“…Rayleigh's theory is commonly used to conduct thermal stability analyses and evaluate the potential for the occurrence of thermally driven convection (or mixing) in boreholes and groundwater wells (Solodov et al
2002; Love et al
2007; Berthold and Börner
2008; Berthold
2010). Thermally driven convection occurs in vertical water columns when the thermal Rayleigh number (
) exceeds the critical thermal Rayleigh number (
; Rayleigh
1916), where a dimensionless Rayleigh number for thermal driven convection
can be determined as:
where
is the gravity acceleration (m s −2 ),
is the thermal expansion coefficient of water (°K −1 ), ∆T is the temperature gradient within the well water column (°K),
radius of the well water column (m),
is the height of the water column (m), v is the kinematic viscosity of water (m 2 s −1 ), and
is the thermal diffusivity of water (m 2 s −1 ).…”