Detailed diagnostic analyses are performed upon a mesoscale numerical simulation of a well-observed gravity-wave event that occurred on 4 January 1994 along the East Coast of the United States. The value of using wavelet analysis to investigate the evolving gravity-wave structure and of using potential vorticity (PV) inversion to study the nature of the flow imbalance in the wave generation region is demonstrated. The cross-stream Lagrangian Rossby number, the residual in the nonlinear balance equation, and the unbalanced geopotential-height field obtained from PV inversion are each evaluated for their usefulness in diagnosing the flow imbalance. All of these fields showed clear evidence of strong imbalance associated with a middle-to-upper tropospheric jet streak, and tropopause fold upstream of the large-amplitude gravity wave several hours before the wave became apparent at the surface.
Analysis indicates that a train of gravity waves was continuously generated by geostrophic adjustment in the exit region of the unbalanced upper-level jet streak as it approached the inflection axis in the height field immediately downstream of the maximum imbalance associated with the tropopause fold. A split front in the middle troposphere, characterized by the advance of the dry conveyor belt above the warm front, was overtaken by one of these propagating waves. During this merger process, a resonant interaction resulted, which promoted the rapid amplification and scale contraction of both the incipient wave (nonlinear wave development) and the split front (frontogenesis). The gravity wave and front aloft became inseparable following this merger. The situation became even more complex within a few hours as the vertical motion enhanced by this front-wave interaction acted upon a saturated, potentially unstable layer to produce elevated moist convection. An analysis of the temporal changes in the vertical profile of wave energy flux suggests that moist convective downdraughts efficiently transported the wave energy from the midlevels downward beneath the warm-front surface, where the wave became ducted. However, pure ducting was not sufficient for maintaining and amplifying the waves; rather, wave-CISK (Conditional Instability of the Second Kind) was crucial.
This complex sequence of nonlinear interactions produced a long-lived, large-amplitude gravity wave that created hazardous winter weather and disrupted society over a broad and highly populated area. Although gravity waves with similar appearance to this large-amplitude wave of depression occasionally have been seen in other strong cyclogenesis cases involving a jet streak ahead of the upper-level trough axis, it is unknown whether other such events share this same sequence of interactions.