By Jaan Kalda
Consider a gas with initial number density n and temperature T. At the initial moment, the gas is spatially uniform, while the macroscopic velocity is parallel to the x-axis with a profile given by v_x(x)=v_0 \sin(kx). The molecules can be treated as rigid spheres of mass m and radius r.
What condition for v_0 must be satisfied so that, at a certain moment and location, a multi-stream flow arises? A flow is considered “multi-stream” at a point x if the local velocity distribution function f(v_x) has at least two local maxima, where each maximum is at least twice the value of the local minimum between them.
Assume that v_0\gg \sqrt {k_BT/m}. It is sufficient to estimate the answer to an order of magnitude; exact numerical prefactors are not required.
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