Large-Eddy Simulations with an Immersed Boundary Method: Pollutant Dispersion over Urban Terrain

Round 1

Reviewer 1 Report

Review of “Large-eddy simulations with an immersed boundary method: pollutant dispersion over urban terrain” by Auguste et al.

This study investigates the plume dispersion during an intense pollutant episode caused by a major explosion at Toulouse city (France) using Large-eddy simulations (LES). The LES is coupled with an Immersed Boundary Method (IBM) to directly represent the drag induced by the 3D shape of buildings and hills on the flow. The results show the potential of the IBM method to capture complex pollutant plumes in real urban areas. The manuscript is generally well-written and presents interesting insights in the numerical modeling over the complex urban area. I recommend publication with minor review.

Major suggestions and comments:

Most of the buildings in the domain are between 5 and 10 m and the spatial grid resolution in the vertical direction is 2 m below 100 m. Then for most area, there are only 2 to 5 points to resolve the urban canopy in the vertical direction. Because the goal of this study is to demonstrate the potential of the IBM in urban applications, it’s important for the authors to prove that this (relatively low) resolution for the urban canopy is enough to resolve the flow features (e.g. horseshow vortex, flow separations/reattachments) around buildings. For Figure 5, the authors over-stated that “All the schemes match the -5/3 well” in line 291. In fact, most cases only have very a short part paralleling to the -5/3 slope and the slope is smaller than -5/3 at high wavenumbers (of which wavelength is still larger than the dissipation range). For some cases, energy accumulation is found at the highest wavenumber. These phenomena need to be explained. The incoming turbulence is initialized in the upstream of the study area. What is the fetch for turbulence to fully develop from the inflow boundary? Does the turbulence reach quasi-stationary state before it enters the interested urban area? The author claimed that the polynomial fit should work better than the exponential fit for the concentration level function of the exposure time. However, only the result of the exponential fit is shown. A comparison between polynomial fit and exponential fit needs to be done to reach such a conclusion.

Minor suggestions and comments:

The authors stated “four runs are realized per set of simulations using various advection schemes” to represent the chaotic nature of the atmosphere turbulence in line 255. However, the essential difference among four runs are not given. Descriptions about the notations for resolved wind, wind fluctuations, subgrid TKE, average methods in subsection 5.1 are not clear.

Comments for author File: Comments.pdf

Author Response

We thank Reviewer 1 for her/his careful and constructive review. The revised manuscript takes into account her/his comments in consideration. Answers to the different comments and questions (in blue) are presented in this document (in dark).

This study investigates the plume dispersion during an intense pollutant episode caused by a major

explosion at Toulouse city (France) using Large-eddy simulations (LES). The LES is coupled with an Immersed Boundary Method (IBM) to directly represent the drag induced by the 3D shape of buildings and hills on the flow. The results show the potential of the IBM method to capture complex pollutant plumes in real urban areas. The manuscript is generally well-written and presents

interesting insights in the numerical modeling over the complex urban area. I recommend publication with minor review.

Major suggestions and comments:

1. Most of the buildings in the domain are between 5 and 10 m and the spatial grid resolution in the

vertical direction is 2 m below 100 m. Then for most area, there are only 2 to 5 points to resolve the urban canopy in the vertical direction. Because the goal of this study is to demonstrate the potential of the IBM in urban applications, it’s important for the authors to prove that this (relatively low) resolution for the urban canopy is enough to resolve the flow features (e.g. horseshow vortex, flow separations/reattachments) around buildings.

The first paper (Auguste et al., 2019) has shown that a high vertical resolution allows the reproduction of these flow features. The study of an isolated cube in a turbulent flow demonstrated that 8 points per side are sufficient to capture the main swirling structure (but not the secondary ones). The wake of buildings higher than 15 m can be considered well represented. The wake of lower buildings would be under resolved. However, the objective here was to simulate the overall impact of the entire city and the friction effect, but not the specific flow in each canyon. The grid-nesting capability of Meso-NH would allow to refine the grid and to focus on some local effects for a specific location. But it is out of the scope of this paper.

