Slantwise convection is the process by which conditional symmetric instability (CSI) is released. During this process, the unstable air mass (strictly speaking, an "air tube"; see below) is driven by an acceleration in a slanted direction as a result of both horizontal and vertical forces. This fundamentally differs from the free upright (gravitational) convection, the latter of which is related to the release of conditional static/gravitational instability and is driven by the buoyancy force in the vertical direction.
Although the upright convection can become tilted under the influence of strong vertical wind shear, it is not equal to slantwise convection.
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This type of instability often exists in baroclinic environments where the temperature gradient/vertical wind shear is strong. Below is the schematic plot of CSI on a y-z plane (a vertical cross-section). We define the direction from WARM to COOL (reverse of temperature gradient) as the y-axis. The strong temperature gradient indicates a zonal wind increasing with height and the shear (thermal wind) pointing outward from the screen. CSI is identified in the area where the saturated equivalent potential temperature surfaces are sloped more steeply than the geostrophic absolute momentum (M) surfaces in this plane. If a hypothetical air tube (extending infinitely along the x-axis) is lifted at a slope between these two surfaces, the saturated equivalent potential temperature of the air tube (quasi-conserved) would become higher than that of the surrounding environment, thus it would experience a positive vertical buoyancy force. Horizontally, the geostrophic absolute momentum of the air tube (quasi-conserved) becomes lower than that of the surrounding environment, thus experiencing a positive horizontal inertial force due to the imbalance between pressure gradient force and Coriolis force.
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Note that different from the gravitational convection tilted by the vertical wind shear, the tilting direction of slantwise convection (i.e., the direction of the net accelerating force) is not along but 90 degree counterclockwise of the vertical wind shear.
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Analogous to CAPE for upright convection, the maximum convective potential energy for slantwise convection, SCAPE, can be defined by taking the integral of the positive buoyancy along the geostrophic absolute momentum surface (instead of vertically), as shown by the yellow shading below. In a barotropic environment, M surfaces are vertically tilted, and thus the formula of SCAPE is equivalent to that of CAPE.
If we then move from the 2-D to the 3-D world, the unstable air tube (extended along the x-axis) results in the often observed banded structure of slantwise convection in midlatitudes. These bands are generally in parallel with the local vertical wind shear (thermal wind). The term "symmetric instability" comes from its theoretic 2D nature with the assumption that the feature is symmetric with respect to the y-axis in the above schematic plot.
References:
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Markowski, P. M. and Y. P. Richardson, 2010: Mesoscale meteorology in midlatitudes. Wiley-Blackwell, 424 pp.
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Schultz, D. M., and P. N. Schumacher, 1999: The use and misuse of conditional symmetric instability. Mon. Wea. Rev.,
127, 2709–2732, https://doi.org/10.1175/1520-0493(1999)127,2709:TUAMOC.2.0.CO;2.
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