arXiv subjects

Cheng-Nian Xiao

Publications and source records attributed to Cheng-Nian Xiao.

7 recordsLinked to original sources

arXiv2026

Long-lived versus nocturnal stable atmospheric boundary layers: DNS characterisation, similarity theory, and regime classification

The stable atmospheric boundary layer (SABL) is broadly classified into two subtypes: the nocturnal SABL, driven primarily by surface cooling, and the long-lived SABL, in which ambient stratification coexists with surface cooling and persists well beyond a single diurnal cycle. Despite its prevalence in polar regions and over open oceans, the long-lived SABL has received comparatively little attention, and a systematic direct numerical simulation (DNS) study distinguishing it from the nocturnal SABL has not previously been reported. Here we present DNS of long-lived SABLs at $Re_D=900$, contrasting weak and strong ambient stratification cases against a nocturnal SABL. A striking feature of the long-lived SABLs is the emergence of a multi-layered thermal structure -- including an intermediate layer of reduced static stability capped by a buoyancy inversion -- driven not by enhanced turbulent mixing, but by a stratification-induced reorganisation of the buoyancy field. Budget analyses identify a turbulent potential energy-centred transport mechanism absent in nocturnal SABLs, lending support to total-energy-based closure approaches. Assessment of an extended Monin--Obukhov similarity theory incorporating a composite length scale $L_*$ shows strong collapse of dimensionless gradients of velocity $ϕ_m$ and potential temperature $ϕ_h$, and a new similarity function for $ϕ_h$ is proposed. Combining DNS with linear stability analysis, we construct a regime map delineating linearly stable, weakly stable, and very stable regimes within a two-parameter dimensionless space, demonstrating the inherently multi-parameter nature of long-lived SABLs and the limitations of single-parameter subgrid-scale parameterisations.

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arXiv2025

Dynamical stability and flow regimes in a stably stratified valley-shaped cavity heated from below

We investigate the three-dimensional stability of a stably stratified fluid in a valley-shaped cavity heated from below using linear stability analysis and direct numerical simulations. We first describe the pure-conduction flow state and derive a dimensionless criterion that provides a lower bound for the onset of instability, valid for any slope angle. We then examine the sequence of flow regimes for a slope angle of $α= 30^{\circ}$ and Prandtl number $Pr = 7$, including two-dimensional steady states, the emergence of a Hopf bifurcation, and the formation of steady and oscillatory three-dimensional structures preceding the transition to fully unsteady, chaotic flow. Although the nonlinear governing equations depend on two dimensionless parameters, we find that the flow dynamics across a wide parameter range collapse to depend on a single parameter--the composite stratification parameter $Π_c$. However, as the system becomes more unstable, sensitivity to the second parameter, $Π_h$, increases. We construct a regime map of all observed flow states as a function of $Π_c$ and $Π_h$, and confirm the onset of chaos using Lyapunov exponents. Across all regimes, asymmetric circulation remains the dominant flow structure, persisting even in time-averaged fields of chaotic states. Finally, we characterize heat transfer in the cavity using the Nusselt number, which scales as $Nu \sim Π_c^{0.43}$ or equivalently $Nu \sim Ra^{0.275}$. This result further establishes $Π_c$ as a key dimensionless parameter governing the flow dynamics preceding the chaotic regime.

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arXiv2024

Self-organization in a stably stratified, valley-shaped enclosure heated from below

We observe the spontaneous onset of three-dimensional motion from a quiescent, purely conductive state of a stably stratified fluid in a V-shaped enclosure heated from below, which ultimately self-organizes into a two-dimensional steady state without any external forcing to the initial configuration. We identify a dominant three-dimensional instability through modal stability analysis. Direct numerical simulations confirm this instability but also reveal that, after an initial period of spontaneous three-dimensional growth, the flow gradually self-organizes into a steady two-dimensional state without external intervention. This self-organization manifests consistently for any arbitrary infinitesimal three-dimensional disturbance to the initial quiescent configuration. We demonstrate that the mechanism driving this self-organization is the increasing dominance of viscous dissipation over buoyant production of disturbance kinetic energy at later stages of flow evolution from the initial quiescent state. Our investigation reveals a flow scenario in which the most natural transition pathway to the final state involves passing through an intermediate state with a higher dimension than the final state itself. Specifically, our final flow state is less complex than the three-dimensional most unstable eigenvector predicted by linear stability analysis. We demonstrate that the entire flow evolution remains non-turbulent throughout and closely aligns with results from linear stability analysis, distinguishing the present flow dynamics from transient chaos, which also features complex transient states that eventually converge to a less complex final state.

