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Mountain-Wave Momentum Flux in an Evolving Synoptic-Scale Flow

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  • 1 Department of Atmospheric Sciences, University of Washington, Seattle, Washington
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Abstract

The evolution of mountain-wave-induced momentum flux is examined through idealized numerical simulations during the passage of a time-evolving synoptic-scale flow over an isolated 3D mountain of height h. The dynamically consistent synoptic-scale flow U accelerates and decelerates with a period of 50 h; the maximum wind arrives over the mountain at 25 h. The synoptic-scale static stability N is constant, so the time dependence of the nonlinearity parameter, ε(t) = Nh/U(t), is symmetric about a minimum value at 25 h.

The evolution of the vertical profile of momentum flux shows substantial asymmetry about the midpoint of the cycle even though the nonlinearity parameter is symmetric. Larger downward momentum fluxes are found during the accelerating phase, and the largest momentum fluxes occur in the mid- and upper troposphere before the maximum background flow arrives at the mountain. For a period of roughly 15 h, this vertical distribution of momentum flux accelerates the lower-tropospheric zonal-mean winds due to low-level momentum flux convergence.

Conservation of wave action and Wentzel–Kramers–Brillouin (WKB) ray tracing are used to reconstruct the time–altitude dependence of the mountain-wave momentum flux in a semianalytic procedure that is completely independent of the full numerical simulations. For quasi-linear cases, the reconstructions show good agreement with the numerical simulations, implying that the basic asymmetry obtained in the full numerical simulations may be interpreted using WKB theory. These results demonstrate that even slow variations in the mean flow, with a time scale of 2 days, play a dominant role in regulating the vertical profile of mountain-wave-induced momentum flux.

The time evolution of cross-mountain pressure drag is also examined in this study. For almost-linear cases, the pressure drag is well predicted under steady-state linear theory by using the instantaneous incident flow. Nevertheless, for mountains high enough to preserve a moderate degree of nonlinearity when the synoptic-scale incident flow is strongest, the evolution of cross-mountain pressure drag is no longer symmetric about the time of maximum wind. A higher drag state is found when the cross-mountain flow is accelerating. These results suggest that the local character of the topographically induced disturbance cannot be solely determined by the instantaneous value of the nonlinearity parameter ε.

Corresponding author address: Chih-Chieh Chen, Dept. of Atmospheric Sciences, University of Washington, Box 351640, Seattle, WA 98195-1640. Email: cchen@atmos.washington.edu

Abstract

The evolution of mountain-wave-induced momentum flux is examined through idealized numerical simulations during the passage of a time-evolving synoptic-scale flow over an isolated 3D mountain of height h. The dynamically consistent synoptic-scale flow U accelerates and decelerates with a period of 50 h; the maximum wind arrives over the mountain at 25 h. The synoptic-scale static stability N is constant, so the time dependence of the nonlinearity parameter, ε(t) = Nh/U(t), is symmetric about a minimum value at 25 h.

The evolution of the vertical profile of momentum flux shows substantial asymmetry about the midpoint of the cycle even though the nonlinearity parameter is symmetric. Larger downward momentum fluxes are found during the accelerating phase, and the largest momentum fluxes occur in the mid- and upper troposphere before the maximum background flow arrives at the mountain. For a period of roughly 15 h, this vertical distribution of momentum flux accelerates the lower-tropospheric zonal-mean winds due to low-level momentum flux convergence.

Conservation of wave action and Wentzel–Kramers–Brillouin (WKB) ray tracing are used to reconstruct the time–altitude dependence of the mountain-wave momentum flux in a semianalytic procedure that is completely independent of the full numerical simulations. For quasi-linear cases, the reconstructions show good agreement with the numerical simulations, implying that the basic asymmetry obtained in the full numerical simulations may be interpreted using WKB theory. These results demonstrate that even slow variations in the mean flow, with a time scale of 2 days, play a dominant role in regulating the vertical profile of mountain-wave-induced momentum flux.

The time evolution of cross-mountain pressure drag is also examined in this study. For almost-linear cases, the pressure drag is well predicted under steady-state linear theory by using the instantaneous incident flow. Nevertheless, for mountains high enough to preserve a moderate degree of nonlinearity when the synoptic-scale incident flow is strongest, the evolution of cross-mountain pressure drag is no longer symmetric about the time of maximum wind. A higher drag state is found when the cross-mountain flow is accelerating. These results suggest that the local character of the topographically induced disturbance cannot be solely determined by the instantaneous value of the nonlinearity parameter ε.

Corresponding author address: Chih-Chieh Chen, Dept. of Atmospheric Sciences, University of Washington, Box 351640, Seattle, WA 98195-1640. Email: cchen@atmos.washington.edu

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