The influence of shear on the Eliassen-Palm relation

Aircraft measurements from the Terrain-Induced Rotor Experiment (T-REX) were the first to directly measure mountain wave energy fluxes (EF). T-REX revealed a disagreement between aircraft observations and Eliassen - Palm linear theory. Energy fluxes were only about 90% of the value predicted by – (U-C) · MF, thus indicating that either EF is too low, momentum flux (MF) is too high, or the waves have a nonzero phase speed (C). Previous publications have suggested that this disagreement could be caused a difference in response time of the instruments used to measure EF and MF, even though all instruments used in the calculation have response times less than the 1 s temporal resolution of the data.

Instead this discrepancy in Eliassen-Palm theory is hypothesized to be caused by partial reflection and trapping of the primary wave. Linear theory and numerical simulations will be presented that show that the non-dimensional ratio, – EF / [U · MF], will be reduced from the theoretical value of unity whenever wave energy extends to the measurement boundaries. This will occur when mountain waves are partially reflected due to positive vertical shear (dU/dz > 0), as is almost always the case at mid-latitudes throughout the troposphere. This result combined with observations from T-REX both show that the Eliassen-Palm relation is an unrealistic simplification whose assumptions are not valid for real-world conditions.