In the MNH-IBM grid, we have added this comment (in red):

« We use a cartesian grid, isotropic for z lower than 100 m with a spatial grid resolution Dx = Dy = Dz =2 m. Above 100 m, the mesh increases gradually in the vertical direction with a stretching of 1.05. The flow features (e.g. horseshow vortex, flow separations/reattachments) around buildings lower than 15 m could be considered vertically underresolved with this vertical resolution, but the objective here is to simulate the overall impact of the entire city and the friction effect, and not the specific flow in each canyon.»

2. For Figure 5, the authors over-stated that “All the schemes match the -5/3 well” in line 291. In fact, most cases only have very a short part paralleling to the -5/3 slope and the slope is smaller than -5/3 at high wavenumbers (of which wavelength is still larger than the dissipation range).

This part has been corrected (addition in red) :

« All the schemes match the -5/3 slope well at wavelengths higher than the effective resolution (i.e. the scale from which the model departs from the -5/3 slope, according to Skamarock (2004)). But the sensitivity of numerical schemes acting far from the immersed interface exhibits significant differences in terms of effective resolution (i.e. the scale from which the model departs from the -5/3 slope, according to Skamarock2004)... »

For some cases, energy accumulation is found at the highest wavenumber. These phenomena need to be explained.

This point was already discussed, but an added sentence is proposed (in red) :

« Concerning the scheme used near the immersed interface, C4/C2 and C4/W3 are very similar, except in the BL (Fig.~\ref{spec}-top) and near the cut-cell scale, where an energy increase can be found with C2. This increase is related to an energy accumulation generated at the immersed interfaces, due to a too low numerical diffusion. A higher numerical diffusion would be better appropriate to filter the 2 Dx numerical mode. Nevertheless, this increase remains weak and does not spread over the largest scales. In the same way, a similar energy increase is observed above the BL due to a too low artificial diffusion associated with C4. »

3. The incoming turbulence is initialized in the upstream of the study area. What is the fetch for turbulence to fully develop from the inflow boundary? Does the turbulence reach quasi- stationary state before it enters the interested urban area?

The fetch is about 3 km upstream of the release point. Hills of about 100 m depth upstream created strong turbulence.

An initial preliminary run with IBM and without release considering stationary large-scale conditions was performed to establish a turbulent state. During this run, the enstrophy, spatially integrated in the studied zone, increased up to a quasi-stationary value corresponding to a saturation value. This characteristic time of saturation was about 15 min. The four minutes following this saturation provided the R1 to R4 initial conditions.

This point has been clarified in The incoming turbulence paragraph, and is presented before in the paper.

4. The author claimed that the polynomial fit should work better than the exponential fit for the concentration level function of the exposure time. However, only the result of the exponential fit is shown. A comparison between polynomial fit and exponential fit need to be done to reach such a conclusion.

The objective was not to propose a general law of the time exposure but to illustrate possible future investigation. Therefore we propose to remove this comment relative to a polynomial fit.

« This formula gives an insight: when the velocity decreases, the diameter increases and the exposure time is longer. Note that the exponential fit is not optimal and a polynomial decrease should fit better. »

Minor suggestions and comments:

1. The authors stated “four runs are realized per set of simulations using various advection schemes” to represent the chaotic nature of the atmosphere turbulence in line 255. However, the essential difference among four runs are not given.

You are right that this part needed to be clarified.

Some modifications have been introduced to clarify this point.

2. Descriptions about the notations for resolved wind, wind fluctuations, subgrid TKE, average

methods in subsection 5.1 are not clear.

You are right that the mathematical notations are a bit tricky. We have removed a part of them.

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper entitled
"Large-eddy simulations with an immersed boundary method: pollutant dispersion over urban terrain"
presents a very good and thorough study of an IBM method that could be combined with LES for urban applications. 

The paper is very well written, and I particularly like the thorough description of the levelset methods in the Appendix, which could have been a paper in itself. 

The interesting part of the paper itself deals with the different convection schemes, I am still wondering what would be the benefit of using the WENO schemes for this kind of application, where it is very unlikely that shocks would occur however. 

I accept the paper for publication. 

Author Response

We thank Reviewer 2 for her/his comments and approval.