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As indicated by the bifurcation diagram (figure 3), the model system predicts zero value for turbulent shear stress in these cases.
The attempts to integrate this empirical information with the general equations of turbulent flows have not been fully satisfactory.
There is one class of unsteady turbulent flows, however, that has been studied in fair detail using moderate to highly sophisticated data, reduction techniques.
When this ratio is of the order unity, the oscillations interact with the turbulent structure.
The responses of turbulent and laminar flows appear to be qualitatively similar.
While this worked well in laminar flow, the spots cooled too rapidly in turbulent flow.
The turbulent structure showed significant departures from equilibrium at all times during the oscillation cycle.
The evolution of the turbulent velocity field in these air data is far more coherent than were such measurements in water.
The constraint a2+p2= 1 ensures that the variance of the turbulent velocity is correct.
A new definition of concentration fluctuations in turbulent flows is proposed.
We regard non-periodic motion as being weakly turbulent.
Furthermore, such flows cannot be easily distinguished from turbulent flows by qualitative observations.
Turbulent inflow data are provided by a separate zero-pressure-gradient boundary-layer simulation.
The gradient-transfer approximation is based on the hypothesis of a turbulent flux proportional to the gradient of the concentration.
Analytic solutions have been derived to model each of the vertical and lateral stages of magma transport in both the laminar and turbulent regimes.
