LES Intercomparison Study for Neutral Boundary Layers: Vertical Cross-Sectional Views

Last updated: May 2026

Case Description: This notebook shows vertical (x-z and y-z plane) cross-sections of the velocity components (\(u\), \(v\), \(w\)) from the modified Andren et al. (1994) neutral boundary layer case. The x-z slices are extracted at three spanwise locations (\(0.25\,L_y\), \(0.5\,L_y\), \(0.75\,L_y\)); the y-z slice is extracted at \(0.5\,L_x\). The 3D fields are sampled at the end of the simulation (~80 h). The reference run is 128x128x128_LASDD_SM_SP.

Load the necessary packages

import numpy as np
import matplotlib.pyplot as plt
from pathlib import Path

Input & Output Directories

# Base directory (jaxalfa/)
def find_repo_root(start=None):
    path = Path(start or ('__file__' in globals() and __file__) or Path.cwd()).resolve()
    for candidate in (path, *path.parents):
        if (candidate / 'examples').is_dir() and (candidate / 'docs').is_dir():
            return candidate
    raise FileNotFoundError('Could not locate jaxalfa repository root')

BaseDir = find_repo_root()

# Reference run: 128x128x128 LASDD-SM single precision
RunDir    = BaseDir / 'examples/NBL_A94/runs/128x128x128_LASDD_SM_DP'
OutputDir = RunDir / 'output'

cfg = {}
exec((RunDir / 'Config.py').read_text(), cfg)

Load 3D fields from T = 80 h

T_snapshot = float(cfg['SimTime'])
dt = float(cfg['dt'])
iter_3D = int(T_snapshot / dt)
field_path = OutputDir / f'ALFA_3DFields_Iteration_{iter_3D}.npz'

if field_path.exists():
    File3D = np.load(field_path)
    u3D  = File3D['u']
    v3D  = File3D['v']
    w3D  = File3D['w']
else:
    nx = int(cfg['nx']); ny = int(cfg['ny']); nz = int(cfg['nz'])
    print(f'Missing {field_path}; plotting NaN placeholders for this run.')
    u3D = np.full((nx, ny, nz), np.nan)
    v3D = np.full((nx, ny, nz), np.nan)
    w3D = np.full((nx, ny, nz), np.nan)

Input Information from the Config File

l_x = float(cfg['l_x'])
l_y = float(cfg['l_y'])
l_z = float(cfg['l_z'])
z_damping = float(cfg.get('z_damping', np.nan))
SimTime = float(cfg['SimTime'])

nx = int(cfg['nx'])
ny = int(cfg['ny'])
nz = int(cfg['nz'])
dx = l_x / nx
dy = l_y / ny
dz = l_z / (nz - 1)
x_axis = dx * np.arange(nx)
y_axis = dy * np.arange(ny)

Derived Variables

# Half levels for u, v, TH variables
z_u = np.array([(k + 0.5) * l_z / (nz - 1) for k in range(nz)])

# Full levels for w
z_w = np.array([k * l_z / (nz - 1) for k in range(nz)])

plt.rcParams.update({
    "text.usetex": True,
    "font.size": 14,
    "axes.labelsize": 16,
    "xtick.labelsize": 12,
    "ytick.labelsize": 12
})

Plot vertical (x-z) cross-section of longitudinal velocity fields

The start of the damping layer is shown by dotted lines.

fig, axes = plt.subplots(3, 1, figsize=(8, 14), constrained_layout=True)

# Selected cross-sections at 0.25*l_y, 0.5*l_y, and 0.75*l_y
j_levels = [int(ny/4), int(ny/2), int(ny*3/4)]

for i, j in enumerate(j_levels):
    im = axes[i].pcolor(x_axis, z_u, u3D[:,j,:].T, cmap='inferno')
    axes[i].set_title(f'Longitudinal Velocity at Y = {j * dy:.1f} m', fontsize=12)
    axes[i].set_xlabel('X (m)')
    axes[i].set_ylabel('Z (m)')
    axes[i].set_aspect('auto')
    axes[i].axhline(y=z_damping, color='k', linestyle=':', linewidth=1.5)
    fig.colorbar(im, ax=axes[i], label='u (m/s)')

plt.suptitle('Simulation: 128x128x128 (LASDD-SM, SP)', fontsize=16)
plt.show()

Plot vertical (x-z) cross-section of lateral velocity fields

The start of the damping layer is shown by dotted lines.

fig, axes = plt.subplots(3, 1, figsize=(8, 14), constrained_layout=True)

# Selected cross-sections at 0.25*l_y, 0.5*l_y, and 0.75*l_y
j_levels = [int(ny/4), int(ny/2), int(ny*3/4)]

for i, j in enumerate(j_levels):
    im = axes[i].pcolor(x_axis, z_u, v3D[:,j,:].T, cmap='inferno')
    axes[i].set_title(f'Lateral Velocity at Y = {j * dy:.1f} m', fontsize=12)
    axes[i].set_xlabel('X (m)')
    axes[i].set_ylabel('Z (m)')
    axes[i].set_aspect('auto')
    axes[i].axhline(y=z_damping, color='k', linestyle=':', linewidth=1.5)
    fig.colorbar(im, ax=axes[i], label='v (m/s)')

plt.suptitle('Simulation: 128x128x128 (LASDD-SM, SP)', fontsize=16)
plt.show()

Plot vertical (x-z) cross-section of vertical velocity fields

The start of the damping layer is shown by dotted lines.

fig, axes = plt.subplots(3, 1, figsize=(8, 14), constrained_layout=True)

# Selected cross-sections at 0.25*l_y, 0.5*l_y, and 0.75*l_y
j_levels = [int(ny/4), int(ny/2), int(ny*3/4)]

for i, j in enumerate(j_levels):
    im = axes[i].pcolor(x_axis, z_w, w3D[:,j,:].T, cmap='inferno')
    axes[i].set_title(f'Vertical Velocity at Y = {j * dy:.1f} m', fontsize=12)
    axes[i].set_xlabel('X (m)')
    axes[i].set_ylabel('Z (m)')
    axes[i].set_aspect('auto')
    axes[i].axhline(y=z_damping, color='k', linestyle=':', linewidth=1.5)
    fig.colorbar(im, ax=axes[i], label='w (m/s)')

plt.suptitle('Simulation: 128x128x128 (LASDD-SM, SP)', fontsize=16)
plt.show()

Plot vertical (y-z) cross-section at :math:`X = 0.5,L_x`

The start of the damping layer is shown by dotted lines.

fig, axes = plt.subplots(1, 3, figsize=(18, 5), constrained_layout=True)

# y-z slice at mid-domain in x
i_slice = int(nx/2)

fields = [
    (u3D[i_slice,:,:].T,  z_u, 'Longitudinal Velocity', 'u (m/s)'),
    (v3D[i_slice,:,:].T,  z_u, 'Lateral Velocity',      'v (m/s)'),
    (w3D[i_slice,:,:].T,  z_w, 'Vertical Velocity',     'w (m/s)'),
]

for ax, (field, z_axis, title, clabel) in zip(axes, fields):
    im = ax.pcolor(y_axis, z_axis, field, cmap='inferno')
    ax.set_title(f'{title} at X = {i_slice * dx:.1f} m', fontsize=12)
    ax.set_xlabel('Y (m)')
    ax.set_ylabel('Z (m)')
    ax.set_aspect('auto')
    ax.axhline(y=z_damping, color='k', linestyle=':', linewidth=1.5)
    fig.colorbar(im, ax=ax, label=clabel)

plt.suptitle('Simulation: 128x128x128 (LASDD-SM, SP)', fontsize=16)
plt.show()