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On the Momentum Flux of Vertically-Propagating Orographic Gravity Waves Excited in Nonhydrostatic Flow over Three-dimensional Orography

Xin Xu 1 , Runqiu Li 1 , Miguel A. C. Teixeira 2 , and Yixiong Lu 3
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  • 1 Key Laboratory of Mesoscale Severe Weather/Ministry of Education, and School of Atmospheric Sciences, Nanjing University, Nanjing 210023, Jiangsu, P. R. China
  • 2 University of Reading, Department of Meteorology, Meteorology Building, Whiteknights Road, Earley Gate, Reading RG6 6ET, UK
  • 3 Beijing Climate Center, China Meteorological Administration, Beijing 100081, P. R. China
Published-online:
05 Apr 2021
DOI:
https://doi.org/10.1175/JAS-D-20-0370.1
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Abstract

This work studies nonhydrostatic effects (NHE) on the momentum flux of orographic gravity waves (OGWs) forced by isolated three-dimensional orography. Based on linear wave theory, an asymptotic expression for low horizonal Froude number (Fr=U2+⁡(γV)2Na where (U, V) is the mean horizontal wind, γ and a are the orography anisotropy and half-width and N is the buoyancy frequency) is derived for the gravity wave momentum flux (GWMF) of vertically-propagating waves. According to this asymptotic solution, which is quite accurate for any value of Fr, NHE can be divided into two terms (NHE1 and NHE2). The first term contains the high-frequency parts of the wave spectrum that are often mistaken as hydrostatic waves, and only depends on Fr. The second term arises from the difference between the dispersion relationships of hydrostatic and nonhydrostatic OGWs. Having an additional dependency on the horizontal wind direction and orography anisotropy, this term can change the GWMF direction. Examination of NHE for OGWs forced by both circular and elliptical orography reveals that the GWMF is reduced as Fr increases, at a faster rate than for two-dimensional OGWs forced by a ridge. At low Fr, the GWMF reduction is mostly attributed to the NHE2 term, whereas the NHE1 term starts to dominate above about Fr = 0.4. The behavior of NHE is mainly determined by Fr, while horizontal wind direction and orography anisotropy play a minor role. Implications of the asymptotic GWMF expression for the parameterization of nonhydrostatic OGWs in high-resolution and/or variable-resolution models are discussed.

Corresponding to: Xin Xu (xinxu@nju.edu.cn), School of Atmospheric Sciences, Nanjing University, No. 163, Xianlin Avenue, Nanjing, Jiangsu, 210023, P. R. China

Abstract

This work studies nonhydrostatic effects (NHE) on the momentum flux of orographic gravity waves (OGWs) forced by isolated three-dimensional orography. Based on linear wave theory, an asymptotic expression for low horizonal Froude number (Fr=U2+⁡(γV)2Na where (U, V) is the mean horizontal wind, γ and a are the orography anisotropy and half-width and N is the buoyancy frequency) is derived for the gravity wave momentum flux (GWMF) of vertically-propagating waves. According to this asymptotic solution, which is quite accurate for any value of Fr, NHE can be divided into two terms (NHE1 and NHE2). The first term contains the high-frequency parts of the wave spectrum that are often mistaken as hydrostatic waves, and only depends on Fr. The second term arises from the difference between the dispersion relationships of hydrostatic and nonhydrostatic OGWs. Having an additional dependency on the horizontal wind direction and orography anisotropy, this term can change the GWMF direction. Examination of NHE for OGWs forced by both circular and elliptical orography reveals that the GWMF is reduced as Fr increases, at a faster rate than for two-dimensional OGWs forced by a ridge. At low Fr, the GWMF reduction is mostly attributed to the NHE2 term, whereas the NHE1 term starts to dominate above about Fr = 0.4. The behavior of NHE is mainly determined by Fr, while horizontal wind direction and orography anisotropy play a minor role. Implications of the asymptotic GWMF expression for the parameterization of nonhydrostatic OGWs in high-resolution and/or variable-resolution models are discussed.

Corresponding to: Xin Xu (xinxu@nju.edu.cn), School of Atmospheric Sciences, Nanjing University, No. 163, Xianlin Avenue, Nanjing, Jiangsu, 210023, P. R. China
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