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This paper describes the numerical study of nonstratified airflow over a real complex terrain. Attention is focused on the mechanism of a local strong wind induced by a topographic effect. In order to clarify the mechanism of the occurrence of strong winds accompanied by the effects of terrain, the use of a numerical simulation is very effective, in which conditions can be set without the influence of ground roughness and temperature distribution. As a result, airflow converged to a small basin of mountain terrain in the upper stream, and local strong wind was generated leeward along the slope of the mountain terrain. Furthermore, the influence of the reproduction accuracy of geographical features, that is, horizontal grid resolution, was examined. Consequently, to reproduce the above-mentioned local strong wind, it was shown that horizontal grid resolution from 50 m to about 100 m was necessary.

The author et al. have been developing a nonstationary and nonlinear wind-synopsis simulator (large-eddy simulation (LES) turbulence model) applicable to analyses of wind synopsis and the diffusion fields of any complex and steep terrain in the world which is called the Research Institute for Applied Mechanics, Kyushu University, COM putational Prediction of Airflow over Complex Terrain (RIAM-COMPACT) [

Typhoon Tokage (0423) approached Kyushu, Japan, on 20 October 2004. Even though it did not make landfall in Kyushu, the range of its strong winds covered a wide area, and Ogimachi (Ogi City at present, hereafter referred to as Ogimachi) in Saga Prefecture suffered extensive damage (

In this research, two tasks were investigated and discussed using the RIAM-COMPACT method described above. A task was to conduct a numerical simulation in a broad range targeting the north-northwest wind direction in order to clarify the mechanism of the strong-wind phenomenon that occurred around Ogimachi. Another task was to investigate the reproducibility of regional-scale terrains, in other words, the effect of horizontal grid resolution on calculation results.

The structure of this paper is as follows. Chapter 2 explains the numerical calculation method. Chapter 3 explains wind-velocity data record when Typhoon 0423 was passing through. Chapter 4 explains calculation results and discussion. Chapter 5 explains the effect of horizontal grid resolution on calculation results. Finally, Chapter 6 is the conclusion.

The numerical calculation method, calculation areas, and boundary conditions are described here. In order to numerically predict wind flows over a complex terrain with a high degree of accuracy, avoiding unstable oscillations, a collocated grid of generalized curvilinear coordinates was used. The collocated grid here is a grid system in which physical velocity components and pressure were defined in the cell centers of the calculation grid, and the variables of contravariant velocity components multiplied by Jacobian are defined in the cell interface. The numerical calculation method was conducted based on the finite-difference method (FDM), and the large-eddy simulation (LES) was conducted. For the governing equations of the flow, a filtered continuity equation for incompressible fluid (Equation (1)) and a filtered Navier-Stokes equation (Equation (2)) were used.

∂ u ¯ i ∂ x i = 0 (1)

∂ u ¯ i ∂ t + u ¯ j ∂ u ¯ i ∂ x j = − ∂ P ¯ ∂ x i + 1 Re ∂ 2 u ¯ i ∂ x j ∂ x j − ∂ τ i j x j (2)

The calculation algorithm was based on the fractional step (F-S) method [

The calculation area and boundary conditions are shown in ^{2} from the center of Ogimachi and the vertical calculation area is 5 km. The topographic geometry data with 100 m horizontal spatial resolution was constructed based on the Geospatial Information Authority of Japan (GSI) with 50 m horizontal spatial resolution. The number of grid points to each direction is 161 × 161 × 51 points in the main-flow-direction (x), spanwise direction (y), and vertical direction (z), respectively. The grid widths of directions x and y were approximately uniform intervals, with a horizontal resolution of approximately 100 m. The grid width was nonuniform in the z direction so that the density of grid points increased smoothly toward the ground surface (Δz_{min} = 3 m). The targeted wind direction was north–northwest. The inflow boundary surface was given with a velocity profile following the 1/7^{th} power law. The upper boundary surface and the side boundary surface were given with slip conditions, and the outflow boundary surface was given with convective outflow conditions. The ground surface was given with no-slip conditions. The nondimensional parameter Re of Equation (2) is a Reynolds number (= U_{in} h/ν). In the present study, the LES is assumed to reproduce the wind tunnel testing. Therefore, the effects of atmospheric stability associated with vertical thermal stratification of the atmosphere and inflow turbulence were neglected. In addition, as in Uchida [^{4}. Here, h is the altitude difference in the calculation domain (h = 1029 m), U_{in} is the wind velocity at the inflow boundary surface at the height of the maximum terrain elevation within the calculation domain and ν is a kinematic coefficient of viscosity. The nondimensional time increment was assumed to be t = 2 × 10^{−3} h/U_{in}.

The Ogimachi and Network for Wind Measurement in Kyushu (NeWMeK) observation sites (Nos. 22 and 27) and Saga University (hereafter referred as to Saga) are shown in

intervals. The No. 22 and 27 NeWNeK observation sites observed strong winds when a typhoon passed through. This is described later. Saga was used as the site for comparison with Ogimachi.

