Rough estimates indicated that under the most optimistic scenarios,
corresponding to the lowest plausible
value for the Planck
scale, black holes could be produced at the rate
of one per second.
A logarithmic
scale is a
scale of measurement that displays the
value of a quantity using intervals
corresponding to orders
of magnitude, rather than a standard linear
scale.
The
corresponding working quasilinear wave equation for the barotropic azonal stream function Ψm ′
of the forced waves with m = 6, 7, and 8 (m waves) with nonzero right - hand side (forcing + eddy friction) yields (34) u˜ ∂ ∂ x (∂ 2Ψm ′ ∂ x2 + ∂ 2Ψm ′ ∂ y2) + β˜ ∂ Ψm ′ ∂ x = 2Ω sin ϕ cos2 ϕT˜u˜ ∂ Tm ′ ∂ x − 2Ω sin ϕcos2 ϕHκu˜ ∂ hor, m ∂ x − (kha2 + kzH2)(∂ 2Ψm ′ ∂ x2 + ∂ 2Ψm ′ ∂ y2), [S3] where x = aλ and y = a ln -LSB-(1 + sin ϕ) / cos ϕ] are the coordinates
of the Mercator projection
of Earth's sphere, with λ as the longitude, H is the characteristic
value of the atmospheric density vertical
scale, T˜ is a constant reference temperature at the EBL, Tm ′ is the m component
of azonal temperature at this level, u˜ = u ¯ / cos ϕ, κ is the ratio
of the zonally averaged module
of the geostrophic wind at the top
of the PBL to that at the EBL (53), hor, m is the m component
of the large -
scale orography height, and kh and kz are the horizontal and vertical eddy diffusion coefficients.