Hydrostatic stability (in red) and
dew point (in green) on a
Skew-T log-P diagram. An air particle at a certain altitude will be stable if its adiabatically modified temperature during an ascent is equal to or cooler than the environment. Similarly, it is stable if its temperature is equal or warmer during a descent. In the case where the temperature is equal, the particle will remain at the new altitude, while in the other cases, it will return to its initial level4. In the diagram on the right, the yellow line represents a raised particle whose temperature remains at first under that of the environment (stable air) which entails no convection. Then in the animation, there is warming surface warming and the raised particle remains warmer than the environment (unstable air). A measure of hydrostatic stability is to record the variation with the vertical of the
equivalent potential temperature (\theta_e): ::*
If \theta_e diminish with altitude leads to unstable airmass ::*
If \theta_e remains the same with altitude leads to neutral airmass ::*
If \theta_e increase with altitude leads to stable airmass. Inertial stability In the same way, a lateral displacement of an air particle changes its absolute vorticity \eta. This is given by the sum of the planetary vorticity, f, and \zeta, the
geostrophic (or relative) vorticity of the parcel: {{center|\eta= \left[ \frac{\partial v}{\partial x} - \frac{\partial u}{\partial y} \right ] + f = \zeta + f \qquad \qquad }} Where : • v and u are the meridional and zonal geostrophic velocities respectively. • x and y correspond to the zonal and meridional coordinates. •
f is the
Coriolis parameter, which describes the component of vorticity around the local vertical that results from the rotation of the reference frame. •
\zeta is the relative vorticity around the local vertical. It is found by taking the vertical component of the curl of the geostrophic velocity. \eta can be positive, null or negative depending on the conditions in which the move is made. As the absolute vortex is almost always positive on the
synoptic scale, one can consider that the atmosphere is generally stable for lateral movement. Inertial stability is low only when \eta is close to zero. Since f is always positive, \eta \le 0 can be satisfied only on the anticyclonic side of a strong maximum of
jet stream or in a
barometric ridge at altitude, where the derivative velocities in the direction of displacement in the equation give a significant negative value. • \Delta M_g = 0 , the particle then remains at the new position because its momentum has not changed • \Delta M_g > 0 , the particle returns to its original position because its momentum is greater than that of the environment • \Delta M_g , the particle continues its displacement because its momentum is smaller than that of the environment.
Slantwise movement Under certain stable hydrostatic and inertial conditions, slantwise displacement may, however, be unstable when the particle changes air mass or wind regime. The figure on the right shows such a situation. The displacement of the air particle is done with respect to kinetic moment lines (\scriptstyle M_g) that increase from left to right and equivalent potential temperature (\scriptstyle \theta_e) that increase with height. ;Lateral movement A Horizontal accelerations (to the left or right of a surface \scriptstyle M_g ) are due to an increase/decrease in the \scriptstyle M_g of the environment in which the particle moves. In these cases, the particle accelerates or slows down to adjust to its new environment. Particule A undergoes a horizontal acceleration that gives it positive
buoyancy as it moves to colder air and decelerates as it moves to a region of smaller \scriptstyle M_g . The particle rises and eventually becomes colder than its new environment. At this point, it has negative buoyancy and begins to descend. In doing so, \scriptstyle M_g increases and the particle returns to its original position. ;Vertical displacement B Vertical movements in this case result in negative buoyancy as the particle encounters warmer air ( \scriptstyle \theta_e increases with height) and horizontal acceleration as it moves to larger surfaces \scriptstyle M_g . As the particle goes down, its \scriptstyle M_g decreases to fit the environment and the particle returns to B. ; Slantwise displacement C Only case C is unstable. Horizontal acceleration combines with a vertical upward disturbance and allows oblique displacement. Indeed, the \scriptstyle \theta_e of the particle is larger than the \scriptstyle \theta_e of the environment. While the momentum of the particle is less than that of the environment. An oblique displacement thus produces a positive buoyancy and an acceleration in the oblique displacement direction which reinforces it. The condition for having conditional symmetric instability in an otherwise stable situation is therefore that: • the slope of \scriptstyle \theta_e is greater than that of \scriptstyle M_g • Laterally displaced air is almost saturated. ==Potential effects==