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This review highlights the profound and unexpected ways in which viscosity varying in space and time can affect flow. The most striking manifestations are through alterations of flow stability, as established in model shear flows and industrial applications. Future studies are needed to address the important effect of viscosity stratification in such diverse environments as Earth's core, the Sun, blood vessels, and the re-entry of spacecraft.

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The linear stability of variable viscosity, miscible core–annular flows is investigated. Consistent with pipe flow of a single fluid, the flow is stable at any Reynolds number when the magnitude of the viscosity ratio is less than a critical value. This is in contrast to the immiscible case without interfacial tension, which is unstable at any viscosity ratio. Beyond the critical value of the viscosity ratio, the flow can be unstable even when the more viscous fluid is in the core. This is in contrast to plane channel flows with finite interface thickness, which are always stabilized relative to single fluid flow when the less viscous fluid is in contact with the wall. If the more viscous fluid occupies the core, the axisymmetric mode usually dominates over the corkscrew mode. It is demonstrated that, for a less viscous core, the corkscrew mode is inviscidly unstable, whereas the axisymmetric mode is unstable for small Reynolds numbers at high Schmidt numbers. For the parameters under consideration, the switchover occurs at an intermediate Schmidt number of about 500. The occurrence of inviscid instability for the corkscrew mode is shown to be consistent with the Rayleigh criterion for pipe flows. In some parameter ranges, the miscible flow is seen to be more unstable than its immiscible counterpart, and the physical reasons for this behaviour are discussed.A detailed parametric study shows that increasing the interface thickness has a uniformly stabilizing effect. The flow is least stable when the interface between the two fluids is located at approximately 0.6 times the tube radius. Unlike for channel flow, there is no sudden change in the stability with radial location of the interface. The instability originates mainly in the less viscous fluid, close to the interface.

The transmission dynamics of highly contagious respiratory diseases like COVID-19 (through coughing/sneezing) is an open problem in the epidemiological studies of such diseases (Bourouiba, JAMA. https ://doi.org/10.1001/jama.2020.4756. 2020). The problem is basically the fluid dynamics of a transient turbulent jet/puff with buoyancy, laden with evaporating droplets carrying the pathogen. A turbulent flow of this nature does not lend itself to reliable estimates through modeling approaches such as RANS (Reynolds-Averaged Navier-Stokes equations) or other droplet-based models. However, direct numerical simulations (DNS) of what may be called "cough/sneeze flows" can play an important role in understanding the spread of the contagion. The objective of this work is to develop a DNS code for studying cough/sneeze flows by a suitable combination of the DNS codes available with the authors (developed to study cumulus cloud flows including thermodynamics of phase change and the dynamics of small water droplets) and to generate useful data on these flows. Recent results from the cumulus cloud simulations are included to highlight the effect of turbulent entrainment (which is one of the key processes in determining the spread of the expiratory flows) on the distribution of liquid water content in a moist plume. Furthermore, preliminary results on the temperature distribution in a "dry cough" (i.e., without inclusion of liquid droplets) are reported to illustrate the large spatial extent and time duration over which the cough flow can persist after the coughing has stopped. We believe that simulations of this kind can help to devise more accurate guidelines for separation distances between neighbors in a group, design better masks, and minimize the spread of respiratory diseases of the COVID-19 type.

The sinking of organic particles produced in the upper sunlit layers of the ocean forms an important limb of the oceanic biological pump, which impacts the sequestration of carbon and resupply of nutrients in the mesopelagic ocean. Particles raining out from the upper ocean undergo remineralization by bacteria colonized on their surface and interior, leading to an attenuation in the sinking flux of organic matter with depth. Here, we formulate a mechanistic model for the depth-dependent, sinking, particulate mass flux constituted by a range of sinking, remineralizing particles. Like previous studies, we find that the model does not achieve the characteristic 'Martin curve' flux profile with a single type of particle, but instead requires a distribution of particle sizes and/or properties. We consider various functional forms of remineralization appropriate for solid/compact particles, and aggregates with an anoxic or oxic interior. We explore the sensitivity of the shape of the flux vs. depth profile to the choice of remineralization function, relative particle density, particle size distribution, and water column density stratification, and find that neither a power-law nor exponential function provides a definitively superior fit to the modeled profiles. The profiles are also sensitive to the time history of the particle source. Varying surface particle size distribution (via the slope of the particle number spectrum) over 3 days to represent a transient phytoplankton bloom results in transient subsurface maxima or pulses in the sinking mass flux. This work contributes to a growing body of mechanistic export flux models that offer scope to incorporate underlying dynamical and biological processes into global carbon cycle models. The oceans absorb about 2.5 × 10 12 kg of carbon from the atmosphere annually, amounting to a net uptake of about 40% of the anthropogenically produced CO 2 since industrialization 1. Understanding the controls on the oceanic uptake of atmospheric CO 2 is important for predicting how the uptake rate might change in the future. The oceanic biological pump 2 plays a significant role in this process: Phytoplankton produce organic matter by taking up dissolved inorganic carbon through photosynthesis in the sunlit ocean. While a major portion of this production is recycled, a small fraction (typically, less than 20%) rains out to depth, carrying with it organic carbon, nutrients and minerals. Such particles are formed through a variety of mechanisms: cells age, form cysts, are ingested and egested by zooplankton, aggregate, coagulate, and gradually sink as 'marine snow'. The sinking material varies in shape, size and character, ranging from individual cells to pellets and aggregates, most of which is rapidly colonized and consumed by heterotrophic bacteria, contributing to the attenuation of the sinking flux with depth (Fig. 1). The shape of the depth-diminishing flux profile has traditionally been characterized by empirical fits to data obtained from particle intercepting sediment traps 3 o...

A comprehensive study of the effect of wall heating or cooling on the linear, transient and secondary growth of instability in channel flow is conducted. The effect of viscosity stratification, heat diffusivity and of buoyancy are estimated separately, with some unexpected results. From linear stability results, it has been accepted that heat diffusivity does not affect stability. However, we show that realistic Prandtl numbers cause a transient growth of disturbances that is an order of magnitude higher than at zero Prandtl number. Buoyancy, even at fairly low levels, gives rise to high levels of subcritical energy growth. Unusually for transient growth, both of these are spanwise-independent and not in the form of streamwise vortices. At moderate Grashof numbers, exponential growth dominates, with distinct Rayleigh-Benard and Poiseuille modes for Grashof numbers upto $\sim 25000$, which merge thereafter. Wall heating has a converse effect on the secondary instability compared to the primary, destabilising significantly when viscosity decreases towards the wall. It is hoped that the work will motivate experimental and numerical efforts to understand the role of wall heating in the control of channel and pipe flows.Comment: Submitted to J. Fluid Mec

Recent direct numerical simulations of the finite-extensibility nonlinear elastic dumbbell model with the Peterlin approximation of non-Newtonian hydrodynamics revealed that the phenomenon of drag reduction by polymer additives exists (albeit in reduced form) also in homogeneous turbulence. We use here a simple shell model for homogeneous viscoelastic flows, which recaptures the essential observations of the full simulations. The simplicity of the shell model allows us to offer a transparent explanation of the main observations. It is shown that the mechanism for drag reduction operates mainly on large scales. Understanding the mechanism allows us to predict how the amount of drag reduction depends on the various parameters in the model. The main conclusion is that drag reduction is not a universal phenomenon; it peaks in a window of parameters such as the Reynolds number and the relaxation rate of the polymer.