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Profile consistency: Difference between revisions
→Directly measuring stiffness
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In the case at hand, the (thermodynamic) force or drive is the heat flux ''Q'', whereas the system response is the (thermodynamic) gradient ''∇ T'' (but see below). | In the case at hand, the (thermodynamic) force or drive is the heat flux ''Q'', whereas the system response is the (thermodynamic) gradient ''∇ T'' (but see below). | ||
A useful measure of stiffness should depend on the quantities (''Δ F'' and ''δ'') in such a way that the extreme case of a totally stiff system would correspond to ''κ = ∞'' (''δ = 0''). | |||
Thus, assuming that profile stiffness is best evidenced in the normalized gradient (or inverse gradient length) ''∇ T / T'' (based on both experimental observation and, e.g., ETG instability theory), an appropriate stiffness definition for the temperature profile could be: | Thus, assuming that profile stiffness is best evidenced in the normalized gradient (or inverse gradient length) ''∇ T / T'' (based on both experimental observation and, e.g., ETG instability theory), an appropriate stiffness definition for the temperature profile could be: | ||
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where the heat flux ''Q'' has been normalized by the pressure ''nT'' so that ''κ'' has the dimension of a heat diffusivity. | where the heat flux ''Q'' has been normalized by the pressure ''nT'' so that ''κ'' has the dimension of a heat diffusivity. | ||
A dimensionless stiffness measure is obtained by normalizing ''κ'' to the background heat diffusivity ''χ'': ''C = κ/χ''. | |||
A non-stiff situation would correspond to ''C = 1'', whereas a stiff situation would yield ''C >> 1''. | |||
One concludes that the stiffness can be measured directly by simply observing the behaviour of the gradients as the drive (''Q'') is changed. | |||
== References == | == References == | ||
<references /> | <references /> | ||