Turbulent Hydrodynamic Flow


In particular weather patterns, I often see the casual weather observer, the weather enthusiast, and even trained meteorologists/forecasters claim, “The models stink!”.  Do the models really stink?  Not really–it is just a natural part of weather variability.  The chaotic nature of the atmosphere has a tendency to display itself in a much more prominent fashion in particular patterns.  In those times, it is the forecasters responsibility to understand the pattern at hand and take those into consideration.

Consider this forecast for the CONUS for the next week.  The NAM 12Z run shows the mess of cyclones/vorticies/shortwaves in the mean flow over the CONUS at 84 hours:

It is a big mess–and one must consider the wider picture before moving on here.

The medium range pattern will be dominated by an active Pacific jet and a +PNA pattern

No anomalous blocking regime exists downstream in the Atlantic–so the westerlies will likely have free reign to flow across the CONUS.  Typically these +PNA patterns are dominated by an active Pacific Jet with a mean upper level ridge over the eastern Pacific-Intermountain West and troughing over the southeastern CONUS.

The main “player” in all this activity is a very active and intense Pacific Jet stream with several short-wavelength and low amplitude upper tropospheric wave disturbances embedded in the fast westerly flow.  Hydrodynamic stability breaks down and perturbations grow and amplify in a non-linear fashion.

The 12Z GFS depicts this perfectly on the dynamic tropopause (top image).  The dynamic tropopause here is depicted using the tropopause pressure–and the jet pattern can be seen in the lower tropopause pressures.

With such a fast and active jet–the Reynolds number becomes rather large and will eventually break down into turbulent flow.

Not only that–but the moist and intense low level marine baroclinic zone is conducive to positive feedback and highly non-linear growth and amplification/baroclinic development.  What eventually develops is a train of chaotic energetic baroclinic waves.  Such a pattern is going to be MUCH more challenging for models to handle than a flow dominated by meandering rossby waves and/or laminar flow.

Do the models stink?  No–quite the opposite in fact.  Does chaos/turbulence rule?  Yes.  Edward Lorenz explained this well in “Nonperiodic Determinstic Flow”.  The Navier-Stokes equations and the dynamical laws can not perfectly account for turbulence in the flow.  It is chaotic–and only a statistical representation is possible.  In other words–we will never be able to perfectly model chaotic/turbulent flow–at least not in our lifetimes.  What eventually happens is tiny errors in the model analysis (timing/amplitude/strength etc.) feeds back rapidly as the waves grow unstably–which eventually results in a very low probability forecast. What can one do under such a forecast scenario?  Ensemble forecasting and a good understanding of the potential wave pattern can make for a much less “jumpy” forecast.  How does one forecast such a pattern?  That will be saved for another post to come.

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About jason ahsenmacher

I am a meteorologist, and I like baroclinic instability. View all posts by jason ahsenmacher

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