Nonlinear Hydrodynamic Interaction Research Articles

Colloid phase separation dynamics driven by chiral turbulent flows

Hydrodynamic interactions significantly influence phase-ordering kinetics in complex fluids. While passive fluid phase separation is well studied, the impact of active components remains relatively unexplored. We examine pure- and quasi-two-dimensional mixtures of attractive colloids and self-rotating particles in a solvent. Varying rotor rotational speed and area fraction yield diverse dynamic patterns such as percolated networks and round droplets composed of passive colloids alone. At intermediate rotation speeds, inertial chiral flows, accompanied by the inverse energy cascade, lead to self-similar power-law coarsening with a growth exponent of 1/2. The flows spontaneously organize within fluid domains, exhibiting turbulent and chiral characteristics. Surprisingly, these turbulent flows can sustain hexatic order hydrodynamically stabilized by the Magnus force under certain conditions. Conversely, at higher speeds, nonlinear hydrodynamic interactions impede phase separation. Our findings illuminate the intriguing dynamic interplay between phase separation and chiral turbulence, effectively bridging the realms of phase ordering and turbulent physics. Published by the American Physical Society 2024

Pairwise interactions between model swimmers at intermediate Reynolds numbers

How do mesoscale swimmers interact with one another when there is finite inertia? Do they repel, attract, how do they arrange? We numerically study simple model swimmers at intermediate Reynolds numbers and find that they form specific stable pairs depending on system parameters (e.g. Reynolds number). By looking at the flow fields, we relate the assemblies with nonlinear hydrodynamic interactions, namely steady streaming flows and discuss implications for the collective behavior beyond pairs.

Symmetry properties of nonlinear hydrodynamic interactions between responsive particles.

Two identical particles driven by the same steady force through a viscous fluid may move relative to one another due to hydrodynamic interactions. The presence or absence of this relative translation has a profound effect on the dynamics of a driven suspension consisting of many particles. We consider a pair of particles which, to linear order in the force, do not interact hydrodynamically. If the system possesses an intrinsic property (such as the shape of the particles, their position with respect to a boundary, or the shape of the boundary) which is affected by the external forcing, hydrodynamic interactions that depend nonlinearly on the force may emerge. We study the general properties of such nonlinear response. Analysis of the symmetries under particle exchange and under force reversal leads to general conclusions concerning the appearance of relative translation and the motion's time reversibility. We demonstrate the applicability of the conclusions in three specific examples: (a) two spheres driven parallel to a wall; (b) two deformable objects driven parallel to their connecting line; and (c) two spheres driven along a curved path. The breaking of time reversibility suggests a possible use of nonlinear hydrodynamic interactions to disperse or assemble particles by an alternating force.

A study of marine slicks damping effect on Doppler spectra of backscattered echoes from rough sea surfaces

ABSTRACT Doppler spectrum of backscattered sea echoes from slick-covered sea surfaces is investigated in this paper, with emphasis on exploring the influence of marine sea slicks damping effect on Doppler spectral signatures including Doppler shift and spectral bandwidth. Model of local balance of wave energy inputs and outputs in wavenumber space is utilized for describing marine slicks damping effect, and the ‘choppy wave’ model is adopted for describing non-linear hydrodynamic interactions between ocean waves. The second-order small-slope approximation model combined with Monte Carlo technique is utilized for evaluating Doppler spectrum of backscattered field from clean or contaminated sea surfaces. Numerical simulations show that Doppler spectral bandwidths in slicks are reduced for almost all of the incidence angles ranging from to , which is qualitatively consistent with wave-tank measurements. The Doppler shifts in slicks, however, can increase or decrease, depending strongly on incidence angle, which is also in qualitative agreement with measurements. The Doppler spectrum of radar sea echoes is promising in the detection marine slicks by virtue of radar Doppler signatures.

