Numerical Buoyancy-Wave Model for Wave Stress and Drag Simulations in the Atmosphere
M. Zirk 1*, R. Room 1, A. Mannik 1, A. Luhamaa 1, M. Kaasik 1, S. Traud 11 Institute of Physics, Tartu University, Tartu 50090, Estonia.
Received 28 November 2012; Accepted (in revised version) 8 May 2013
Available online 15 August 2013
Orographic drag formation is investigated using a numerical wave model (NWM), based on the pressure-coordinate dynamics of non-hydrostatic HIRLAM. The surface drag, wave stress (vertical flux of horizontal momentum), and wave drag are split to the longitudinal and transverse components and presented as Fourier sums of their spectral amplitudes weighted with the power spectrum of relative orographic height. The NWM is accomplished, enabling a spectral investigation of the buoyancy wave stress, and drag generation by orography and is then applied to a cold front, characterised by low static stability of the upper troposphere, large vertical and directional wind variations, and intensive trapped wave generation downstream of obstacles. Resonances are discovered in the stress and drag spectra in the form of high narrow peaks. The stress conservation problem is revisited. Longitudinal stress conserves in unidirectional flow, 2D orography conditions, but becomes convergent for rotating wind or 3D orography. Even in the convergent case the vertical momentum flux from the troposphere to stratosphere remains substantial. The transverse stress never conserves. Disappearing at the surface and on the top, it realises the main momentum exchange between lower an upper parts of the troposphere. Existence of stationary stratospheric quasi-turbulence (SQT) is established above wind minimum in the stratosphere.
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PACS: 92.60.Kc, 92.70.Bc, 92.60.hh, 02.30.Nw, 47.11.Kb, 47.27.er
Key words: Fourier spectrum, orographic buoyancy waves, surface drag, wave drag, wave stress, momentum flux, wave equation, numerical wave modelling.
Email: Marko.Zirk@ut.ee (M. Zirk), email@example.com (R. Room), Aarne.Mannik@ut.ee (A. Mannik), Andres.Luhamaa@ut.ee (A. Luhamaa), Marko.Kaasik@ut.ee (M. Kaasik), Sebastian.Traud@ut.ee (S. Traud)