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Simulation of stably stratified flow in complex terrain: flow structures and dividing streamline

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Abstract

The advanced research version of the weather research and forecasting model was employed to simulate Intense Operational Periods of the field campaigns of the Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) Program with a 0.5 km horizontal resolution. The focus was on synoptically dominated stably stratified periods, with the mean flow approaching a strongly non-symmetrical rugged topography—the Granite Mountain of the US Army Dugway Proving Ground, Utah. The model was validated against a comprehensive set of MATERHORN data. The special in-house developed software enabled calculations of energetics and pressure anomalies along individual streamlines and tracing of spatial trajectories of streamlines. Owing to complexities of natural flows, for example, the directional shear (skewed vertical velocity profiles) and irregular topographic shape, the flow patterns depend on multiple parameters, although in idealized cases the flow is described by a single parameter (Froude number or a variant). Streamlines at different altitudes of a given location diverged rapidly, making it difficult to study the dividing streamline concept. The new software allowed identification of the dividing streamline passing over the highest crest (summit) of the mountains and its trajectory. The upstream height of the dividing streamline did not follow the well-known Sheppard’s formula. Three cases of flow patterns are presented, identified based on the presence of lee waves, flow separation, horizontal vortex shedding and hydraulics jumps.

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Acknowledgements

This research was funded by the US Office of Naval Research Award # N00014-11-1-0709, Mountain Terrain Atmospheric Modelling and Observations (MATERHORN) Program. During the latter part of the work, the work was supported by NSF Grant AGS-1565535. It has also been supported by the European Union and the State of Hungary in the framework of TÁMOP-4.2.1.B-11/2/KMR-2011-0002 Instrument. Additional support was provided by the University of Notre Dame’s Centre for Research Computing through computational and storage resources (we specifically acknowledge the assistance of Dodi Heryadi). We are thankful to Jeffrey Massey from the University of Utah for the updated land cover and soil data. Furthermore, we would like to thank Aaron S. Donahue for creative inspiration in the computations of this work.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN, 46556, USA

    Z. Silver, R. Dimitrova, T. Zsedrovits & H. J. S. Fernando

  2. Department of Meteorology and Geophysics, Faculty of Physics, Sofia University “St. Kliment Ohridski”, 1164, Sofia, Bulgaria

    R. Dimitrova

  3. Faculty of Information Technology and Bionics, Pazmany Peter Catholic University, Budapest, 1088, Hungary

    T. Zsedrovits

  4. Department of Infrastructure Engineering, University of Melbourne, Melbourne, VIC, 3010, Australia

    P. G. Baines

  5. Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA

    H. J. S. Fernando

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  1. Z. Silver
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Correspondence to Z. Silver.

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Appendix: A new computational tool for visualization and analysis

Appendix: A new computational tool for visualization and analysis

A new numerical and visualization tool was developed that enabled tracing of 3D stream surfaces, or a single 3D streamline throughout the model domain. The program is written in the Matlab environment. It is capable of interpolating not only the path of a streamline through the model domain in 3D, but also computes any of the 3D WRF variables along the streamline that includes, but is not limited to kinetic and potential energies, Brunt-Väisälä Frequency, pressure perturbations, and buoyancy frequency. These values were computed at every given point along a streamline. The mixing ratio, pressure, and potential temperature are all interpolated along the line that is tangent to the 3D velocity vector field.

The software was first tested against an analytical streamline solution in 3D, and furthermore, a step size refinement was tested within the model domain. The position (in x, y, z), which is contained within the domain should be selected to initiate the sequence of finding the points along a streamline. This position can be used in one of the three ways. First, it may be used to start a streamline, and the streamline will continue until it reaches a boundary of the domain or a maximum horizontal distance within the domain at which distance the streamline will be terminated. Second, the point can be selected as the ending point, and the distance that the streamline should begin upstream may be specified. The third option allows extracting a vertical slice along a specified angle (from the north) along with the horizontal extent of the line

To test the software, we used 133 time periods that were driven by large-scale flow during the early morning hours. The origin point of these streamlines was refined to locate the exact height that would produce a line that reached the mountaintop (summit) of the mountain. Since the analysis incorporated streamlines that originated from many different locations in the simulation domain, depending on the flow direction for a particular time period, the streamlines were grouped based on the wind direction from which the dividing streamline approached the obstacle. Each direction group must be considered separately. Ultimately this tool allowed for the Sheppard criterion to be evaluated for realistic atmospheric conditions.

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Silver, Z., Dimitrova, R., Zsedrovits, T. et al. Simulation of stably stratified flow in complex terrain: flow structures and dividing streamline. Environ Fluid Mech 20, 1281–1311 (2020). https://doi.org/10.1007/s10652-018-9648-y

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