Doppler spectra of electromagnetic wave scattered from an object flying above time-varying nonlinear sea surfaces

ABSTRACTDoppler spectra of electromagnetic wave scattered from an object flying above time-varying nonlinear sea surfaces are investigated by utilizing a hybrid algorithm combining method of moments (MoM) and Kirchhoff approximation (KA). The “choppy wave” model is employed for describing nonlinear hydrodynamic interactions between ocean waves. Doppler spectra of scattered wave are simulated and analyzed for different incidence angles, target velocities, target heights, sea states as well as sea surface models, and an obvious broadening of Doppler spectrum is observed due to the coupling scattering between the flying target and rough sea surfaces. In comparison with the normalized radar cross section, Doppler spectra of scattered wave have the advantage of extracting information regarding target flying above dynamic sea surfaces. This study is of great value for the analysis of coupling scattering between flying target and rough sea surface as well as for the detection low-flying target in sea clutter environment.

Impact of axial loads on the sound directivity of angular contact ceramic ball bearings

This paper mainly focuses on the sound directivity of the angular contact ceramic ball bearing applied to the ceramic motorized spindle. The nonlinear dynamic model is proposed with consideration of axial load, nonlinear hydrodynamic forces and interaction between balls and cage. Then the sub-source decomposition method is introduced for the establishment of an acoustic radiation model. Sound pressure levels along the circumferential direction are used as evaluation indexes of sound directivity, and the sound directivity with axial loads at different rotation speed are analyzed. Results indicate that the sound directivity tends to be obvious with the increase of rotation speed, and the axial loads have significant influence on the deviation angles of directivity performance. This work provides insights into monitoring the acoustic performance of ceramic bearings, and can guide further research and development.

Synchronisation through learning for two self-propelled swimmers

The coordinated motion by multiple swimmers is a fundamental component in fish schooling. The flow field induced by the motion of each self-propelled swimmer implies non-linear hydrodynamic interactions among the members of a group. How do swimmers compensate for such hydrodynamic interactions in coordinated patterns? We provide an answer to this riddle though simulations of two, self-propelled, fish-like bodies that employ a learning algorithm to synchronise their swimming patterns. We distinguish between learned motion patterns and the commonly used a-priori specified movements, that are imposed on the swimmers without feedback from their hydrodynamic interactions. First, we demonstrate that two rigid bodies executing pre-specified motions, with an alternating leader and follower, can result in substantial drag-reduction and intermittent thrust generation. In turn, we study two self-propelled swimmers arranged in a leader-follower configuration, with a-priori specified body-deformations. These two self-propelled swimmers do not sustain their tandem configuration. The follower experiences either an increase or decrease in swimming speed, depending on the initial conditions, while the swimming of the leader remains largely unaffected. This indicates that a-priori specified patterns are not sufficient to sustain synchronised swimming. We then examine a tandem of swimmers where the leader has a steady gait and the follower learns to synchronize its motion, to overcome the forces induced by the leader’s vortex wake. The follower employs reinforcement learning to adapt its swimming-kinematics so as to minimize its lateral deviations from the leader’s path. Swimming in such a sustained synchronised tandem yields up to reduction in energy expenditure for the follower, in addition to a increase in its swimming-efficiency. The present results show that two self-propelled swimmers can be synchronised by adapting their motion patterns to compensate for flow-structure interactions. Moreover, swimmers can exploit the vortical structures of their flow field so that synchronised swimming is energetically beneficial.

Doppler spectrum of polarimetric scattering field from two-dimensional time-varying nonlinear sea surfaces

Polarimetric scattering model of second-order small-slope approxi-mation combined with “choppy wave" model (CWM) for describing nonlinear hydrodynamic interactions between ocean waves is utilized in this paper to investigate the influence of sea surface nonlinearities on backscattering coefficient as well as Doppler spectrum signatures including Doppler shift and spectral bandwidth. Simulation results show that at moderate to large incidence angles the Doppler shift and spectral bandwidth of the CWM nonlinear sea surfaces are significantly larger than those of linear sea surfaces, in particular at low grazing angles. In addition, Doppler signatures show distinct polarization dependence, and most importantly the cross-polarized Doppler signatures significantly differ from the co-polarized ones. It is also indicated that co-polarized Doppler shift increases obviously with wind speed increasing, whereas the cross-polarized Doppler shift looks less sensitive to wind speed variations. The difference of Doppler signatures between co- and cross-polarization is potentially valuable for ocean remote sensing applications, especially for observing very high winds.

Purely hydrodynamic ordering of rotating disks at a finite Reynolds number.

