# 5.3 Wooding Number

As mentioned in the previous section, application of the Rayleigh number is limited to systems without a background flow field. Wooding (1960) analyzed the case of a boundary layer that grows by diffusion in the presence of a flow that opposes diffusion. Situations like these are found below the bottom of salt lakes that receive groundwater input by upward seepage (Simmons et al., 2002; Simmons et al., 1999; Wooding et al., 1997), salt pans (Bauer et al., 2006) or where groundwater discharges into the ocean (Greskowiak, 2014). A stable boundary layer occurs when the diffusive flux equals the opposing advective flux (Figure 15).

Wooding et al. (1997) defined the characteristic thickness *δ *of the boundary layer as shown in Equation 28.

(28) |

When *H* is replaced by *δ* in Equation 26, the boundary layer Rayleigh number, or Wooding number, becomes Equation 29.

(29) |

Based on linear perturbation analysis, Wooding (1960) determined the value of the critical boundary Rayleigh number to be . For values less than 7 which are situations with high *q*_{z} or low Δ*ρ*, the boundary layer initially increases and then reaches a stable thickness. For values greater than 7 which are situations with low *q*_{z} or high Δ*ρ*, the boundary layer continues to increase and never stabilizes.

High values of *q*_{z} tend to stabilize the system, as shown in Figure 16. The colored lines mark the boundary between the stable and unstable regime for a range of values of *q*_{z} that may be encountered in groundwater systems. Fluxes of *q*_{z} > 0.1 m d^{−1} are required to prevent instabilities from amplifying in the most permeable aquifers.