Recording Time: 20 October 2004, 10 minutes, from 16:30 to 16:40. | ||||
---|---|---|---|---|

NeWMek | Max. Instantaneous Wind Velocity (m/s) | Wind Direction | Average Wind Velocity (m/s) | Wind Direction |

No. 22 (51 m) | 31.4 | North Northeast | 18.1 | Northeast |

No. 27 (18 m) | 17.6 | North-Northeast | 10.4 | North-Northeast |

In this section, flow visualization in the neighborhood of Ogimachi is shown, and the mechanism of strong-wind generation in the neighborhood of Ogimachi is discussed. Velocity-vector diagrams (instantaneous flow field) at 20 m above the ground are shown in _{in}) ≤ 1.3, and this range is shown by being divided into 30. Therefore, the areas in which contours are shown mean that they locally have stronger winds than the surrounding areas. Pay attention to Ogimachi and Saga in

It was clarified that the generation sources of speed-increasing areas in the surroundings of Ogimachi are in the areas indicated with the solid lines in

upper stream, which leads to gap flows, so to speak. Furthermore, as shown in

In this section, more quantitative discussions are outlined.

time variations (20 and 30 m above ground) of real-scale velocity components of main-flow-direction (x). For the purpose of comparison, the time-history waveform of Saga (20 and 30 m above ground) is also shown with it. The way to convert the nondimensional wind-velocity value that was output from the numerical simulation to a realistic scale is explained. In this calculation, wind velocities and times are normalized, as shown in Equations (3) and (4), based on the reference scales.

Normalization of Wind Velocities and Times

u i | nondimensional = u i | actualscale / U i n (3)

t | nondimensional = t | actualscale / ( h / U i n ) (4)

Superscript (−) to which the spatial filter was applied is omitted as a matter of convenience. In order to convert wind velocity and time to real-scale values, you only have to substitute the values of specific reference scale h (m) and U_{in} (m/s). As for wind velocity, U_{in} (m/s) was set so that the nondimensional average wind-velocity value corresponding to the No. 22 (51 m above ground) NeWMeK observation site coincides with the average wind velocity (18.1 m/s) for ten minutes from 16:30 to 16:40, 20 October 2004, shown in

As shown in

The average speed profile of main-flow-direction (x) and the vertical profile of standard deviation are shown in _{in}. In

Point | Average Value (m/s) of Main-Flow-Direction (x) Velocity Components |
---|---|

Ogimachi, 20 m above ground | 11.8 |

Ogimachi, 30 m above ground | 16.9 |

Saga, 20 m above ground | 3.6 |

Saga, 30 m above ground | 5.6 |

vertical profile of the standard deviation shown in

It was shown in the previous section that subtle changes of topographic reliefs become a source of topographic wind generation (local strong wind, gap flow in this research). Therefore, in order to reproduce such flow phenomena using a numerical simulation, it is very important to clarify how accurately small terrains should be reproduced, in other words, to what extent is horizontal grid resolution required. In this research, three cases of numerical simulations with different grid dissolutions were conducted, and the above problems are discussed.

The calculation area is the area surrounded by a solid line, as shown in

_{in}) ≤ 1.3 into 30 in the same way as before. The speed-increasing flow, from a small basin of mountain terrain in the upper stream of Ogimachi, can be observed in the resolution shown in

Horizontal Grid Resolution (Δx = Δy) | Number of Grid Points (NX × NY × NZ) | Minimum Altitude, Maximum Altitude, Altitude Difference; Unit, m | |
---|---|---|---|

Case 1 | 50 m | 201 × 121 × 51 | 4.0, 832.0, 828.0 |

Case 2 | 100 m | 101 × 61 × 52 | 4.0, 820.0, 816.0 |

Case 3 | 200 m | 51 × 31 × 51 | 4.0, 801.0, 797.0 |

The effects of the grid resolution can be understood more clearly by showing the time-history waveform of the speed-variation component. _{ave}) at 200 m above ground. Both the vertical and the horizontal axis are on a nondimensional scale. The time scale of the horizontal axis almost corresponds to the real scale of

The mechanism of the generation of strong winds generated in Ogimachi, Saga Prefecture caused by Typhoon 0423 was investigated using a nonstationary and nonlinear wind-synopsis simulator, RIAMM-COMPACT. Furthermore, a discussion was conducted about how the difference of terrain reproducibility, grid resolution, which is required for the reproduction of these topographic strong winds, affects the calculation result. The findings obtained in this research are as follows:

1) The direction of the wind at the time when the damage was caused by Typhoon 0423 ranged from northeast to north-northwest, and it was shown that the Tenzan Mountains located in the north side of Ogimachi had an influence on that.

2) It was observed that there is a small basin in the mountain terrain in the upper stream of Ogimachi and all flows were converging there. In other words, it became clear that it is highly possible that the strong winds that were generated in the areas surrounding Ogimachi were caused by wind flows converging to a small basin of mountain terrain in the upper stream and formed a gap flow.

3) It was shown that a horizontal resolution of 50 - 100 m is required for the reproducibility of local-scale terrain.

This work is an update of the previous conference abstract [

This work was supported by JSPS KAKENHI Grant Number 17H02053.

The author declares no conflict of interest.

Uchida, T. (2019) Numerical Prediction of Strong Wind Induced by Topographic Effect. Open Journal of Fluid Dynamics, 9, 224-240. https://doi.org/10.4236/ojfd.2019.93015