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tokens: outflow. Left: HST image of the young stellar jet HH 34 and its bow shock (from Hartigan et al. 2011 ). Right: expanded views of the bow shock and the putative Mach stem. The structured bow shock in HH 47 (Hartigan et al. 2011 ) is another potential example where transient Mach stems may occur. This object resolves into what appear to be dozens of small knots in high-resolution images. Surprisingly, these bright points form and dissipate on timescales of a decade, which is difficult to explain if they represent discrete knots of high density that plow through the working surface of the flow. In both HH 34 and HH 47, the shock velocity is ∼100 km s −1 and the knot size ∼7.5 × 10 14 cm, and so τ F ∼ 2.4 years. The numerical models imply that we should expect any transient Mach stems to evolve on a timescale of about a decade, in agreement with the observations. The postshock regions of cooling astrophysical shocks are complex and contain various zones of ionization for each element. Hence, these regions are not characterized by a single value of γ . However, the overall dynamical effects of cooling in bow shocks have been well-established for some time (e.g., Blondin et al. 1990 ). A critical parameter is the ratio of the cooling-zone distance d COOL to the obstacle size . When this ratio is ≳1, the gas acts like an adiabatic flow with γ = 5/3 where the maximum size of a Mach stem will be comparable to . In the opposite limit, when the obstacle is very large compared with the cooling length, the gas behaves dynamically as if it is isothermal. An isothermal shock has γ = 1 where no Mach stems are possible. In this case, Mach stems only exist on scale sizes ≲ d COOL . Hence, the maximum size of a Mach stem should be the smaller of d COOL or . The cooling distance scales inversely as the preshock density and directly as a power of the shock velocity (e.g., Hartigan et al. 1987 ), and also depends on the strength of the magnetic field (Hartigan Wright 2015 ). Hence, whether or not two intersecting bow shocks create a substantial Mach stem depends on the shock velocity, density, magnetic field strength, and the sizes of the bows. Overall, Mach stems should be most common when size scales are small enough to render cooling unimportant in the dynamics. The distribution of clumps in the flow and ambient medium ultimately determines whether or not Mach stems will form and grow in any situation, with the optimal separation for Mach stem growth being several times the diameter of the obstacles in a flow with moderate Mach number. The widest range of allowable obstacle separations occurs when cooling is least important (Section 4.1.2 ). Cooling distances in the HH 34 and HH 47 bow shocks are on the order of the size of the transient bright knots in these objects (Hartigan et al. 2011 ). Hence, the effective γ for these spatial scales is ∼5/3, which is favorable for Mach stem growth. In a future paper, we will present simulations of intersecting