Mohammad Mohaghar

The effect of initial conditions on transition to turbulence is studied in a variable-density shock-driven flow. Richtmyer–Meshkov instability (RMI) evolution of fluid interfaces with two different imposed initial perturbations is observed before and after interaction with a second shock reflected from the end wall of a shock tube (reshock). The first perturbation is a predominantly single-mode long-wavelength interface which is formed by inclining the entire tube to 80 ∘ relative to the horizontal, yielding an amplitude-to-wavelength ratio, ?/?=0.088 , and thus can be considered as half the wavelength of a triangular wave. The second interface is multi-mode, and contains additional shorter-wavelength perturbations due to the imposition of shear and buoyancy on the inclined perturbation of the first case. In both cases, the interface consists of a nitrogen-acetone mixture as the light gas over carbon dioxide as the heavy gas (Atwood number, A∼0.22 ) and the shock Mach number is M≈1.55 . The initial condition was characterized through Proper Orthogonal Decomposition and density energy spectra from a large set of initial condition images. The evolving density and velocity fields are measured simultaneously using planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV) techniques. Density, velocity, and density–velocity cross-statistics are calculated using ensemble averaging to investigate the effects of additional modes on the mixing and turbulence quantities. The density and velocity data show that a distinct memory of the initial conditions is maintained in the flow before interaction with reshock. After reshock, the influence of the long-wavelength inclined perturbation present in both initial conditions is still apparent, but the distinction between the two cases becomes less evident as smaller scales are present even in the single-mode case. Several methods are used to calculate the Reynolds number and turbulence length scales, which indicate a transition to a more turbulent state after reshock. Further evidence of transition to turbulence after reshock is observed in the velocity and density fluctuation spectra, where a scaling close to −5/3 is observed for almost one decade, and in the enstrophy fluctuation spectra, where a scaling close to 1/3 is observed for a similar range. Also, based on normalized cross correlation spectra, local isotropy is reached at lower wave numbers in the multi-mode case compared with the single-mode case before reshock. By breakdown of large scales to small scales after reshock, rapid decay can be observed in cross-correlation spectra in both cases.

The effects of incident shock strength on the mixing transition in the Richtmyer–Meshkov instability (RMI) are experimentally investigated using simultaneous density–velocity measurements. This effort uses a shock with an incident Mach number of 1.9, in concert with previous work at Mach 1.55 (Mohaghar et al., J. Fluid Mech., vol. 831, 2017 pp. 779–825) where each case is followed by a reshock wave. Single- and multi-mode interfaces are used to quantify the effect of initial conditions on the evolution of the RMI. The interface between light and heavy gases ( N2/CO2 , Atwood number, A≈0.22 ; amplitude to wavelength ratio of 0.088) is created in an inclined shock tube at 80∘ relative to the horizontal, resulting in a predominantly single-mode perturbation. To investigate the effects of initial perturbations on the mixing transition, a multi-mode inclined interface is also created via shear and buoyancy superposed on the dominant inclined perturbation. The evolution of mixing is investigated via the density fields by computing mixed mass and mixed-mass thickness, along with mixing width, mixedness and the density self-correlation (DSC). It is shown that the amount of mixing is dependent on both initial conditions and incident shock Mach number. Evolution of the density self-correlation is discussed and the relative importance of different DSC terms is shown through fields and spanwise-averaged profiles. The localized distribution of vorticity and the development of roll-up features in the flow are studied through the evolution of interface wrinkling and length of the interface edge, which indicate that the vorticity concentration shows a strong dependence on the Mach number. The contribution of different terms in the Favre-averaged Reynolds stress is shown, and while the mean density-velocity fluctuation correlation term, ?⟨?⟩⟨ui′uj′⟩ , is dominant, a high dependency on the initial condition and reshock is observed for the turbulent mass-flux term. Mixing transition is analysed through two criteria: the Reynolds number (Dimotakis, J. Fluid Mech., vol. 409, 2000, pp. 69–98) for mixing transition and Zhou (Phys. Plasmas, vol. 14 (8), 2007, 082701 for minimum state) and the time-dependent length scales (Robey et al., Phys. Plasmas, vol. 10 (3), 2003, 614622; Zhou et al., Phys. Rev. E, vol. 67 (5), 2003, 056305). The Reynolds number threshold is surpassed in all cases after reshock. In addition, the Reynolds number is around the threshold range for the multi-mode, high Mach number case ( M∼1.9 ) before reshock. However, the time-dependent length-scale threshold is surpassed by all cases only at the latest time after reshock, while all cases at early times after reshock and the high Mach number case at the latest time before reshock fall around the threshold. The scaling analysis of the turbulent kinetic energy spectra after reshock at the latest time, at which mixing transition analysis suggests that an inertial range has formed, indicates power scaling of −1.8±0.05 for the low Mach number case and −2.1±0.1 for the higher Mach number case. This could possibly be related to the high anisotropy observed in this flow resulting from strong, large-scale streamwise fluctuations produced by large-scale shear.

