### Abstract

Scale analysis indicates that five nondimensional parameters (R_{0}
^{2}, ε, μ, λ and kλ) characterize the disturbance generated by the steady flow of a uniform wind (U_{0}, V_{0}) incident on a mountain ridge of width a. Here μ = h_{0}/H_{R} is the ratio of the mountain height h_{0} to the deformation depth H_{R} = fa/N where f is the Coriolis parameter and N is the static buoyancy frequency. The parameters λ = H_{R}/H and kλ are the ratios of H_{R} to the density scale height H and the potential temperature scale height H/k respectively. There are two Rossby numbers; ε = V_{0}/fa, and R_{0} = U_{0}/fa. If R_{0}
^{2} ≤ 1, then the mountain-parallel flow is in approximate geostrophic balance and the flow is semigeostrophic. If the flow is anelastic (λ ≃ 1), no direct correspondence between the two approximations was found. However the anelastic effects are qualitatively similar for the two and lead to: i) an increase in the strength of the mountain anticyclone, ii) a reduction in the extent (and possible elimination) of the zone of blocked, cyclonic flow, iii) a permanent turning of the flow proportional to the mass of air displaced by the mountain, and iv) an increase in the ageostrophic cross-mountain flow. The last result implies an earlier breakdown of semigeostrophic theory for anelastic flow over topography. Apart from a strengthening of the cold potential temperature anomaly over the mountain, the presence of a finite potential temperature scale height (ie k nonzero) does not significantly alter the flow solution. -from Authors

Original language | English (US) |
---|---|

Pages (from-to) | 1020-1029 |

Number of pages | 10 |

Journal | Journal of the Atmospheric Sciences |

Volume | 45 |

Issue number | 6 |

DOIs | |

State | Published - Jan 1 1988 |

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### All Science Journal Classification (ASJC) codes

- Atmospheric Science

### Cite this

*Journal of the Atmospheric Sciences*,

*45*(6), 1020-1029. https://doi.org/10.1175/1520-0469(1988)045<1020:ASFOAM>2.0.CO;2

}

*Journal of the Atmospheric Sciences*, vol. 45, no. 6, pp. 1020-1029. https://doi.org/10.1175/1520-0469(1988)045<1020:ASFOAM>2.0.CO;2

**Anelastic semigeostrophic flow over a mountain ridge.** / Bannon, Peter R.; Pe-Cheng Chu, Chu.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Anelastic semigeostrophic flow over a mountain ridge

AU - Bannon, Peter R.

AU - Pe-Cheng Chu, Chu

PY - 1988/1/1

Y1 - 1988/1/1

N2 - Scale analysis indicates that five nondimensional parameters (R0 2, ε, μ, λ and kλ) characterize the disturbance generated by the steady flow of a uniform wind (U0, V0) incident on a mountain ridge of width a. Here μ = h0/HR is the ratio of the mountain height h0 to the deformation depth HR = fa/N where f is the Coriolis parameter and N is the static buoyancy frequency. The parameters λ = HR/H and kλ are the ratios of HR to the density scale height H and the potential temperature scale height H/k respectively. There are two Rossby numbers; ε = V0/fa, and R0 = U0/fa. If R0 2 ≤ 1, then the mountain-parallel flow is in approximate geostrophic balance and the flow is semigeostrophic. If the flow is anelastic (λ ≃ 1), no direct correspondence between the two approximations was found. However the anelastic effects are qualitatively similar for the two and lead to: i) an increase in the strength of the mountain anticyclone, ii) a reduction in the extent (and possible elimination) of the zone of blocked, cyclonic flow, iii) a permanent turning of the flow proportional to the mass of air displaced by the mountain, and iv) an increase in the ageostrophic cross-mountain flow. The last result implies an earlier breakdown of semigeostrophic theory for anelastic flow over topography. Apart from a strengthening of the cold potential temperature anomaly over the mountain, the presence of a finite potential temperature scale height (ie k nonzero) does not significantly alter the flow solution. -from Authors

AB - Scale analysis indicates that five nondimensional parameters (R0 2, ε, μ, λ and kλ) characterize the disturbance generated by the steady flow of a uniform wind (U0, V0) incident on a mountain ridge of width a. Here μ = h0/HR is the ratio of the mountain height h0 to the deformation depth HR = fa/N where f is the Coriolis parameter and N is the static buoyancy frequency. The parameters λ = HR/H and kλ are the ratios of HR to the density scale height H and the potential temperature scale height H/k respectively. There are two Rossby numbers; ε = V0/fa, and R0 = U0/fa. If R0 2 ≤ 1, then the mountain-parallel flow is in approximate geostrophic balance and the flow is semigeostrophic. If the flow is anelastic (λ ≃ 1), no direct correspondence between the two approximations was found. However the anelastic effects are qualitatively similar for the two and lead to: i) an increase in the strength of the mountain anticyclone, ii) a reduction in the extent (and possible elimination) of the zone of blocked, cyclonic flow, iii) a permanent turning of the flow proportional to the mass of air displaced by the mountain, and iv) an increase in the ageostrophic cross-mountain flow. The last result implies an earlier breakdown of semigeostrophic theory for anelastic flow over topography. Apart from a strengthening of the cold potential temperature anomaly over the mountain, the presence of a finite potential temperature scale height (ie k nonzero) does not significantly alter the flow solution. -from Authors

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U2 - 10.1175/1520-0469(1988)045<1020:ASFOAM>2.0.CO;2

DO - 10.1175/1520-0469(1988)045<1020:ASFOAM>2.0.CO;2

M3 - Article

AN - SCOPUS:0024190186

VL - 45

SP - 1020

EP - 1029

JO - Journals of the Atmospheric Sciences

JF - Journals of the Atmospheric Sciences

SN - 0022-4928

IS - 6

ER -