A Transient Temperature Solution for Bore-Hole Model Testing
Abstract Transient temperature variations in a vertical column of ice with horizontally uniform conditions, constant vertical strain-rate and specified surface temperature, and basal heat flux can be calculated analytically. The solution consists of eigenfunctions which are forms of the confluent hy...
| Published in: | Journal of Glaciology |
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| Main Authors: | , |
| Format: | Article in Journal/Newspaper |
| Language: | English |
| Published: |
Cambridge University Press (CUP)
1987
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| Subjects: | |
| Online Access: | http://dx.doi.org/10.1017/s0022143000008613 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000008613 |
| Summary: | Abstract Transient temperature variations in a vertical column of ice with horizontally uniform conditions, constant vertical strain-rate and specified surface temperature, and basal heat flux can be calculated analytically. The solution consists of eigenfunctions which are forms of the confluent hypergeometric function. This solution shows that advection and diffusion have clearly separated areas of dominance, with diffusion being a sufficient approximation for small-scale perturbations in the temperature profile and advection placing an upper limit on the response time of the ice sheet as a whole. This solution is useful for analysis and testing of numerical models, for evaluation of the response time of an ice sheet and for exploratory analysis of real bore-hole data. The lowest eigenvalue of the solution determines the time-scale for transient decay of temperature anomalies. The time-scale can be determined for more general strain-rates using a finite-difference approximation to the linearized energy-balance equation. |
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