3.4 Local Winds

Local winds are driven by local heating differences rather than large-scale pressure systems. They include sea breezes, mountain-valley winds, and thermally-driven circulations.

Sea/Land Breeze

Sea Breeze (Day)

Land heats faster → rising air over land → low pressure → onshore flow from sea

Typically develops mid-morning, peaks afternoon

Land Breeze (Night)

Land cools faster → sinking air over land → high pressure → offshore flow

Weaker than sea breeze, develops after midnight

Solenoidal (Thermal Circulation) Term

$$\frac{D\Gamma}{Dt} = -\oint \frac{1}{\rho}\nabla p \cdot d\vec{l} = -\oint \alpha\, dp$$

Circulation generated when density and pressure surfaces are misaligned (differential heating)

Sea Breeze Pressure Perturbation

$$\Delta p' \approx \rho\, g\, \Delta z \approx \rho\, g\, H\frac{\Delta T}{T}$$

Hydrostatic pressure difference from differential heating over depth $H$

Mountain-Valley Winds

Anabatic (Upslope) Wind

Daytime: Sun heats mountain slopes → warm air rises → upslope flow

Katabatic (Downslope) Wind

Nighttime: Radiative cooling on slopes → dense cold air drains downhill

Can be very strong over ice sheets (Antarctica: 300 km/h!)

Froude Number for Mountain Flows

$$Fr = \frac{U}{NH}$$

$N$ = Brunt-Vaisala frequency, $H$ = mountain height. $Fr < 1$: flow blocked; $Fr > 1$: flow goes over

Mountain Wave Vertical Wavelength

$$\lambda_z = \frac{2\pi U}{N}$$

Vertically propagating gravity waves forced by flow over topography

Foehn & Chinook Winds

Warm, dry winds on the lee side of mountains. Air forced over mountains loses moisture on the windward side (precipitation), then warms at the dry adiabatic rate descending.

Foehn Warming Calculation

$$\Delta T = (\Gamma_d - \Gamma_m)\,\Delta z$$

$\Gamma_d \approx 9.8$ K/km (dry adiabatic), $\Gamma_m \approx 6$ K/km (moist adiabatic), $\Delta z$ = mountain height

Hydraulic Jump Condition

$$Fr_{local} = \frac{U_{local}}{\sqrt{g'h}} > 1 \quad \Rightarrow \quad \text{supercritical flow, hydraulic jump possible}$$

Rapid deceleration on lee side dissipates kinetic energy as turbulence

Foehn

Alps (Europe)

Chinook

Rocky Mountains (N. America)

Santa Ana

Southern California

Interactive Simulation: Sea Breeze Circulation Model

Python

Models the diurnal cycle of land-sea temperature contrast and the resulting sea/land breeze circulation. Shows temperature time series, thermal contrast, hydrostatic pressure perturbation, and wind reversal through the day-night cycle.

sea_breeze_model.py83 lines

import numpy as np
import matplotlib.pyplot as plt

# Diurnal cycle: 24 hours
hours = np.linspace(0, 24, 300)

# Land and sea temperature models
T_sea = 20 + 1.5 * np.sin(2 * np.pi * (hours - 14) / 24)   # small amplitude
T_land = 20 + 8.0 * np.sin(2 * np.pi * (hours - 14) / 24)  # large amplitude
delta_T = T_land - T_sea

# Sea breeze wind: proportional to temperature contrast
# Positive = onshore (sea to land), negative = offshore (land breeze)
rho = 1.2; g = 9.81; H = 1000; T_mean = 293
# Simplified pressure perturbation and wind
dp = rho * g * H * delta_T / T_mean  # Pa
wind = 0.15 * delta_T  # simplified scaling (m/s)

fig, axes = plt.subplots(2, 2, figsize=(13, 9))
fig.patch.set_facecolor('#0f172a')
for ax in axes.flat:
    ax.set_facecolor('#1e293b')
    ax.tick_params(colors='#cbd5e1')
    for spine in ax.spines.values():
        spine.set_color('#334155')
    ax.grid(True, color='#334155', alpha=0.4)
    ax.set_xlim(0, 24)
    ax.set_xticks(np.arange(0, 25, 3))

