► A model for the distribution of M. colonies over the water depth is presented. ► We apply the Langevin–Fokker–Planck equation. ► We combine a hydrodynamic and a rate of density change models. ► The ...model compares satisfactorily with available field observations. ► The distribution of colonies depends on wind speed and colony size.
In this research we introduce a coupled column model to simulate the vertical migration of Microcystis aeruginosa in natural lakes. M. aeruginosa is a unicellular cyanobacteria that form colonies. They produce toxins and therefore become a potential threat to water quality and human health. Understanding the distribution of this species in space and time is important for improving water management strategies. The model we propose includes both hydrodynamics and physiological responses including explicitly buoyancy regulation in Microcystis cells. Our model applies the Langevin–Fokker–Planck approach to simulate the total colony number concentration along the water column. This approach allows the description of sinking and rising velocities of colonies of different sizes and compositions subjected to turbulent mixing. The model is first applied to the 30m deep Lake Vlietland in the Netherlands for the summer of 2009. During this summer, the lake showed high blooms of Microcystis which eventually led to scum formation along the shore. The simulations show the preferential distribution of M. aeruginosa through the water column and their strong dependency on colony size. On a daily cycle, small colonies (50–200μm) do not remain near the surface but are highly concentrated in the middle of the epilimnion, whereas large colonies (≥800μm) are able to migrate to greater depths and concentrate only temporarily near the surface. For comparing our computer model with available measurements of Microcystis concentration distributions we applied it to Lakes IJsselmeer and Vinkeveen. The results show a good agreement with the observations of diurnal changes in buoyancy status.
The collapse of turbulence in a pressure‐driven, cooled channel flow is studied by using 3D direct numerical simulations (DNS) in combination with theoretical analysis using a local similarity model. ...Previous studies with DNS reported a definite collapse of turbulence in cases when the normalized surface cooling h/L (with h the channel depth and L the Obukhov length) exceeded a value of 0.5. A recent study by the present authors succeeded in explaining this collapse using the so‐called maximum sustainable heat flux (MSHF) theory. This states that collapse may occur when the ambient momentum of the flow is too weak to transport enough heat downward to compensate for the surface cooling. The MSHF theory predicts that, in pressure‐driven flows, acceleration of the fluid after collapse will eventually cause a regeneration of turbulence, in contrast with the aforementioned DNS results. It also predicts that the flow should be able to survive ‘supercritical’ cooling rates, in cases when sufficient momentum is applied to the initial state. Here, both predictions are confirmed using DNS simulations. It is also shown that in DNS a recovery of turbulence will occur naturally, provided that perturbations of finite amplitude are imposed on the laminarized state and provided that sufficient time for flow acceleration is allowed. As such, we conclude that the collapse of turbulence in this configuration is a temporary, transient phenomenon for which a universal cooling rate does not exist. Finally, in the present work a one‐to‐one comparison between a parametrized, local similarity model and the turbulence‐resolving model (DNS) is made. Although local similarity originates from observations that represent much larger Reynolds numbers than those covered by our DNS simulations, both methods appear to predict very similar mean velocity (and temperature) profiles. This suggests that in‐depth analysis with DNS can be an attractive complementary tool with which to study atmospheric physics, in addition to tools that are able to represent high Reynolds number flows like large‐eddy simulations.
We report flow measurements in rotating Rayleigh–Bénard convection in the rotationally constrained geostrophic regime. We apply stereoscopic particle image velocimetry to measure the three components ...of velocity in a horizontal cross-section of a water-filled cylindrical convection vessel. At a constant, small Ekman number $Ek=5\times 10^{-8}$, we vary the Rayleigh number $Ra$ between $10^{11}$ and $4\times 10^{12}$ to cover various subregimes observed in geostrophic convection. We also include one non-rotating experiment. The scaling of the velocity fluctuations (expressed as the Reynolds number $Re$) is compared to theoretical relations expressing balances of viscous–Archimedean–Coriolis (VAC) and Coriolis–inertial–Archimedean (CIA) forces. Based on our results we cannot decide which balance is most applicable here; both scaling relations match equally well. A comparison of the current data with several other literature datasets indicates a convergence towards diffusion-free scaling of velocity as $Ek$ decreases. However, at lower $Ra$, the use of confined domains leads to prominent convection in the wall mode near the sidewall. Kinetic energy spectra point at an overall flow organisation into a quadrupolar vortex filling the cross-section. This quadrupolar vortex is a quasi-two-dimensional feature; it manifests only in energy spectra based on the horizontal velocity components. At larger $Ra$, the spectra reveal the development of a scaling range with exponent close to $-5/3$, the classical exponent for inertial range scaling in three-dimensional turbulence. The steeper $Re(Ra)$ scaling at low $Ek$ and development of a scaling range in the energy spectra are distinct indicators that a fully developed, diffusion-free turbulent bulk flow state is approached, sketching clear perspectives for further investigation.