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arXiv2024

An unusual bifurcation scenario in a stably stratified, valley-shaped enclosure heated from below

We delineate the structure of steady laminar flows within a stably stratified, valley-shaped triangular cavity heated from below through linear stability analysis and Navier-Stokes simulations. We derive an exact solution to the quiescent conduction state, and characterize the flow via the stratification perturbation parameter, $Π_s$, which is a measure of the strength of the surface heat flux relative to the background stable stratification. Beyond a threshold value of $Π_s$, two unstable eigenmodes appear, one marked by a dominant central circulation, and the other one exhibiting dual circulations of equal strength. Through Navier-Stokes simulations, we confirm that the central-circulation eigenmode generates a pair of asymmetric steady states, whereas the dual-circulation eigenmode leads to distinct upslope and downslope symmetric steady states. Linear stability analysis and Navier-Stokes simulations jointly confirm the instability of the two symmetric steady states, both of which transition to the asymmetric steady state under a perturbation. Thus, for a given set of dimensionless parameters, the Navier-Stokes equations admit at least five possible steady-state solutions. Two of these solutions, namely the quiescent, pure conduction state and the counter-intuitive symmetric downslope state, have previously been overlooked in heated, stably stratified, valley-shaped enclosures. These five flow solutions reveal an intriguing bifurcation structure, including both a perfect pitchfork bifurcation and a nested bifurcation that gives rise to two distinct states. The inner bifurcation, while resembling a pitchfork in some respects, does not break any symmetry of the valley due to the lack of any possible horizontal axis of symmetry. The categorization of this inner bifurcation remains an unresolved matter, as it does not conform to any established descriptions of canonical bifurcations.

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arXiv2022

Speaker-wire vortices in stratified anabatic Prandtl slope flows and their secondary instabilities

Stationary longitudinal vortical rolls emerge in katabatic and anabatic Prandtl slope flows due to the dominance of the normal component of the buoyancy force over flow shear. Here, we further identify self pairing of these longitudinal rolls as a unique flow structure. The topology of the counter-rotating vortex pair bears a striking resemblance to speaker-wires and their interaction with each other is a precursor to further destabilization and breakdown of the flow field into smaller structures. On its own, a speaker-wire vortex retains its unique topology without any vortex reconnection or breakup. For a fixed slope angle $α=3^{\circ}$ and at a constant Prandtl number, we analyse the saturated state of speaker-wire vortices and perform a bi-global linear stability analysis based on their stationary state. We establish the existence of both fundamental and subharmonic secondary instabilities depending on the circulation and transverse wavelength of the base state of speaker-wire vortices. The dominance of subharmonic modes relative to the fundamental mode helps explain the relative stability of a single vortex pair compared to the vortex dynamics in presence of two or an even number of pairs.These instability modes are essential for the bending and merging of multiple speaker-wire vortices, which break up and lead to more dynamically unstable states, eventually paving the way for transition towards turbulence. This process is demonstrated via direct numerical simulations with which we are able to track the nonlinear temporal evolution of these instabilities.

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arXiv2021

Impact of stratification mechanisms on turbulent characteristics of stable open-channel flows

Flow over a surface can be stratified by imposing a fixed mean vertical temperature (density) gradient profile throughout or via cooling at the surface. These distinct mechanisms can act simultaneously to establish a stable stratification in a flow. Here, we perform a series of direct numerical simulations of open-channel flows to study adaptation of a neutrally stratified turbulent flow under the combined or independent action of the aforementioned mechanisms. We force the fully developed flow with a constant mass flow rate. This flow forcing technique enables us to keep the bulk Reynolds number constant throughout our investigation and avoid complications arising from the acceleration of the bulk flow when a constant pressure gradient approach were to be adopted to force the flow instead. When both stratification mechanisms are active, the dimensionless stratification perturbation number emerges as an external flow control parameter, in addition to the Reynolds, Froude, and Prandtl numbers. We demonstrate that significant deviations from the Monin-Obukhov similarity formulation are possible when both types of stratification mechanisms are active within an otherwise weakly stable flow, even when the flux Richardson number is well below 0.2. An extended version of the similarity theory due to Zilitinkevich and Calanca shows promise in predicting the dimensionless shear for cases where both types of stratification mechanisms are active, but the extended theory is less accurate for gradients of scalar. The degree of deviation from neutral dimensionless shear as a function of the vertical coordinate emerges as a qualitative measure of the strength of stable stratification for all the cases investigated in this study.

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arXiv2019

Linear Stability of Katabatic Slope Flows with Ambient Wind Forcing

We investigate the stability of katabatic slope flows over an infinitely wide and uniformly cooled planar surface subject to an additional forcing due to a uniform downslope wind field aloft. We adopt an extension of Prandtl's original model for slope flows (Lykosov & Gutman 1972) to derive the base flow, which constitutes an interesting basic state in stability analysis because it cannot be reduced to a single universal form independent of external parameters. We apply a linear modal analysis to this basic state to demonstrate that for a fixed Prandtl number and slope angle, two independent dimensionless parameters are sufficient to describe the flow stability. One of these parameters is the stratification perturbation number that we have introduced in Xiao & Senocak (2019). The second parameter, which we will henceforth designate the wind forcing number, is hitherto uncharted and can be interpreted as the ratio of the kinetic energy of the ambient wind aloft to the damping due to viscosity and stabilizing effect of the background stratification. For a fixed Prandtl number, stationary transverse and travelling longitudinal modes of instabilities can emerge, depending on the value of the slope angle and the aforementioned dimensionless numbers. The influence of ambient wind forcing on the base flow's stability is complicated as the ambient wind can be both stabilizing as well as destabilizing for a certain range of the parameters. Our results constitute a strong counter-evidence against the current practice of relying solely on the gradient Richardson number to describe the dynamic stability of stratified atmospheric slope flows.

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