Turbulent Layers Associated with a Critical Level in the Planetary Boundary Layer

Abstract

Formation of thin turbulent layers in a stably stratified fluid is discussed in combination with a critical level and internal gravity waves.A series of numerical simulations by using nonlinear model of an incompressible fluid reveal that very thin unstable layers (local Richardson number <0.25) are formed in the vicinity of the critical level. Mini-K-H billows can be expected to grow up and break into turbulence in the thin unstable layers. Long-time numerical calculations show that such thin unstable layers which contain the mini-K-H billows and turbulence roll up at their edges and form Cat's eye patterns associated with large amplitude K-H billows deformed by the critical level. This result also seems to open a new perspective to the critical level theory itself.Some observations in the planetary boundary layer provide good evidences to the results of the present numerical simulations.

The Effects of Middle Atmosphere Turbulence on Coupling between Atmospheric Regions

“…Other simulations (e.g. TANAKA, 1975) have shown the formation of Kelvin-Helmholtz billows, which develop temperature profiles something like those shown in Fig. 6, and which do not necessarily lead to regions of anisotropic turbulence, but the details of the final breakdown of the instability can not usually be followed due to computer limitations in such models.…”

The transient critical‐level interaction in a Boussinesq fluid

“…The coupling between an incident gravity wave and the mean flow was considered in more detail by Jones and Houghton [1971]. For a maintained incident wave forcing, Tanaka [1975] and Fritts [1978] found the criticallevel interaction and the induced unstable layers to be displaced toward the wave source with time, a consequence of the mean flow accelerations induced by the vertical divergence of the incident wave Reynolds stress near the critical level. The nonlinear numerical investigation of Fritts [ 1979] showed that nonlinear interactions near a critical level may transfer wave action to higher harmonics of the incident wave, resulting in both large-scale waves radiating away above and below the critical level and small-scale motions which initiate the breakdown of the induced dynamically and/or convectively unstable layers.…”

The Evolution of a Nonlinear Critical Layer for Internal Gravity Waves

“…The K-H waves thus excited break into turbulence as was demonstrated by Geller et al (1975) andTanaka (1975 …”

“…Geller et al (1975) and Tanaka (1975) found by numerical simulation that unstable thin regions where total Richardson number is less than 1/4 develop in the vicinity of a critical level as time elapses even if the flow is dynamically stable at the initial instant.…”