A model based on the Lattice Boltzmann method is developed to study the flow of reactive electro-kinetic fluids in porous media. The momentum, concentration and electric/potential fields are ...simulated via the Navier–Stokes, advection–diffusion/Nernst–Planck and Poisson equations, respectively. With this model, the total density and velocity fields, the concentration of reactants and reaction products, including neutral and ionized species, the electric potential and the interaction forces between the fields can be studied, and thus we provide an insight into the interplay between chemistry, flow and the geometry of the porous medium. The results show that the conversion efficiency of the reaction can be strongly influenced by the fluid velocity, reactant concentration and by porosity of the porous medium. The fluid velocity determines how long the reactants stay in the reaction areas, the reactant concentration controls the amount of the reaction material and with different dielectric constant, the porous medium can distort the electric field differently. All these factors make the reaction conversion efficiency display a non-trivial and non-monotonic behaviour as a function of the flow and reaction parameters. To better illustrate the dependence of the reaction conversion efficiency on the control parameters, based on the input from a number of numerical investigations, we developed a phenomenological model of the reactor. This model is capable of capturing the main features of the causal relationship between the performance of the reactor and the main test parameters. Using this model, one could optimize the choice of reaction and flow parameters in order to improve the performance of the reactor and achieve higher production rates.
This article is part of the theme issue ‘Progress in mesoscale methods for fluid dynamics simulation’.
The effects of an axial rotation on the turbulent convective flow because of an adverse temperature gradient in a water-filled upright cylindrical vessel are investigated. Both direct numerical ...simulations and experiments applying stereoscopic particle image velocimetry are performed. The focus is on the gathering of turbulence statistics that describe the effects of rotation on turbulent Rayleigh–Bénard convection. Rotation is an important addition, which is relevant in many geophysical and astrophysical flow phenomena. A constant Rayleigh number (dimensionless strength of the destabilizing temperature gradient) Ra = 109 and Prandtl number (describing the diffusive fluid properties) σ = 6.4 are applied. The rotation rate, given by the convective Rossby number Ro (ratio of buoyancy and Coriolis force), takes values in the range 0.045 ≤ Ro ≤ ∞, i.e. between rotation-dominated flow and zero rotation. Generally, rotation attenuates the intensity of the turbulence and promotes the formation of slender vertical tube-like vortices rather than the global circulation cell observed without rotation. Above Ro ≈ 3 there is hardly any effect of the rotation on the flow. The root-mean-square (r.m.s.) values of vertical velocity and vertical vorticity show an increase when Ro is lowered below Ro ≈ 3, which may be an indication of the activation of the Ekman pumping mechanism in the boundary layers at the bottom and top plates. The r.m.s. fluctuations of horizontal and vertical velocity, in both experiment and simulation, decrease with decreasing Ro and show an approximate power-law behaviour of the shape Ro0.2 in the range 0.1 ≲ Ro ≲ 2. In the same Ro range the temperature r.m.s. fluctuations show an opposite trend, with an approximate negative power-law exponent Ro−0.32. In this Rossby number range the r.m.s. vorticity has hardly any dependence on Ro, apart from an increase close to the plates for Ro approaching 0.1. Below Ro ≈ 0.1 there is strong damping of turbulence by rotation, as the r.m.s. velocities and vorticities as well as the turbulent heat transfer are strongly diminished. The active Ekman boundary layers near the bottom and top plates cause a bias towards cyclonic vorticity in the flow, as is shown with probability density functions of vorticity. Rotation induces a correlation between vertical vorticity and vertical velocity close to the top and bottom plates: near the top plate downward velocity is correlated with positive/cyclonic vorticity and vice versa (close to the bottom plate upward velocity is correlated with positive vorticity), pointing to the vortical plumes. In contrast with the well-mixed mean isothermal bulk of non-rotating convection, rotation causes a mean bulk temperature gradient. The viscous boundary layers scale as the theoretical Ekman and Stewartson layers with rotation, while the thermal boundary layer is unaffected by rotation. Rotation enhances differences in local anisotropy, quantified using the invariants of the anisotropy tensor: under rotation there is strong turbulence anisotropy in the centre, while near the plates a near-isotropic state is found.