This experimental study investigates the effects of Reynolds number ($5000\le \text{Re}\le 20000$, where $\text{Re}=UH/\nu$) and initial release diameter (2.2 mm $\le D\le$ 9.4 mm) on the scalar power spectra, fractal geometry, and turbulent length scales of high-Schmidt-number passive scalar fields resulting from an isokinetic release in a turbulent boundary layer. The turbulence analysis is based on 12 000 scalar fields collected using the planar laser-induced fluorescence technique for each case at six locations downstream. The scalar integral length scale and scalar Taylor microscale are calculated directly from the fields using the autocorrelation function and variance/gradient of the concentration fluctuation fields. With increasing downstream distance, the Taylor microscale decreases and the integral length scale increases, each to an asymptotic value. This indicates a larger range of scales exists as the scalar becomes more mixed, as one would expect. For locations beyond $x/H\ge 10$ (where $H$ is the flow depth), the self-similarity condition is observed by considering the ratio between the scalar integral length scale and scalar Taylor microscale. Local isotropy is approached as measured by computing the ratio of longitudinal to transverse scalar Taylor microscales, and a change in the growth rate is observed for the fractal dimension computed from a planar section of the interfaces in the concentration fluctuation fields. The spectral slope magnitude in the inertial-convective regime decreases near the source ($x/H<10$) due to the large-scale anisotropy. In the self-similar regime ($x/H\ge 10$), the scaling-exponent is found to be dependent on the initial release diameter. The lower wave-number portion of the inertial-convective regime, where the scales are larger than or closer to the scale of the nozzle diameter, scales close to ${}^{}$ scaling in agreement with the cascade-bypass situation, and the spectral slope in the upper wave-number portion of the inertial-convective regime is found to be closer to $-5/3$. The viscous-convective scaling behavior deviated significantly from Batchelor’s -1 scaling law, clearly disputing the generality of Batchelor’s arguments. Intermittency analysis, using computation of the intermittency factor as well as probability density functions of the fluctuating scalar gradient, suggests that the discrepancy between theory and observations for the scaling of the viscous-convective regime can be explained by the high intermittency in the small scales of the scalar fluctuations.

To provide insight to the dynamics of weakly non-linear standing internal waves, the density and velocity fields are measured using combined planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV) techniques. A laboratory scale apparatus was created to generate standing internal waves in a two-layer stratified system. Experimental results are presented for two configurations with a density jump of 1.1 kg/m3 and 1.5 kg/m3 (separately). The interface location, wave amplitude and period, interface thickness, convection transport terms, fluid velocity, shear strain rate, and vorticity are quantified and analyzed at fixed phases in the wave cycle. The comparison between the internal wave frequency computed from the experimental results and the dispersion relationship resulting from the theoretical third-order Stokes internal-wave solution confirms that the laboratory-generated waves demonstrate non-linear behavior. The interface detected from experimental PLIF images indicated that due to the non-linear effects, a steeper wave with a sharper-looking interface at anti-node locations was formed in comparison with the theoretical linear sinusoidal shape. Further, the magnitude of shear strain rate and vorticity computed from experimental PIV measurements had a sharp, non-linear increase along the interface compared to the one computed from the linear theory. This non-linear trend in shear strain rate and vorticity can lead to the generation of sharper interface and short-period (i.e., higher frequency) non-linear internal waves.

