Interactive simulation of wind-induced near-inertial motions and their biogeochemical impacts by Claudio Iturra
Momentum Equations with Coriolis Effect:
$$\frac{\partial u}{\partial t} - fv = -\frac{1}{\rho}\frac{\partial p}{\partial x} + \frac{\tau_x}{\rho h}$$
$$\frac{\partial v}{\partial t} + fu = -\frac{1}{\rho}\frac{\partial p}{\partial y} + \frac{\tau_y}{\rho h}$$
Where: $f = 2\Omega \sin(\phi)$ is the Coriolis parameter
$$f = 2\Omega \sin(\phi) = 1.458 \times 10^{-4} \sin(\phi) \text{ rad/s}$$
Inertial Period: $T_i = \frac{2\pi}{f} = \frac{2\pi}{2\Omega \sin(\phi)}$
When wind stress acts on the ocean surface, it generates currents that are deflected by the Coriolis force. This creates circular or elliptical motion at the inertial frequency.
Key Process: Wind → Surface stress → Momentum input → Coriolis deflection → Inertial oscillations
Sea-land breeze cycles create periodic wind stress that can resonantly excite near-inertial motions when the wind frequency matches the local inertial frequency.
Resonance Condition: $\omega_{wind} \approx f$
Storms provide impulsive wind stress that efficiently generates near-inertial oscillations. The rotating wind field of storms can particularly enhance these motions.
Energy Input: Proportional to $|\tau|^2$ where $\tau$ is wind stress
Near-inertial oscillations enhance vertical mixing, affecting:
In coastal regions, near-inertial oscillations interact with:
Current Settings:
Latitude: 35°
Inertial Period: 20.1 hours
Wind Pattern: Diurnal
Max Wind Speed: 10 m/s
Near-inertial oscillations increase vertical shear, leading to enhanced turbulent mixing. This breaks down stratification and promotes vertical exchange of heat, salt, and biogeochemical tracers.
The oscillatory motion creates a "nutrient pump" effect, bringing nutrient-rich deep water to the euphotic zone, supporting primary productivity in coastal ecosystems.
Enhanced mixing affects oxygen distribution, potentially alleviating hypoxic conditions in coastal waters or, conversely, increasing oxygen consumption through enhanced biological activity.
Near-inertial mixing influences carbon export by affecting particle aggregation, sinking rates, and the efficiency of the biological pump in coastal regions.