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Core annular flow theory is used to model the parallel flow of fluids of different phases and has been used to describe drag reduction in the context of internal flows bounded by superhydrophobic surfaces. The work presented here is an extension of core annular flow theory to the study of the adiabatic section of heat pipes. Our aim is to develop a first-principles estimate of the conditions necessary to maximize the (counter) flow of liquid and vapor and, by extension, the axial flow of heat. The planar and axisymmetric geometries are examined as are heat pipes containing vs being devoid of a wick. In the wick vs no-wick cases, the peripheral return flow of liquid is, respectively, driven by capillarity and by gravity. Our model is used to predict velocity profiles and the flux-maximizing pressure gradient ratio (vapor-to-liquid). We further obtain estimates for the optimum thickness of the liquid layer. Note finally that when the liquid flow occurs via capillary pumping, there is a minimum surface tension below which the wick cannot supply a sufficient flow of liquid. We characterize this critical point in terms of the properties of the working fluid and of the wick.

We report upon a laboratory experimental study of dense full- and partial-depth locks released gravity currents propagating through a two-layer ambient and over sinusoidal topography of amplitude A and wavelength λ. Attention is restricted to a Boussinesq flow regime and the initial (or slumping) stage of motion. Because of the presence of the topography, the lower layer depth and channel depth vary in the downstream direction by as much as ±52% and ±40%, respectively. Despite such large variations, the instantaneous gravity current front speed typically changes by only a small amount from its average value, U. We conclude that the reason for this unexpected observation is a counterbalancing between the contraction/expansion of the channel on one hand and along-slope variations of the buoyancy force on the other hand. Compared to the case of gravity current flow over a horizontal surface, the topography has a retarding effect on U; we characterize the variation of U with the following parameters: A, A/...

Gravity currents produced by partial-depth lock-release and travelling along the base of a two-layer stratified ambient are investigated as they propagate along a rising slope. The initial gravity current front speed is found to be consistent with a theory adapted from Shin et al. [“Gravity currents produced by lock exchange,” J. Fluid Mech. 521, 1-34 (2004)] to the case of partial-depth currents in two-layer ambients. The subsequent evolution depends on the gravity current speed relative to the speed of the interfacial disturbance it creates. The deceleration of supercritical gravity currents, which travel faster than the interfacial disturbance, is gradual and agrees well with the relationship developed by Marleau et al. [“Gravity currents propagating up a slope,” Phys. Fluids 26, 046605 (2014)] for upslope gravity currents in uniform density ambients. In several subcritical cases, the gravity current suddenly came to rest as a consequence of interactions with the interfacial disturbance. The disturbance amplitude, speed, and width are found to be nearly constant during its evolution. In cases for which the ambient interface intersected the bottom slope, the amplitude, speed, and width were nearly constant up to the point where the lower layer shallowed and the disturbance transformed into an upslope-propagating gravity current.

Bottom propagating gravity currents resulting from full- and partial-depth lock-release experiments are investigated as they approach and then propagate up a rising slope. Consistent with the prediction of a WKB-like theory, the gravity current front decelerates in a nearly uniform manner along the slope as 0.112g′s(D/H)(2 − D/H), in which g′ is the reduced gravity, s is the slope, D is the initial lock-fluid height, and H is the ambient fluid height. The shape of the gravity current as it decelerates over relatively steep slopes is found to be self similar with a nearly linear decrease of the head height between the start of the slope and up to 80% of the distance to the nose. Some deviation from self-similar behaviour is found in cases with small s because of the comparatively large volume of fluid in the gravity current tail that flows downslope while the front continues to advance upwards.

By adapting the Foppl-von Karman equation, which describes the deformation of a thin elastic membrane, we present an analysis of the buckling pattern of a thin, very viscous fluid layer subject to shear in an axisymmetric geometry. A linear stability analysis yields a differential eigenvalue problem, whose solution, obtained using spectral techniques, yields the most unstable azimuthal wave-number, m⋆. Contrary to the discussion of Slim et al. [J. Fluid Mech. 694, 5–28 (2012)]10.1017/jfm.2011.437, it is argued that the axisymmetric problem shares the same degeneracy as its rectilinear counterpart, i.e., at the onset of instability, m⋆ is indefinitely large. Away from this point, however, a comparison with analogue experimental results is both possible and generally favorable. In this vein, we describe the laboratory apparatus used to make new measurements of m⋆, the phase speed and the wave amplitude; note that no prediction concerning the latter two quantities can be made using the present theory. Experi...

We consider the propagation of a gravity current of density ρc at the bottom of a two-layer stratified ambient in a horizontal channel of height H, in the high-Reynolds number Boussinesq domain. The study emphasizes theoretical-analytical modeling, however, experimental and Navier-Stokes simulation data are also presented and their comparison with theory is discussed. The stratification parameters are S = (ρ1 − ρ2)/(ρc − ρ2) where ρ is the fluid density, and φ = h1R/H where h1R is the (unperturbed) ambient interface height. Here, 1 and 2 denote, respectively, the lower and upper layer and c denotes the gravity current. The reduced gravity is defined as g′ = (ρc/ρ2 − 1)g. Rigorous results are obtained for the steady-state analogue of the classical problem of Benjamin [J. Fluid Mech. 31, 209 (1968)]10.1017/S0022112068000133, in which the half-infinite gravity current has thickness h and speed U. We thereby demonstrate that the Froude number F=U/(g′h)1/2 is a function of a = h/H, S, and φ. In general, two so...