# Latest papers in fluid mechanics

### Geometric optimization of riblet-textured surfaces for drag reduction in laminar boundary layer flows

Micro-scale riblets are shown to systematically modify viscous skin friction in laminar flows at high Reynolds numbers. The textured denticles of native sharkskin are widely cited as a natural example of this passive drag reduction mechanism. Since the structure of a viscous boundary layer evolves along the plate, the local frictional drag changes are known empirically to be a function of the length of the plate in the flow direction, as well as the riblet spacing, and the ratio of the height to spacing of the riblets. Here, we aim to establish a canonical theory for high Reynolds number laminar flow over V-groove riblets to explore the self-similarity of the velocity profiles and the evolution of the total frictional drag exerted on plates of different lengths. Scaling analysis, conformal mapping, and numerical calculations are combined to show that the potential drag reduction achieved using riblet surfaces depends on an appropriately rescaled form of the Reynolds number and on the aspect ratio of the riblets (defined in terms of the ratio of the height to spacing of the texture). We show that riblet surfaces require a scaled Reynolds number lower than a maximum threshold to be drag-reducing and that the change in drag is a nonmonotonic function of the aspect ratio of the riblet texture. This physical scaling and the computational results presented here can be used to explain the underlying physical mechanism of this mode of passive drag reduction to rationalize the geometric dimensions of shark denticles, as well as the results of experiments with shark denticle replicas of various sizes, and guide designs for optimizing the textural parameters that result in friction-reducing surfaces.

### A direct numerical simulation study of the influence of flame-generated vorticity on reaction-zone-surface area in weakly turbulent premixed combustion

Direct numerical simulation data obtained from two statistically stationary, one-dimensional, planar, weakly turbulent, premixed flames are analyzed in order to examine the influence of flame-generated vorticity on the surface area of the reaction zone. The two flames are associated with the flamelet combustion regime and are characterized by two significantly different density ratios σ = 7.53 and 2.5, with all other things being roughly equal. The obtained results indicate that generation of vorticity due to baroclinic torque within flamelets can impede wrinkling of the reaction surface, reduce its area, and, hence, decrease the burning rate. Thus, these results call for revisiting the widely accepted concept of combustion acceleration due to flame-generated turbulence. In particular, in the case of σ = 7.53, the local stretch rate, which quantifies the local rate of increase or decrease in the surface area, is predominantly negative in regions characterized by a large magnitude of enstrophy or a large magnitude of the baroclinic torque term in the enstrophy transport equation, with the effect being more pronounced at larger values of the mean combustion progress variable. If the density ratio is low, e.g., σ = 2.5, the baroclinic torque weakly affects the vorticity field within the mean flame brush and the aforementioned effect is not pronounced.

### Pumping flow model in a microchannel with propagative rhythmic membrane contraction

A pumping flow model in a microchannel with a single attached membrane subjected to propagative contraction is presented in this article. The lubrication theory is used to approximate the induced flow field at a low Reynolds number flow regime. A well-posed expression for the wall profile is derived to describe the membrane propagative mode of rhythmic contractions. Unlike our previously derived pumping model “nonpropagative” where at least two membranes that operate with time-lag are required to produce unidirectional flow, the present results demonstrate that an inelastic channel with a single membrane contraction that operates in a “propagative” mode can produce unidirectional flow and work as a micropump. The model can be used to understand flow transport in many biological systems including but not limited to insect respiration, urine flow, and fluid dynamics of duodenum and intestine. The present pumping paradigm is relatively easy to fabricate and is expected to be useful in many biomedical applications.

### Response modes of erythrocytes in high-frequency oscillatory shear flows

Due to its capability of duplicating the deformation scenario of erythrocytes (red blood cells), in in vivo time scales, passing through interendothelial slits in the spleen, the understanding of the dynamic response of erythrocytes in oscillatory shear flows is of critical importance to the development of an effective in vitro methodology to study the mechanics, metabolism, and aging procedure in vivo [R. Asaro et al., “Erythrocyte aging, protection via vesiculation: An analysis methodology via oscillatory flow,” Front. Physiol. 9, 1607 (2018)]. Accordingly, we conducted a systematic computational investigation of the dynamics of erythrocytes in high-frequency oscillatory shear flows by using a fluid-cell interaction model based on the Stokes-flow framework and a multiscale structural depiction of the cell. Within the range of parameters we consider, we identify five different response modes (wheeling, tilted wheeling, tank treading mode 1, tank treading mode 2, and irregular). The occurrence and stability of these response modes depend on the frequency of the flow, the peak capillary number, the viscosity ratio, the initial orientation of the cell, and the stress-free state of the protein skeleton. Through long-term simulations [[math] periods], mode switching events have been discovered, during which the cell transfers from one mode to another, often via an intermediate transient mode. The deformation of the skeleton and the contact stress between the skeleton and the lipid bilayer are computed since these are of direct importance to describing vital cell phenomena such as vesiculation by which the cell protects itself from premature elimination.

### Clusterlike instabilities in bubble-plume-driven flows

Author(s): Sai Ankit Etha, Anupam Jena, and Rajaram Lakkaraju

Continuous release of gas bubbles in large numbers from a localized source in a liquid column, popularly known as “bubble plumes”, is very relevant in nature and industries. The bubble plumes morphologically consist of a long continuous stem supporting a dispersed head. Through our direct numerical ...

[Phys. Rev. E 99, 053101] Published Wed May 01, 2019

### Role of parasitic modes in nonlinear closure via the resolvent feedback loop

Author(s): Kevin Rosenberg, Sean Symon, and Beverley J. McKeon

The representation of self-sustaining processes via resolvent analysis for turbulent flows is improved where the resolvent operator is not low rank by approximating the nonlinear forcing using parasitic modes, with analogy to weakly nonlinear analysis near critical Reynolds numbers.

[Phys. Rev. Fluids 4, 052601(R)] Published Wed May 01, 2019

### Dynamics of nonlinear Alfvén waves in the shallow water magnetohydrodynamic equations

Author(s): Martin Magill, Aaron Coutino, Benjamin A. Storer, Marek Stastna, and Francis J. Poulin

Vortices in a model of the solar tachocline decay into pairs of stable donutlike Alfvén waves. These propagate zonally in opposite directions, colliding periodically. Nonlinear effects distort the waves significantly after each collision, but between collisions their shapes and speed remain fixed.

[Phys. Rev. Fluids 4, 053701] Published Wed May 01, 2019