Questions: 1. (10 pts total). A supercell thunderstorm is defined as a convective storm that has a quasisteady, rotating updraft (mesocyclone). Both cyclonic and anti-cyclonic rotating supercells are physically possible. This is actually observed in nature, often early in the mesocyclogenesis process, when two opposing, rotating updrafts develop nearly simultaneously. Eventually, the convective storm splits into a "right-moving" or cyclonic supercell, and a "left-moving" or anticyclonic supercell. Typically, the left-mover dissipates fairly quickly while the right-mover becomes dominant. Answer the following questions concerning supercells. a.) ( 5 pts). What type of horizontal force balance applies in supercells? Using this, explain why both cyclonic and anti-cyclonic rotation is possible by using words, math (i.e., equations and sign analyses), and diagrams. b.) ( 5 pts ). Use the concept of vorticity tilting to explain how both cyclonic and anticyclonic rotation develops. Assume that horizontal winds increase with height (i.e., vertical wind shear), and the storm updraft is associated with a maximum in upward vertical motion (i.e., w increases across some horizontal distance approaching the updraft core and decreases moving away from the core). Answer this by using words, math, and diagrams.

Solution Steps

In supercells, the primary horizontal force balance is the geostrophic balance, which involves the Coriolis force and the pressure gradient force. This balance can be expressed as:

\[ f \mathbf{v} = -\frac{1}{\rho} \nabla p \]

where \( f \) is the Coriolis parameter, \( \mathbf{v} \) is the wind velocity, \( \rho \) is the air density, and \( \nabla p \) is the pressure gradient. In a supercell, the rotation (mesocyclone) is influenced by this balance, allowing for both cyclonic and anticyclonic rotations. The Coriolis force can act in either direction depending on the hemisphere, enabling both types of rotation.

Cyclonic rotation is counterclockwise in the Northern Hemisphere, while anticyclonic rotation is clockwise. The geostrophic balance allows for both rotations because the Coriolis force can deflect winds to the right (in the Northern Hemisphere) or left (in the Southern Hemisphere), depending on the initial conditions and the pressure gradient. This dual possibility is why both cyclonic and anticyclonic rotations can develop in supercells.

Vorticity tilting is a key process in the development of rotation within supercells. Vertical wind shear, where horizontal winds increase with height, creates horizontal vorticity. As the storm's updraft intensifies, it tilts this horizontal vorticity into the vertical, contributing to the development of a rotating updraft.

Mathematically, the vorticity equation can be expressed as:

\[ \frac{D\boldsymbol{\omega}}{Dt} = (\boldsymbol{\omega} \cdot \nabla) \mathbf{v} + \text{tilting} + \text{stretching} + \text{baroclinic} \]

The tilting term is crucial here, as it represents the conversion of horizontal vorticity into vertical vorticity. The updraft's vertical motion (\( w \)) increases across a horizontal distance towards the updraft core, enhancing the tilting effect and leading to both cyclonic and anticyclonic rotations.

Final Answer