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| T_G(t, {\bf r}) = T_{GS}({\bf r}) + T_Y(t, z) + T_D(t, z) |
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G_T({\bf r}) = \frac{j_z}{\lambda_r({\bf r})} |
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\nabla T_{GS} = \lambda^{-1}\rho_e \, c_e \frac{\partial T_G}{\partial t} + \nabla \left( \lambda \nabla T_G \right) = q({\bf r}) |
| \cdot {\bf j} | | rot_j | | alignment | left |
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\nabla \times {\bf j} = 0 |
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anchor | | {GS}(G(t, x, y, z = z_s) = T_s |
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T_Y | z) = \delta T_A \, \exp \left[ \, {(z_s-z}) \sqrt{\frac{\pi}{a_{en} \, A_T}} \, \right] \, \cos \left[ \, 2 \pi \frac{t - \delta t_A}{A_T} + (z_s -z) \sqrt {\frac{\pi}{a_{en} \, A_T}} \, \right]
| | T_z | T_D(t,z) = \delta | D | , \exp \left[ \, {(z_s-z}) \sqrt{\frac{\pi}{a_{en} \, D_T}} \, \right] \, \cos \left[ \, 2 \pi \frac{t - \delta t_D}{D_T} + (z_s -z) \sqrt {\frac{\pi}{a_{en} \, D_T}} \, \right]Neutral LayerBig]_{z=z_{ref}} = {\bf j}_{ref}(x,y) |
| | | z | NH_n = \sqrt{\frac{a_{en} \, A_T }{\pi}} \, \ln \frac{\delta T_A }{\delta T_{\rm cut} |
z_n = z_s + H_n |
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G_T({\bf r}) = \frac{j_z}{\lambda_r({\bf r})} |
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See Also
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Geology / Geothermal Temperature Field
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