Thermal conductivity of multiwalled carbon nanotubes ͑CNT's͒ prepared using a microwave plasma chemical vapor deposition system is investigated using a pulsed photothermal reflectance technique. We find that the average thermal conductivity of carbon nanotube films, with the film thickness from 10 to 50 m, is around 15 W/m K at room temperature and independent of the tube length. Taking a small volume filling fraction of CNT's into account, the effective nanotube thermal conductivity could be 2ϫ10 2 W/m K, which is smaller than the thermal conductivity of diamond and in-plane graphite by a factor of 9 and 7.5, respectively.

We investigate fully developed turbulence in stratified plane Couette flows using direct numerical simulations similar to those reported by Deusebioet al.(J. Fluid Mech., vol. 781, 2015, pp. 298–329) expanding the range of Prandtl number$Pr$examined by two orders of magnitude from 0.7 up to 70. Significant effects of$Pr$on the heat and momentum fluxes across the channel gap and on the mean temperature and velocity profile are observed. These effects can be described through a mixing length model coupling Monin–Obukhov (M–O) similarity theory and van Driest damping functions. We then employ M–O theory to formulate similarity scalings for various flow diagnostics for the stratified turbulence in the gap interior. The midchannel gap gradient Richardson number$Ri_{g}$is determined by the length scale ratio$h/L$, where$h$is the half-channel gap depth and$L$is the Obukhov length scale. As$h/L$approaches very large values,$Ri_{g}$asymptotes to a maximum characteristic value of approximately 0.2. The buoyancy Reynolds number$Re_{b}\equiv \unicode[STIX]{x1D700}/(\unicode[STIX]{x1D708}N^{2})$, where$\unicode[STIX]{x1D700}$is the dissipation,$\unicode[STIX]{x1D708}$is the kinematic viscosity and$N$is the buoyancy frequency defined in terms of the local mean density gradient, scales linearly with the length scale ratio$L^{+}\equiv L/\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}}$, where$\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}}$is the near-wall viscous scale. The flux Richardson number$Ri_{f}\equiv -B/P$, where$B$is the buoyancy flux and$P$is the shear production, is found to be proportional to$Ri_{g}$. This then leads to a turbulent Prandtl number$Pr_{t}\equiv \unicode[STIX]{x1D708}_{t}/\unicode[STIX]{x1D705}_{t}$of order unity, where$\unicode[STIX]{x1D708}_{t}$and$\unicode[STIX]{x1D705}_{t}$are the turbulent viscosity and diffusivity respectively, which is consistent with Reynolds analogy. The turbulent Froude number$Fr_{h}\equiv \unicode[STIX]{x1D700}/(NU^{\prime 2})$, where$U^{\prime }$is a turbulent horizontal velocity scale, is found to vary like$Ri_{g}^{-1/2}$. All these scalings are consistent with our numerical data and appear to be independent of$Pr$. The classical Osborn model based on turbulent kinetic energy balance in statistically stationary stratified sheared turbulence (Osborn,J. Phys. Oceanogr., vol. 10, 1980, pp. 83–89), together with M–O scalings, results in a parameterization of$\unicode[STIX]{x1D705}_{t}/\unicode[STIX]{x1D708}\sim \unicode[STIX]{x1D708}_{t}/\unicode[STIX]{x1D708}\sim Re_{b}Ri_{g}/(1-Ri_{g})$. With this parameterization validated through direct numerical simulation data, we provide physical interpretations of these results in the context of M–O similarity theory. These results are also discussed and rationalized with respect to other parameterizations in the literature. This paper demonstrates the role of M–O similarity in setting the mixing efficiency of equilibrated constant-flux layers, and the effects of Prandtl number on mixing in wall-bounded stratified turbulent flows.

