Instability of a thin viscous film flowing under an inclined substrate: steady patterns

Hydrodynamic-driven morphogenesis of karst draperies: spatio-temporal analysis of the two-dimensional impulse response

“…This invariance suggests that the response can be evaluated in the context of a steady pattern asymptotic analysis, introduced in Lerisson et al. (2020) for the front analysis of a propagating steady wavepacket, known as spatio-spatial stability analysis.…”

“…In Lerisson et al. (2020) and Ledda et al. (2020) the conditions for the existence of steady patterns and the selection mechanisms for a thin film flowing under an inclined planar substrate in the absence of inertial effects were experimentally and numerically studied.…”

Instability of a thin viscous film flowing under an inclined substrate: the emergence and stability of rivulets

“…In this section, we briefly present selected results from the study of Lerisson et al (2020) in the presence and absence of the spanwise inlet forcing devices shown in figure 1(a). Figure 2(a) shows a film thickness distribution obtained using an absorption technique (reproduced from Lerisson et al 2020). The inlet spanwise thickness profile is amplified, and streamwise-saturated and steady rivulets are observed downstream.…”

“…where A = 10 −2 , andh N = 0.54 is the initial value of the thickness that gives, for a pure streamwise saturated structure, the same local flow rate in the streamwise direction as a flat film of thickness h = 1 ( § 5.3 in Lerisson et al 2020). We introduce the moving reference frame at the linear advection velocity u (ξ = x − ut, y).…”

“…The experimental apparatus is the same as that described in Lerisson et al. (2020) (see figure 1). The substrate is an orientable glass plate of length mm and width mm, whose angle with respect to the vertical is varied from to .…”