Self-organization of moving objects in hydrodynamic environments has recently attracted considerable attention in connection to natural phenomena and living systems. However, the underlying physical mechanism is much less clear due to the intrinsically nonequilibrium nature, compared with self-organization of thermal systems. Hydrodynamic interactions are believed to play a crucial role in such phenomena. To elucidate the fundamental physical nature of many-body hydrodynamic interactions at a finite Reynolds number, here we study a system of co-rotating hard disks in a two-dimensional viscous fluid at zero temperature. Despite the absence of thermal noise, this system exhibits rich phase behaviours, including a fluid state with diffusive dynamics, a cluster state, a hexatic state, a glassy state, a plastic crystal state and phase demixing. We reveal that these behaviours are induced by the off-axis and many-body nature of nonlinear hydrodynamic interactions and the finite time required for propagating the interactions by momentum diffusion.

Assessing chlorophyll variability in relation to the environmental regime in Pagasitikos Gulf, Greece

Pagasitikos Gulf (Greece), presents an interesting area as it depicts strongly non-linear ecosystem characteristics. It is a shallow coastal area where the marine ecosystem picture is strongly influenced by non-linear hydrodynamic interactions and instabilities. In this study, we explore and assess the major influential variables of the surface phytoplankton biomass (Chlorophyll-a). Several different physical and biogeochemical parameters were used (sea surface temperature [SST], mixed layer depth [MLD], salinity, phosphates and nitrates) to identify which variables control or significantly affect the surface Chl-a of Pagasitikos Gulf for the period of 2001–2005. The variables were derived from a coupled hydrodynamic-biogeochemical model and remotely sensed data from SeaWiFS and AVHRR sensor. Generalised Additive Models (GAMs) were used to examine the relationships between Chlorophyll-a and the environmental regime. GAM analysis showed that the combined effects of the variables used, explained 71% of the surface chlorophyll variation. The order of importance of the variables (based on GAM probability) is p=0.01 (for both phosphate and nitrate), MLD: p=0.0197, salinity: p=0.022, and SST: p=0.046. The results clearly indicated the importance of deep mixing for Pagasitikos Gulf, as the surface phytoplankton blooms appeared to be favoured by cold, nutrient rich, well mixed and higher salinity waters. GAMs indicated that SST plays a significant role having a strong negative relationship with Chl-a, where the highest concentration is reached at 12–15°C and minimum at 22–26°C. Chl-a ceases to increase after 37.9‰ of salinity and 40m of MLD, while minimum concentration is found at 10m of MLD, with a subsequent increase as the waters become more mixed. Phosphate and nitrates appeared to be of equal importance with Chl-a exhibiting an increase along with the nutrients.

Processes governing the flow redistribution in sharp river bends

Insight is provided in hydrodynamic processes governing the velocity redistribution in sharp river bends based on simulations of three recent experiments by means of Blanckaert and de Vriend's (2003, 2010) reduced-order nonlinear model without curvature restrictions. This model successfully simulated the flow redistribution and the secondary flow in all three experiments. The results indicate that the flow redistribution is primarily governed by topographic steering, curvature variations and secondary flow, in a broad range of different configurations, including mildly to sharply curved bends, narrow to shallow bends, smooth to rough bends, bends with additional complexities such as horizontal recirculation zones or patches of riverbed vegetation. The relative importance of these three dominant processes is case dependent, and controlled by the parameters Cf−1H/B, R/B and streamwise curvature variations. The first parameter characterizes a river reach, whereas the second and third parameters are characteristics of individual bends. Major differences exist between the hydrodynamic processes in mildly and sharply curved bends. First, velocity redistribution induced by curvature variations is negligible in mildly curved bends, but the dominant process in sharp bends. This result is relevant, because most meander models are based on the assumption of weak-curvature variations. Second, nonlinear hydrodynamic interactions play a dominant role in sharp bends, where mild-curvature models overpredict the secondary flow and in some cases even falsely identify it as the dominant process governing the velocity redistribution, which leads to unsatisfactory flow predictions. The reduction in secondary flow strength provoked by the nonlinear hydrodynamic interactions is accompanied by a reduction in the transverse bed slope, which reduces the effect of topographic steering.