Finite-amplitude manifestations of stratified shear flow instabilities and their spatio-temporal coherent structures are believed to play an important role in turbulent geophysical flows. Such shear flows commonly have layers separated by sharp density interfaces, and are therefore susceptible to the so-called Holmboe instability, and its finite-amplitude manifestation, the Holmboe wave. In this paper, we describe and elucidate the origin of an apparently previously unreported long-lived coherent structure in a sustained stratified shear flow generated in the laboratory by exchange flow through an inclined square duct connecting two reservoirs filled with fluids of different densities. Using a novel measurement technique allowing for time-resolved, near-instantaneous measurements of the three-component velocity and density fields simultaneously over a three-dimensional volume, we describe the three-dimensional geometry and spatio-temporal dynamics of this structure. We identify it as a finite-amplitude, nonlinear, asymmetric confined Holmboe wave (CHW), and highlight the importance of its spanwise (lateral) confinement by the duct boundaries. We pay particular attention to the spanwise vorticity, which exhibits a travelling, near-periodic structure of sheared, distorted, prolate spheroids with a wide ‘body’ and a narrower ‘head’. Using temporal linear stability analysis on the two-dimensional streamwise-averaged experimental flow, we solve for three-dimensional perturbations having two-dimensional, cross-sectionally confined eigenfunctions and a streamwise normal mode. We show that the dispersion relation and the three-dimensional spatial structure of the fastest-growing confined Holmboe instability are in good agreement with those of the observed confined Holmboe wave. We also compare those results with a classical linear analysis of two-dimensional perturbations (i.e. with no spanwise dependence) on a one-dimensional base flow. We conclude that the lateral confinement is an important ingredient of the confined Holmboe instability, which gives rise to the CHW, with implications for many inherently confined geophysical flows such as in valleys, estuaries, straits or deep ocean trenches. Our results suggest that the CHW is an example of an experimentally observed, inherently nonlinear, robust, long-lived coherent structure which has developed from a linear instability. We conjecture that the CHW is a promising candidate for a class of exact coherent states underpinning the dynamics of more disordered, yet continually forced stratified shear flows.

The mixing properties of statically stable density interfaces subject to imposed vertical shear are studied using direct numerical simulations of stratified plane Couette flow. The simulations are designed to investigate possible self-maintaining mechanisms of sharp density interfaces motivated by Phillips’ argument (Deep-Sea Res., vol. 19, 1972, pp. 79–81) by which layers and interfaces can spontaneously form due to vertical variations of diapycnal flux. At the start of each simulation, a sharp density interface with the same initial thickness is introduced at the midplane between two flat, horizontal walls counter-moving at velocities$\pm U_{w}$. Particular attention is paid to the effects of varying Prandtl number$\mathit{Pr}\equiv \unicode[STIX]{x1D708}/\unicode[STIX]{x1D705}$, where$\unicode[STIX]{x1D708}$and$\unicode[STIX]{x1D705}$are the molecular kinematic viscosity and diffusivity respectively, over two orders of magnitude from 0.7, 7 and 70. Varying$\mathit{Pr}$enables the system to access a considerable range of characteristic turbulent Péclet numbers$\mathit{Pe}_{\ast }\equiv {\mathcal{U}}_{\ast }{\mathcal{L}}_{\ast }/\unicode[STIX]{x1D705}$, where${\mathcal{U}}_{\ast }$and${\mathcal{L}}_{\ast }$are characteristic velocity and length scales, respectively, of the motion which acts to ‘scour’ the density interface. The dynamics of the interface varies with the stability of the interface which is characterised by a bulk Richardson number$\mathit{Ri}\,\equiv \,b_{0}h/U_{w}^{2}$, where$b_{0}$is half the initial buoyancy difference across the interface and$h$is the half-height of the channel. Shear-induced turbulence occurs at small$\mathit{Ri}$, whereas internal waves propagating on the interface dominate at large$\mathit{Ri}$. For a highly stable (i.e. large$\mathit{Ri}$) interface at sufficiently large$\mathit{Pe}_{\ast }$, the complex interfacial dynamics allows the interface to remain sharp. This ‘self-sharpening’ is due to the combined effects of the ‘scouring’ induced by the turbulence external to the interface and comparatively weak molecular diffusion across the core region of the interface. The effective diapycnal diffusivity and irreversible buoyancy flux are quantified in the tracer-based reference coordinate proposed by Winters & D’Asaro (J. Fluid Mech., vol. 317, 1996, pp. 179–193) and Nakamura (J. Atmos. Sci., vol. 53, 1996, pp. 1524–1537), which enables a detailed investigation of the self-sharpening process by analysing the local budget of buoyancy gradient in the reference coordinate. We further discuss the dependence of the effective diffusivity and overall mixing efficiency on the characteristic parameters of the flow, such as the buoyancy Reynolds number and the local gradient Richardson number, and highlight the possible role of the molecular properties of fluids on diapycnal mixing.

We report on a study, employing direct numerical simulations, of the turbulent/nonturbulent interface of a wake in a stably stratified fluid. It is found that thresholds for both enstrophy and potential enstrophy are needed to identify the interface. Using conditional averaging relative to the location of the interface, various quantities of interest are examined. The thickness of the interface is found to scale with the Kolmogorov scale. From an examination of the Ozmidov and Kolmogorov length scales as well as the buoyancy Reynolds number, it is found that the buoyancy Reynolds number decreases and becomes of order 1 near the interface, indicating the suppression of the turbulence there by the stable stratification. Finally the overall rate of loss of energy due to internal wave radiation is found to be comparable to the overall rate of loss due to turbulent kinetic energy dissipation.