# Panel 1: Temperature time series
ax1 = axes[0, 0]
ax1.plot(hours, T_land, color='#f87171', linewidth=2.5, label='Land')
ax1.plot(hours, T_sea, color='#38bdf8', linewidth=2.5, label='Sea')
ax1.set_xlabel('Hour of day', color='#cbd5e1')
ax1.set_ylabel('Temperature (C)', color='#cbd5e1')
ax1.set_title('Land & Sea Temperature', color='#cbd5e1', fontsize=12)
ax1.legend(fontsize=9, facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1')
ax1.axvspan(6, 18, alpha=0.07, color='#fbbf24', label='Daytime')

# Panel 2: Temperature difference
ax2 = axes[0, 1]
ax2.plot(hours, delta_T, color='#a78bfa', linewidth=2.5)
ax2.fill_between(hours, 0, delta_T, where=delta_T > 0, color='#f87171', alpha=0.2, label='Land warmer')
ax2.fill_between(hours, 0, delta_T, where=delta_T < 0, color='#38bdf8', alpha=0.2, label='Sea warmer')
ax2.axhline(y=0, color='#cbd5e1', linewidth=0.8)
ax2.set_xlabel('Hour of day', color='#cbd5e1')
ax2.set_ylabel('T_land - T_sea (K)', color='#cbd5e1')
ax2.set_title('Land-Sea Temperature Contrast', color='#cbd5e1', fontsize=12)
ax2.legend(fontsize=8, facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1')

# Panel 3: Pressure perturbation
ax3 = axes[1, 0]
ax3.plot(hours, dp, color='#34d399', linewidth=2.5)
ax3.fill_between(hours, 0, dp, where=dp > 0, color='#f87171', alpha=0.15)
ax3.fill_between(hours, 0, dp, where=dp < 0, color='#38bdf8', alpha=0.15)
ax3.axhline(y=0, color='#cbd5e1', linewidth=0.8)
ax3.set_xlabel('Hour of day', color='#cbd5e1')
ax3.set_ylabel('Pressure perturbation (Pa)', color='#cbd5e1')
ax3.set_title('Hydrostatic Pressure Perturbation', color='#cbd5e1', fontsize=12)

# Panel 4: Wind speed
ax4 = axes[1, 1]
ax4.plot(hours, wind, color='#fbbf24', linewidth=2.5)
ax4.fill_between(hours, 0, wind, where=wind > 0, color='#f87171', alpha=0.15, label='Sea breeze (onshore)')
ax4.fill_between(hours, 0, wind, where=wind < 0, color='#38bdf8', alpha=0.15, label='Land breeze (offshore)')
ax4.axhline(y=0, color='#cbd5e1', linewidth=0.8)
ax4.set_xlabel('Hour of day', color='#cbd5e1')
ax4.set_ylabel('Wind speed (m/s)', color='#cbd5e1')
ax4.set_title('Sea/Land Breeze Wind', color='#cbd5e1', fontsize=12)
ax4.legend(fontsize=8, facecolor='#1e293b', edgecolor='#334155', labelcolor='#cbd5e1')

plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor=fig.get_facecolor())

print("=== Sea Breeze Circulation Model ===")
print(f"Max land temp: {T_land.max():.1f} C at ~14:00")
print(f"Max sea temp:  {T_sea.max():.1f} C at ~14:00")
print(f"Max contrast:  {delta_T.max():.1f} K (land warmer, afternoon)")
print(f"Min contrast:  {delta_T.min():.1f} K (sea warmer, night)")
print(f"Max sea breeze wind: {wind.max():.1f} m/s (onshore)")
print(f"Max land breeze wind: {abs(wind.min()):.1f} m/s (offshore)")
print(f"Max pressure perturbation: {dp.max():.1f} Pa")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

← 3.3 Boundary Layer Part 4: Synoptic Meteorology →