Dynamics of a Compound Vesicle in Shear Flow

The dynamics of a compound vesicle (a lipid bilayer membrane enclosing a fluid with a suspended particle) in shear flow is investigated by using both numerical simulations and theoretical analysis. We find that the nonlinear hydrodynamic interaction between the inclusion and the confining membrane gives rise to new features of the vesicle dynamics: The transition from tank treading to tumbling can occur in the absence of any viscosity mismatch, and a vesicle can swing if the enclosed particle is nonspherical. Our results highlight the complex effects of internal cellular structures have on cell dynamics in microcirculatory flows. For example, parasites in malaria-infected erythrocytes increase cytoplasmic viscosity, which leads to increase in blood viscosity.

Hydrodynamic processes in sharp meander bends and their morphological implications

The migration rate of sharp meander bends exhibits large variance and indicates that some sharply curved bends tend to stabilize. These observations remain unexplained. This paper examines three hydrodynamic processes in sharp bends with fixed banks and discusses their morphological implications: secondary flow saturation, outer-banks cells, and inner-bank flow separation. Predictions from a reduced-order hydrodynamic model show that nonlinear hydrodynamic interactions limit the growth of the secondary flow. This process is called the saturation of the secondary flow. For outer-bank cells and inner-bank flow separation, the analysis relies on experimental findings from flume studies in channels with fixed and mobile beds. The experiments reveal that outer-bank cells exist near steep as well as shelving banks and amplify with increasing steepness and roughness of the outer bank, and especially with increasing curvature. The effects of flow separation at the inner bank are found to be strongly conditioned by flow-sediment interactions, which lead to an increased scour depth near the outer bank and increased velocities near the toe of that bank. Overall the results suggest that secondary flow saturation and outer-bank cells tend to inhibit meander migration, whereas inner-bank separation may enhance migration. The relative importance of these three hydrodynamic processes depends on hydraulic, geometric, and sedimentologic conditions, which is consistent with the large variance in observed migration rates. The results suggest that large shallow rivers have the most dynamic meandering behavior, while the occurrence of stabilized meanders seems to be favored in narrow rivers.

Stretching of polymer chains by fluctuating flow fields

We investigate polymer stretching by fluctuating flow fields via numerical solutions of the Brownian dynamics of multibead polymer chains taking into account nonlinear elasticity, hydrodynamic interactions and good solvent, excluded volume interaction effects. By varying the scaling exponent of the energy spectrum whilst keeping the same Reynolds and Deborah numbers, as well as microscale length and turnover times, we show that steeper spectra are associated with stronger stretching. We compute the probability density functions of chain length, and explain their main features by examining explicit molecular histories. We quantify the interaction between strain rate tensor structure and chain geometry as a means of understanding better the different stretching mechanisms in mild, moderate and strong polymer stretching regimes.

INTERACTION OF A FLOATING ELLIPTIC CYLINDER WITH A VIBRATING CIRCULAR CYLINDER

The nonlinear hydrodynamic interaction between a floating elliptic cylinder and a vibrating circular cylinder immersed in an infinite fluid was investigated. By taking the added masses of the two-cylinder system into account, the dynamical equations of motion were formulated from the Lagrange equations of motion. The dynamical behaviors of these two cylinders were analyzed numerically for some typical situations, and the results show that the presence of a vibrating circular cylinder has a significant influence on the planar motion of a floating elliptic cylinder. The hydrodynamic interaction between them results in complicated nonlinear behaviors of the floating cylinder. It is found that oscillatory motion of the elliptic cylinder takes place in response to the vibrating mode of the circular one.

Sea surface probing with L-band Doppler radar: experiment and theory

In a first part, this paper describes radar experiments aimed at probing the sea surface from the coast. To capture small-scale changes in a coastal environment, a flexible high resolution, Doppler L-band radar with high resolution in range has been used. The data exhibit significant sensitivity to current and wind, which justifies the development of a model for inversion. The second part of the paper is thus devoted to our first attempt to model radar echoes, in order to accurately describe the influence of the geophysical parameters of interest. Here, the focus is put on waves generated by a local wind. The key point consists in taking properly into account non-linear hydrodynamic interactions between waves to generate a realistic moving sea surface. From the electromagnetic point of view, since standard low-frequency approximations no longer hold at L-band, a small-slope approximation has been implemented to compute the backscattered field. Numerical results show that for light winds (less than 5 m s −1) the model correctly predicts the behaviour of the data with respect to wind speed and direction. To cite this article: M. Saillard et al., C. R. Physique 6 (2005).

