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Two-dimensional direct numerical simulations are used to study the impact of deep gaps on laminar-turbulent transition in compressible boundary-layer flow. For these, the gap depth-to-width ratio is always larger than five. They are located on a flat plate without pressure gradient. A steady base flow is used with a Mach number of 0.6, freestream temperature of 288 K, and free-stream pressure of 1 bar. Subsequently, Tollmien-Schlichting waves are introduced by suction and blowing at the wall, and their growth over the gap is evaluated by N factors. The influence of the gap on laminar-turbulent transition is quantified by the difference ΔN compared with the N factor obtained for a flat plate without gap. A periodic influence of the gap depth on ΔN is observed. In the direct numerical simulations, acoustic waves enter the gap and form a standing wave due to reflections, similar as occurring in organ pipes. The feedback of the standing wave on the boundary-layer flow above is essential for the observed ΔN variations. In a second case, the influence of a specific gap placed in front of a forward-facing step is studied as well. Here, a reduction of the N factor and hence a delay of transition, relative to the flow with step alone, are reached due to the presence of the gap. Nomenclature A = dimensionless amplitude A m = dimensionless maximum amplitude in vertical direction a = normalized amplitudẽ c = speed of sound, m∕s c p = heat capacity at constant pressure, J∕K c v = heat capacity at constant volume, J∕K d = dimensionless gap depth h = dimensionless step height L ref = reference length, m Ma = Mach number N = factor describing amplification of TS waves n = factor describing the amplification of a TS wave for one frequency Pr = Prandtl number p = dimensionless pressure p w = dimensionless wall pressure Re d = Reynolds number based on the gap depth r = receptivity factor t = time, s u = dimensionless horizontal velocity v = dimensionless vertical velocity w = dimensionless gap width x = dimensionless length in horizontal direction y = dimensionless length in vertical direction α = phase shift between waves γ = heat capacity ratio ΔN = deviation of an N factor from the N factor of the flat plate Δα = constant phase shift between standing wave and new TS wave δ = boundary-layer thickness, m δ 1 = displacement thickness, m λ = dimensionless wave length μ = dynamic viscosity, kg∕s · mρ = density, kg∕m 3 τ w = dimensionless wall shear stress ω = dimensionless circular frequency ∼ = dimensional quantities Subscripts an = antinode amplitude of standing wave dis = disturbances (fluctuations) of flow quantities do = values of downward traveling waves in the gap op = values at the gap opening res = amplitude of superposition of TS waves up = values of upward traveling waves in the gap ∞ = free-stream quantities

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