Mesoscale model diagnostics to determine the existence of Unbalanced Flow and Wave ducting mechanisms
Van Tuyl and Young determined that gravity-inertia waves are preferentially generated just downstream of a jet core when the flow is unbalanced in the sense that the Lagrangian-Rossby number which measures the relative importance of the parcel acceleration to the coriolis acceleration is larger than 0.5. The simplified version of the Lagrangian-Rossby number is defined by the following equation

where Vag  is the transverse ageostrophic component of the geostrophic wind. Large parcel divergence and Ro 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

• There must be a layer of static stability defined as the duct depth near the surface (D1)
• There must not be a critical level (Zc) within the lower stable layer, which would lead to absorption of wave energy. The critical level is defined as the level where the wind speed in the  direction of wave propagation is equal to the wave phase speed.
• The stable layer must have sufficient depth to contain 0.25 of the wavelength corresponding to the phase speed
• There must be a layer of conditional instability (D2) above the stable layer. This "reflecting layer"  prevents the wave from propagating its energy out of the stable duct layer.
The duct depth (D1) is defined as

1    2

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.

where....

p1=lowest pressure level taken at or near the ground (typically 950 mb, the default value) - Potential temperature @ p1 used
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).