The present study concerns the Lagrangian dynamics of three-dimensional (3D) buoyancy-driven cavity flows under steady and laminar conditions due to a global temperature gradient imposed via an ...opposite hot and cold sidewall. This serves as the archetypal configuration for natural-convection flows in which (contrary to the well-known Rayleigh–Bénard flow) gravity is perpendicular (instead of parallel) to the global temperature gradient. Limited insight into the Lagrangian properties of this class of flows, despite its relevance to observed flow phenomena as well as scalar transport, motivates this study. The 3D Lagrangian dynamics are investigated in terms of the generic structure and associated transport properties of the global streamline pattern (‘Lagrangian flow topology’) by both theoretical and computational analyses. The Grashof number
$Gr$
is the principal control parameter for the flow topology: limit
$Gr=0$
yields a trivial state of closed streamlines;
$Gr>0$
induces symmetry breaking by fluid inertia and buoyancy and thus causes formation of toroidal coherent structures (‘primary tori’) embedded in chaotic streamlines governed by Hamiltonian mechanisms. Fluid inertia prevails for ‘smaller’
$Gr$
and gives behaviour that is dynamically entirely analogous to 3D lid-driven cavity flows. Buoyancy-induced bifurcation of the flow topology occurs for ‘larger’
$Gr$
and underlies the emergence of ‘secondary rolls’ observed in the literature and to date unreported secondary tori for ‘larger’ Prandtl numbers
$Pr$
. Key to these dynamics are stagnation points and corresponding heteroclinic manifold interactions.
When the classical Rayleigh–Bénard (RB) system is rotated about its vertical axis roughly three regimes can be identified. In regime I (weak rotation) the large-scale circulation (LSC) is the ...dominant feature of the flow. In regime II (moderate rotation) the LSC is replaced by vertically aligned vortices. Regime III (strong rotation) is characterized by suppression of the vertical velocity fluctuations. Using results from experiments and direct numerical simulations of RB convection for a cell with a diameter-to-height aspect ratio equal to one at $\mathit{Ra}\ensuremath{\sim} 1{0}^{8} \text{{\ndash}} 1{0}^{9} $ ($\mathit{Pr}= 4\text{{\ndash}} 6$) and $0\lesssim 1/ \mathit{Ro}\lesssim 25$ we identified the characteristics of the azimuthal temperature profiles at the sidewall in the different regimes. In regime I the azimuthal wall temperature profile shows a cosine shape and a vertical temperature gradient due to plumes that travel with the LSC close to the sidewall. In regimes II and III this cosine profile disappears, but the vertical wall temperature gradient is still observed. It turns out that the vertical wall temperature gradient in regimes II and III has a different origin than that observed in regime I. It is caused by boundary layer dynamics characteristic for rotating flows, which drives a secondary flow that transports hot fluid up the sidewall in the lower part of the container and cold fluid downwards along the sidewall in the top part.
Field observations and theoretical analysis are used to investigate the appearance of different nocturnal boundary layer regimes. Recent theoretical findings predict the appearance of two different ...regimes: the continuously turbulent (weakly stable) boundary layer and the relatively "quiet" (very stable) boundary layer. A large number of nights (approximately 4500 in total) are analyzed using an ensemble averaging technique. The observations support the existence of these two fundamentally different regimes: weakly stable (turbulent) nights rapidly reach a steady state (within 2-3 h). In contrast, very stable nights reach a steady state much later after a transition period (2-6 h). During this period turbulence is weak and nonstationary. To characterize the regime, a new parameter is introduced: the shear capacity. This parameter compares the actual shear after sunset with the minimum shear needed to sustain continuous turbulence. In turn, the minimum shear is dictated by the heat flux demand at the surface (net radiative cooling), so that the shear capacity combines flow information with knowledge of the boundary condition. It is shown that the shear capacity enables prediction of the flow regimes. The prognostic strength of this nondimensional parameter appears to outperform the traditional ones like the similarity parameter z/L and the gradient Richardson number R sub(i) as a regime indicator.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
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