ALBERT

Description: We report results on rotating stratified turbulence in the absence of forcing and with large-scale isotropic initial conditions using direct numerical simulations computed on grids of up to 4096 3 points. The Reynolds and Froude numbers are, respectively, equal to Re = 5.4 × 10 4 and Fr = 0.0242. The ratio of the Brunt-Väisälä to the inertial wave frequency, N / f , is taken to be equal to 4.95, a choice appropriate to model the dynamics of the southern abyssal ocean at mid latitudes. This gives a global buoyancy Reynolds number R B = ReFr 2 ≈ 32, a value sufficient for some isotropy to be recovered in the small scales beyond the Ozmidov scale, but still moderate enough that the intermediate scales where waves are prevalent are well resolved. We concentrate on the large-scale dynamics, for which we find a spectrum compatible with the Bolgiano-Obukhov scaling. This scaling is also found for geostrophically balanced initial conditions on a run at a lower resolution and hence lower R B ≈ 4. Furthermore, we confirm that the Froude number based on a typical vertical length scale is of order unity, with strong gradients in the vertical. Two characteristic scales emerge from this computation and are identified from sharp variations in the spectral distribution of either total energy or helicity. A spectral break is also observed at a scale at which the partition of energy between the kinetic and potential modes changes abruptly, and beyond which a Kolmogorov-like spectrum recovers. Large slanted layers are ubiquitous in the flow, in the velocity and temperature fields, with local overturning events indicated by small local Richardson numbers and strong localized vortex tangles . Finally, a small large-scale enhancement of energy directly attributable to the effect of rotation is also observed.

Description: This paper presents an experimental and numerical investigation of the entry of a rigid square flat plate into pure and aerated water. Attention is focused on the measurement and calculation of the slamming loads on the plate. The experimental study was carried out in the ocean basin at Plymouth University’s COAST laboratory. The present numerical approach extends a two-dimensional hydro-code to compute three-dimensional hydrodynamic impact problems. The impact loads on the structure computed by the numerical model compare well with laboratory measurements. It is revealed that the impact loading consists of distinctive features including (1) shock loading with a high pressure peak, (2) fluid expansion loading associated with very low sub-atmospheric pressure close to the saturated vapour pressure, and (3) less severe secondary reloading with super-atmospheric pressure. It is also disclosed that aeration introduced into water can effectively reduce local pressures and total forces on the flat plate. The peak impact loading on the plate can be reduced by half or even more with 1.6% aeration in water. At the same time, the lifespan of shock loading is prolonged by aeration, and the variation of impulse is less sensitive to the change of aeration than the peak loading.

Description: Large altitude asymptotic approximations are derived for vertical displacements due to mountain waves generated by hydrostatic wind flow over arbitrary topography. This leads to new asymptotic analytic expressions for wave-induced vertical displacement for mountains with an elliptical Gaussian shape and with the major axis oriented at any angle relative to the background wind. The motivation is to understand local maxima in vertical displacement amplitude at a given height for elliptical mountains aligned at oblique angles to the wind direction, as identified in Eckermann et al. [“Effects of horizontal geometrical spreading on the parameterization of orographic gravity-wave drag. Part 1: Numerical transform solutions,” J. Atmos. Sci. 72 , 2330–2347 (2015)]. The standard stationary phase method reproduces one type of local amplitude maximum that migrates downwind with increasing altitude. Another type of local amplitude maximum stays close to the vertical axis over the center of the mountain, and a new generalized stationary phase method is developed to describe this other type of local amplitude maximum and the horizontal variation of wave-induced vertical displacement near the vertical axis of the mountain in the large altitude limit. The new generalized stationary phase method describes the asymptotic behavior of integrals where the asymptotic parameter is raised to two different powers (1/2 and 1) rather than just one power as in the standard stationary phase method. The vertical displacement formulas are initially derived assuming a uniform background wind but are extended to accommodate both vertical shear with a fixed wind direction and vertical variations in the buoyancy frequency.

Description: We perform the systematic numerical study of high vorticity structures that develop in the 3D incompressible Euler equations from generic large-scale initial conditions. We observe that a multitude of high vorticity structures appear in the form of thin vorticity sheets (pancakes). Our analysis reveals the self-similarity of the pancakes evolution, which is governed by two different exponents e − t / T ℓ and e t / T ω describing compression in the transverse direction and the vorticity growth, respectively, with the universal ratio T ℓ / T ω ≈ 2/3. We relate development of these structures to the gradual formation of the Kolmogorov energy spectrum E k ∝   k −5/3 , which we observe in a fully inviscid system. With the spectral analysis, we demonstrate that the energy transfer to small scales is performed through the pancake structures, which accumulate in the Kolmogorov interval of scales and evolve according to the scaling law ω max ∝ ℓ −2/3 for the local vorticity maximums ω max and the transverse pancake scales ℓ.

