 Equatorial deformation radius

For an equatorial beta plane and a shallow water wave speed $c$, the natural meridional trapping scale is $R_{\mathrm{eq}}=\sqrt{c/\beta }$. A decaying equatorial Kelvin wave has $\eta \propto e^{-y^2/(2R_{\mathrm{eq}}^2)}$. An envelope written $e^{-y^2/L^2}$ instead uses $L=\sqrt{2}{R}_{\mathrm{eq}}$; stating the exponent convention prevents a factor-of-two error in the meridional Cauchy momentum equation.