Precise temperature monitoring in boreholes: evidence for oscillatory convection? Part II: theory and interpretation
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In the previous part of this work (Cermak, Safanda and Bodri, this volume p.MMM) we have described experimental data and quantified the heterogeneity features of the microtemperature time series. The spectral analysis and the local growth of the second moment technique revealed scaling structure of all observed time series generally similar and suggested the presence of two temperature forming processes. The longer-scale part can be attributed to the heat conduction in compositional and structural heterogeneous solid rocks, further affected by various local conditions. Short-scale temperature oscillations are produced by the intra-hole fluid convection due to inherent instability of water column filling the hole. Here we present how the observational evidence is supported by the results of the computer simulations. The exact modes of intra-hole convection may be different, ranging from quasi-periodic (“quiescent”) state to close of turbulence. As demonstrated by numerical modeling and referred on laboratory experiments, at higher Rayleigh numbers the periodic character of oscillation characteristic for “quiescent” regime is superseded by stochastic features. This so called “oscillatory” convection occurs due to instability within the horizontal boundary layers between the individual convectional cells. In spite of the fact that the basic convective cell motion is maintained and convection is characterized by slow motion, the oscillatory intra-hole flow and corresponding temperature patterns exhibit typical features of turbulence. The idea of boundary layer instability as a source of stochastic temperature fluctuations could explain many distinct features of borehole temperatures that previously cannot be interpreted.
KeywordsTemperature monitoring Intra-hole convection Numerical modeling Oscillatory regime
We have greatly profited from the discussions with our colleagues when preparing this work. Special thanks are to two anonymous reviewers who have read the original text and offered valuable comments. Most of the reported studies were done under the co-operation programme between the Czech and Hungarian Academies of Sciences. The support of the Czech participation was partly provided by the Grant Agency of the Czech Republic (project GACR 205/03/0998) and the institutional expenses were funding from the research programmes Z3012916 and K3046108.
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