Dynamic Critical Phenomena of Polymer Solutions

Recently, a systematic experiment measuring critical anomaly of viscosity of polymer solutions has been reported by Tanaka et al. [Phys. Rev. E 65 (2002) 021802]. According to their experiments, the dynamic critical exponent of viscosity y c drastically decreases with increasing the molecular weight. In this article the kinetic coefficients renormalized by the non-linear hydrodynamic interaction are calculated by the mode coupling theory. We predict that the critical divergence of viscosity should be suppressed with increasing the molecular weight. The diffusion constant and the dynamic structure factor are also calculated. The present results explicitly show that the critical dynamics of polymer solutions should be affected by an extra spatio-temporal scale intrinsic to polymer solutions, and are consistent with the experiment of Tanaka et al.

Can non-linear structure form at the era of decoupling?

The effects of large-scale fluctuations on small-scale isothermal modes at the epoch of recombination are analysed. We find the following. (a) Albeit the fact that primordial fluctuations were at this epoch still well in the linear regime, a significant non-linear radiation hydrodynamic interaction could have taken place. (b) Short-wavelength isothermal fluctuations are unstable. Their growth rate is an exponential function of the amplitude of the large-scale fluctuations and is therefore very sensitive to the initial conditions. (c) The observed cosmic microwave background radiation (CMBR) fluctuations are of order of the limit above which the effect should be significant. Thus, depending on their exact value, the effect may be negligible or lead to structure formation out of the isothermal fluctuations within the period of recombination. (d) If the cosmological parameters are within the prescribed regime, the effect should be detectable through induced deviations in the Planck spectrum. (e) The sensitivity of the effect to the initial conditions provides a tool to set limits on various cosmological parameters with emphasis on the type and amplitude of the primordial fluctuation spectrum. (f) Under proper conditions, the effect may be responsible for the formation of sub-globular-cluster sized objects at particularly high redshifts. (g) Under certain circumstances, it can also affect horizon-sized large-scale structure.

Low-Frequency Micromotion of DEP-Levitated Plant Protoplasts: III. Rationalization of Higher Harmonics

Experimental observations, previously reported in this series of papers, in the low-frequency regime of the spectrum in dielectrophoretically levitated plant protoplasts, have revealed higher harmonics to the fundamental driving field frequency (when ≤50 Hz). Our previous modeling of the nonlinear dynamics of this micromotion have failed to reproduce or indicate the source of this phenomena. The existing dynamical micromotion model, a highly nonlinear second-order differential equation constructed on the basis of Newton's second law to the situation of a particle levitated in an inhomogeneous electric field, has been extended to include: (a) cubic nonlinearity in the dielectrophoretic forces, (b) convective flow contributions as described by Oseen's equation, and (c) a novel mathematical model to describe the nonlinear dependence of the particle surface charge on the electric field frequency of the driver based on the solution of a Langevin or stochastic equation. Numerical integration of the vector field by means of a Runge–Kutta sixth-order algorithm has shown that neither the inhomogeneity of the electric field, as realized in dielectrophoresis of the suspended particle, nor the nonlinear hydrodynamic interaction of the particle with the medium are responsible for the appearance of the higher harmonics. Incorporation of the frequency-dependent surface charge modeling, however, has given good agreement with the experimental observations. Fast Fourier transforms of the numerical solutions show the experimentally observed higher harmonics in the micromotion attesting to the significance of the electric field-dependent dissociation constant of the carboxylic groups in the surface proteins. Phase plane portrait solutions when examined over several frequencies provide a means of estimating the surface charge of the plant protoplasts.

Persistence of a pattern of surface gravity waves

The observation of ship Kelvin wakes by the Seasat synthetic aperture radar raises a question concerning the persistence of patterns of surface gravity waves. Time scales vary with wavelength and environmental conditions. The range extends from fractions of a second at the shortest wavelengths to many days for ocean swell. Several mechanisms for destroying a wave pattern are investigated here. These are viscous dissipation, direct wind‐wave interaction, and nonlinear hydrodynamic interaction with ambient surface waves. The nonlinear hydrodynamic interactions appear to be the most significant.