The flow field around bioinspired magnetic-responsive soft materials that mimic the symmetry-breaking mechanisms in swimming animals, such as pteropods and manta rays, is studied using the tomographic particle image velocimetry (tomo-PIV) technique. Magnetic-responsive material appendages are actuated by an oscillating external magnetic field. The fluid flow induced by two types of actuation is quantified. First, a single actuation mode involves alternating upward and downward bending motions. Second, an asymmetric multimodal actuation encompasses upward folding and downward bending motions by locating an asymmetric joint at the midpoint of the appendage. The formed vorticity field, vortex structure, and viscous energy dissipation rate in the surrounding fluid are observed to be weaker for the multimodal actuation case. The multimodal appendage moves with reduced flow resistance, leading to faster appendage velocity during the downward power stroke. Furthermore, the study examines the effect of an asymmetric magnetic field cycle on the flow field by extending the time interval of the applied positive voltage (upstroke motion) compared to the duration of the negative applied voltage (downstroke motion). The asymmetric cycle and extended stopping period provide time for greater dissipation of the formed vorticity field. Thus, the peak values of vorticity and viscous dissipation rate decrease to smaller magnitudes compared to the symmetric cycle case. These findings demonstrate that the utilization of symmetry-breaking morphology and an asymmetric cycle enhances stroke performance, offering promising avenues for achieving greater effectiveness in underwater propulsion.

The swimming characteristics achieved by flapping wings, translating motion, and shell pitching are studied from observations of shelled Antarctic pteropods (aquatic snails nicknamed ‘sea butterflies’). These pteropods (Limacina helicina antarctica) swim with a pair of parapodia (or “wings”) via a unique flapping propulsion mechanism that incorporates similar techniques as observed in small flying insects. The geometric scaling of wing span (L), wing chord (c), and minor shell diameter (d) with respect to major shell diameter (D) reveal geometric similitude. Thus, major shell diameter (D) is the only length scale required to describe the size of the pteropods. The motion of swimming pteropods is characterized using flapping, translational, and rotational Reynolds numbers (i.e. Re_f, Re_U, and Re_Ω). A critical value of flapping Reynolds number, Re_f=35, is found for the onset of translating and pitching locomotion. Finally, the relationship is obtained for the Strouhal number (St_A=fA/U) for the pteropods using the geometric scalings and the translational and flapping Reynolds numbers. The Strouhal number is found to be between 0.2 and 0.4, which indicates general agreement with other oscillating organisms moving with high propulsion efficiency.

The hydrodynamic disturbance generated by the adult copepod Euchaeta antarctica during cruise swimming is quantified. Kinematic results are compared to previous results reported for different Euchaeta species. The results reveal a linear relationship between cruise speed and prosome length across Euchaeta species, indicating a size-proportional trend that is indicative of a complicated interaction of species size and environmental factors such as fluid temperature and viscosity. The detailed fluid flow measurements using the tomographic Particle Image Velocimetry (tomo-PIV) technique provide insight into copepod cruise propulsion during turning events in comparison to straight motions. During straight swimming, E. antarctica demonstrates streamlined flow patterns and reduced vorticity in the near-body fluid shear layer, which is beneficial for sustained motion and energy conservation. In contrast, turning maneuvers are characterized by maximum flow velocities reaching 1.5 times greater values than during straight cruising with increased flow field complexity and enhanced vorticity. The viscous dissipation rate generated in the flow disturbance is also greater during turning events, with the total dissipation rate reaching 3.5 − 3.8 × 10^(−8) W compared to 2.6 − 2.8 × 10^(−8) W during straight cruising. The flow disturbance also generates a hydrodynamic cue that prey may sense in order to avoid the predator E. antarctica. For the adult E. antarctica, the hydrodynamic cue extends to a volume that is 11–13 times larger than the copepod exoskeleton volume during the straight swimming motion and 22–25 times larger during the turn events.