arXiv subjects

Heinz Blatter

Publications and source records attributed to Heinz Blatter.

3 recordsLinked to original sources

arXiv2016

Comparison of thermodynamics solvers in the polythermal ice sheet model SICOPOLIS

In order to model the thermal structure of polythermal ice sheets accurately, energy-conserving schemes and correct tracking of the cold-temperate transition surface (CTS) are necessary. We compare four different thermodynamics solvers in the ice sheet model SICOPOLIS. Two exist already, namely a two-layer polythermal scheme (POLY) and a single-phase cold-ice scheme (COLD), while the other two are newly-implemented, one-layer enthalpy schemes, namely a conventional scheme (ENTC) and a melting-CTS scheme (ENTM). The comparison uses scenarios of the EISMINT Phase 2 Simplified Geometry Experiments (Payne and others, 2000, J. Glaciol. 46, 227-238). The POLY scheme is used as a reference against which the performance of the other schemes is tested. Both the COLD scheme and the ENTC scheme fail to produce a continuous temperature gradient across the CTS, which is explicitly enforced by the ENTM scheme. ENTM is more precise than ENTC for determining the position of the CTS, while the performance of both schemes is good for the temperature/water-content profiles in the entire ice column. Therefore, the one-layer enthalpy schemes ENTC and ENTM are viable, easier implementable alternatives to the POLY scheme with its need to handle two different numerical domains for cold and temperate ice.

physics.ao-ph↗

arXiv2015

Comparison and verification of enthalpy schemes for polythermal glaciers and ice sheets with a one-dimensional model

The enthalpy method for the thermodynamics of polythermal glaciers and ice sheets is tested and verified by a one-dimensional problem (parallel-sided slab). The enthalpy method alone does not include explicitly the transition conditions at the cold-temperate transition surface (CTS) that separates the upper cold from the lower temperate layer. However, these conditions are important for correctly determining the position of the CTS. For the numerical solution of the polythermal slab problem, we consider a two-layer front-tracking scheme as well as three different one-layer schemes (conventional one-layer scheme, one-layer melting CTS scheme, one-layer freezing CTS scheme). Computed steady-state temperature and water-content profiles are verified with exact solutions, and transient solutions computed by the one-layer schemes are compared with those of the two-layer scheme, considered to be a reliable reference. While the conventional one-layer scheme (that does not include the transition conditions at the CTS) can produce correct solutions for melting conditions at the CTS, it is more reliable to enforce the transition conditions explicitly. For freezing conditions, it is imperative to enforce them because the conventional one-layer scheme cannot handle the associated discontinuities. The suggested numerical schemes are suitable for implementation in three-dimensional glacier and ice-sheet models.

physics.ao-ph↗

arXiv2006

Intergalactic spaceflight: an uncommon way to relativistic kinematics and dynamics

In the Special Theory of Relativity space and time intervals are different in different frames of reference. As a consequence, the quantity 'velocity' of classical mechanics splits into different quantities in Special Relativity, coordinate velocity, proper velocity and rapidity. The introduction and clear distinction of these quantities provides a basis to introduce the kinematics of uniform and accelerated motion in an elementary and intuitive way. Furthermore, rapidity links kinematics to dynamics and provides a rigorous way to derive Newtons Second Law in the relativistic version. Although the covariant tensorial notation of relativity is a powerful tool for dealing with relativistic problems, its mathematical difficulties may obscure the physical background of relativity for undergraduate students. Proper velocity and proper acceleration are the spatial components of the relativistic velocity and acceleration vectors, and thus, they provide a possibility to introduce and justify the vectorial notation of spacetime. The use of the three different quantities describing 'velocity' is applied to discuss the problems arising in a thought experiment of a relativistic spaceflight.

physics.ed-ph↗