Conditional symmetric instability, or CSI, is a form of convective instability in a fluid subject to temperature differences in a uniform rotation frame of reference while it is thermally stable in the vertical and dynamically in the horizontal (inertial stability). The instability in this case develop only in an inclined plane with respect to the two axes mentioned and that is why it can give rise to a so-called "slantwise convection" if the air parcel is almost saturated and moved laterally and vertically in a CSI area. This concept is mainly used in meteorology to explain the mesoscale formation of intense precipitation bands in an otherwise stable region, such as in front of a warm front. The same phenomenon is also applicable to oceanography.

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 (${\displaystyle \theta _{e}}$):

In the same way, a lateral displacement of an air particle changes its absolute vorticity ${\displaystyle \eta }$. This is given by the sum of the planetary vorticity, ${\displaystyle f}$, and ${\displaystyle \zeta }$, the geostrophic (or relative) vorticity of the parcel:

Where :

${\displaystyle \eta }$ 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 ${\displaystyle \eta }$ is close to zero. Since ${\displaystyle f}$ is always positive, ${\displaystyle \eta \leq 0}$ 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.

The variation of the angular momentum indicate the stability:

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 (${\displaystyle \scriptstyle M_{g}}$) that increase from left to right and equivalent potential temperature (${\displaystyle \scriptstyle \theta _{e}}$) that increase with height.