where Vag is the transverse ageostrophic component of the geostrophic wind. Large parcel divergence and RoL greater than 0.5 have been shown to occur as a jet streak approaches a highly diffluent area in mesoscale model simulations.
The existence of large parcel divergence violates the nonlinear balance equation.
1 2 3 4
where the terms are the Laplacian of geopotential (1), the Jacobian
of the winds (2), the vorticity term (3) and the beta effect term (4).
Gravity waves are often seen emanating from these regions of diagnosed imbalance.
Click here for a schematic of the key points a forecaster must consider to determine unbalanced flow and evaluate wave ducting mechanisms
The Role of Wave-Ducting Processes in Gravity Wave Maintenance
Click here to access a prototype sounding which illustrates the wave ducting mechanism.
In order to have sufficient wave ducting you need the following mechanisms
Where the terms are the wave phase (1) and the ducted phase speeds divided by the Brunt-Vaisala frequency number (2).
The efficiency of a ducting mechanism must also be taken into consideration through the Duct factor equation.
p1=lowest pressure level taken at or near the
ground (typically 950 mb, the default value) - Potential temperature @
p2=pressure level of top of low-level stable duct layer (default = 800 mb, but adjustable, depending upon inspection of soundings for the day) - Potential temperature @ p2 used
p3=pressure level of bottom of conditionally unstable layer (default = 800 mb, but often higher is better, depending upon inspection of soundings for the day) - Equivalent Potential temperature @ p3 used
p4=pressure level of top of conditionally unstable layer (often the tropopause, or use 400 mb default) - Equivalent Potential temperature @ p4 used
The reasoning behind this easily calculated parameter is than an efficient duct, according to the linear theory of Lindzen and Tung (1976) is one in which there exists a conditionally unstable layer (800-400 mb) above a very stable surface based layer (950-800 mb).
Schneider (1990) and Koch and O'Handley (1997) found that maximum wave amplitude occurs in regions where weak mid-level static stability overlaid a strong stable layer. Rapid amplification of a wave occurred as it entered a region of highly stable cold air damming east of the Appalachians (Bosart and Seimon, 1988).