and not feasible to investigate tsunami behavior in the Alaskan coastal zone, due to the low population density in this area