On the Thermal Structure of Steady Free Jets in the Non-adiabatic States
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**Session 40 -- Numerical Techniques and Models**
*Display presentation, Tuesday, 10, 1995, 9:20am - 6:30pm*

## [40.01] On the Thermal Structure of Steady Free Jets in the Non-adiabatic States

*Masaaski Kondo (SAO)*
The steady state of free jets are considered in the phase
space, composed of pressure $p$, density $\rho$, and the ratio of
velocity angle from the axis over radial distance $A$, where
trajectories of fluids in a jet form a leaf structure. To simpify the
problem, elementary thermal processes of cooling and heating are
assumed. Cooling is due to free-free emission and heating depends only
on density in the power law of $\rho^n$. The state of the jet is
characterised by three parameters: Mach number $M_0$, effective
coefficients of cooling $c_0$ and heating $h_0$, which are normalized
quantities at the orifice. The numerical calculations are performed mainly
for the case of $M_0=10$, by using the characteristic method in
axially symmetric configuration.
In the adiabatic case of $c_0=h_0=0$, the free jet expands at
the rate of the asymptotically saturated magnitude of $A$, which is
proportional to $M_0$. On-the-other-hand, in the case where cooling is
in action, the pressure is affected to decrease. However, the density
does not change much.

When heating is effective to halt the pressure and
temperature decreasing, the difference of power $n$ on heating brings
the following features.

1) The case of $n<0.5$: A thermal instability is seen on the
axial region of jets where the parameters $c_0$ and $h_0$
satisfy the restricted condition. This is the bifurcation
phenomena of structural stability occuring at the critical pin-point
in the phase space. In the unstable region, density is growing, but
pressure and temperature are decreasing. On the other side, the
temperature is rising in the outer rarefied region.

2) The case of $n>0.5$: The jets are quite stable. Slender jets
are formed under the restricted condition; e.g. $h_0 < 0.3 c_0$, in
the case of $n=1$, where both of the inner and outer regions keep a
constant temperature.

Investigations on the above phase space help us to construct
models for various types of astrophysical jets such as Cyg A and 3C273.

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