Description: We study the flow of two immiscible, Newtonian fluids in a periodically constricted tube driven by a constant pressure gradient. Our volume-of-fluid algorithm is used to solve the governing equations. First, the code is validated by comparing its predictions to previously reported results for stratified and pulsing flow. Then, it is used to capture accurately all the significant topological changes that take place. Initially, the fluids have a core-annular arrangement, which is found to either remain the same or change to a different arrangement depending on the fluid properties, the pressure driving the flow, or the flow geometry. The flow-patterns that appear are the core-annular, segmented, churn, spray, and segregated flow. The predicted scalings near pinching of the core fluid concur with similarity predictions and earlier numerical results [I. Cohen et al. , “Two fluid drop snap-off problem: Experiments and theory,” Phys. Rev. Lett. 83 , 1147–1150 (1999)]. Flow-pattern maps are constructed in terms of the Reynolds and Weber numbers. Our result provides deeper insights into the mechanism of the pattern transitions and is in agreement with previous studies on core-annular flow [Ch. Kouris and J. Tsamopoulos, “Core-annular flow in a periodically constricted circular tube, I. Steady state, linear stability and energy analysis,” J. Fluid Mech. 432 , 31–68 (2001) and Ch. Kouris et al. , “Comparison of spectral and finite element methods applied to the study of interfacial instabilities of the core-annular flow in an undulating tube,” Int. J. Numer. Methods Fluids 39 (1), 41–73 (2002)], segmented flow [E. Lac and J. D. Sherwood, “Motion of a drop along the centreline of a capillary in a pressure-driven flow,” J. Fluid Mech. 640 , 27–54 (2009)], and churn flow [R. Y. Bai et al. , “Lubricated pipelining—Stability of core annular-flow. 5. Experiments and comparison with theory,” J. Fluid Mech. 240 , 97–132 (1992)].

Description: This article presents the results of experimental investigations of the process of transition from two-dimensional (2D) to three-dimensional (3D) waves in liquid films falling down a vertical plate. The method of laser induced fluorescence was used to obtain instant shapes of three dimensional waves and to investigate the regularities of formation of 3D wave patterns arising due to transverse instability of 2D waves. The obtained results were compared to the results from the published literature on the modeling of 3D wave regimes of film flow. Although many details of 3D wave patterns correspond well, there are a few significant distinctions between our experiments and modeling. In particular, during 2D-3D wave transition, we observed a strong transverse redistribution of liquid leading to the formation of rivulets on the surface of isothermal liquid film, which is a phenomenon not described previously. Possible discrepancies between modeling and experiments, including applicability of boundary layer models and downstream periodic boundary conditions, are discussed. The authors hope that the results presented in the article are of interest not only for modeling of film flows but also for practical applications because at large distances from the film inlet due to 2D-3D wave transition the local flow rates can differ several times at the transverse distances of about 1 cm, which is an effect that cannot be neglected.

Description: The direct molecular simulation (DMS) approach is used to predict the internal energy relaxation and dissociation dynamics of high-temperature nitrogen. An ab initio potential energy surface (PES) is used to calculate the dynamics of two interacting nitrogen molecules by providing forces between the four atoms. In the near-equilibrium limit, it is shown that DMS reproduces the results obtained from well-established quasiclassical trajectory (QCT) analysis, verifying the validity of the approach. DMS is used to predict the vibrational relaxation time constant for N 2 –N 2 collisions and its temperature dependence, which are in close agreement with existing experiments and theory. Using both QCT and DMS with the same PES, we find that dissociation significantly depletes the upper vibrational energy levels. As a result, across a wide temperature range, the dissociation rate is found to be approximately 4–5 times lower compared to the rates computed using QCT with Boltzmann energy distributions. DMS calculations predict a quasi-steady-state distribution of rotational and vibrational energies in which the rate of depletion of high-energy states due to dissociation is balanced by their rate of repopulation due to collisional processes. The DMS approach simulates the evolution of internal energy distributions and their coupling to dissociation without the need to precompute rates or cross sections for all possible energy transitions. These benchmark results could be used to develop new computational fluid dynamics models for high-enthalpy flow applications.

Description: The objective of the paper is to study the effect of wall bending resistance on the motion of an initially spherical capsule freely suspended in shear flow. We consider a capsule with a given thickness made of a three-dimensional homogeneous elastic material. A numerical method is used to model the fluid-structure interactions coupling a boundary integral method for the fluids with a shell finite element method for the capsule envelope. For a given wall material, the capsule deformability strongly decreases when the wall bending resistance increases. But, if one expresses the same results as a function of the two-dimensional mechanical properties of the mid-surface, which is how the capsule wall is modeled in the thin-shell model, the capsule deformed shape is identical to the one predicted for a capsule devoid of bending resistance. The bending rigidity is found to have a negligible influence on the overall deformation of an initially spherical capsule, which therefore depends only on the elastic stretching of the mid-surface. Still, the bending resistance of the wall must be accounted for to model the buckling phenomenon, which is observed locally at low flow strength. We show that the wrinkle wavelength is only a function of the wall bending resistance and provide the correlation law. Such results can then be used to infer values of the bending modulus and wall thickness from experiments on spherical capsules in simple shear flow.

Description: An exact solution is found for laminar fluid flow along the grooves of a family of surfaces whose shape is given by the Lambert W-function. This simple solution allows for the slip length in the direction parallel to the grooves to be calculated exactly. With this analytical model, we establish the regime of validity for a previously untested perturbation theory intended for calculating the surface mobility tensor of arbitrary periodic surfaces, finding that it compares well to the exact expression for nearly all choices of parameters of the conformal map. To test this perturbation theory further, the mobility tensor is evaluated for a simple sinusoidal surface for flow both parallel and perpendicular to the grooves, finding that the perturbation theory is less accurate in the latter of these two cases.