Penetrative Convection Research Articles

Madden–Julian Oscillation and the Winter Rainfall in Taiwan

Abstract This study discusses major impacts of the Madden–Julian oscillation (MJO) on the winter (November–April) rainfall in Taiwan. The results show that Taiwan has more rainfall in MJO phases 3 and 4 (MJO convectively active phase in the Indian Ocean and the western part of the Maritime Continent), and less rainfall in phases 7 and 8 (the western Pacific warm pool area). Mechanisms associated with the MJO are suggested as follows. 1) The tropics to midlatitude wave train: when the MJO moves to the middle Indian Ocean, a Matsuno–Gill-type pattern is induced. The feature of this tropical atmospheric response to the MJO diabatic heating is a pair of upper-level anomalous anticyclones symmetric about the equator to the west of the heating. The northern anomalous anticyclone over the Arabian Sea and northern India induces a northeastward-propagating wave train to the midlatitudes. The wave pattern consists of a cyclonic anomaly centered at East Asia that enhances the winter rainfall in Taiwan. 2) Increase of moisture supply from the South China Sea: when the MJO convection approaches Sumatra and Java of the Maritime Continent, the eastward penetration of equatorial convection enhances a low-level southerly flow that transports the moisture northward to Taiwan and southern China. As a consequence, with the increase of moisture supply from the south, more winter monsoon rainfall is observed in Taiwan.

Resonant Penetrative Convection with an Internal Heat Source/Sink

We develop a detailed linear instability and nonlinear stability analysis for the situation of convection in a horizontal plane layer of fluid when there is a heat sink/source which is linear in the vertical coordinate which is in the opposite direction to gravity. This can give rise to a scenario where the layer effectively splits into three sublayers. In the lowest one the fluid has a tendency to be convectively unstable while in the intermediate layer it will be gravitationally stable. In the top layer there is again the possibility for the layer to be unstable. This results in a problem where convection may initiate in either the lowest layer, the upmost layer, or perhaps in both sublayers simultaneously. In the last case there is the possibility of resonance between the upmost and lowest layers. In all cases penetrative convection may occur where convective movement in one layer induces motion in an adjacent sublayer. In certain cases the critical Rayleigh number for thermal convection may display a very rapid increase which is much greater than normal. Such behaviour may have application in energy research such as in thermal insulation.

Three dimensional simulations of penetrative convection in a porous medium with internal heat sources

The problem of penetrative convection in a fluid saturated porous medium heated internally is analysed. The linear instability theory and nonlinear energy theory are derived and then tested using three dimensions simulation. Critical Rayleigh numbers are obtained numerically for the case of a uniform heat source in a layer with two fixed surfaces. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using a three dimensional simulation. Our results show that the linear threshold accurately predicts the onset of instability in the basic steady state. However, the required time to arrive at the basic steady state increases significantly as the Rayleigh number tends to the linear threshold.

TOWARD CONNECTING CORE-COLLAPSE SUPERNOVA THEORY WITH OBSERVATIONS. I. SHOCK REVIVAL IN A 15M☉BLUE SUPERGIANT PROGENITOR WITH SN 1987A ENERGETICS

We study the evolution of the collapsing core of a 15 Msun blue supergiant supernova progenitor from the core bounce until 1.5 seconds later. We present a sample of hydrodynamic models parameterized to match the explosion energetics of SN 1987A. We find the spatial model dimensionality to be an important contributing factor in the explosion process. Compared to two-dimensional simulations, our three-dimensional models require lower neutrino luminosities to produce equally energetic explosions. We estimate that the convective engine in our models is 4% more efficient in three dimensions than in two dimensions. We propose that the greater efficiency of the convective engine found in three-dimensional simulations might be due to the larger surface-to-volume ratio of convective plumes, which aids in distributing energy deposited by neutrinos. We do not find evidence of the standing accretion shock instability nor turbulence being a key factor in powering the explosion in our models. Instead, the analysis of the energy transport in the post-shock region reveals characteristics of penetrative convection. The explosion energy decreases dramatically once the resolution is inadequate to capture the morphology of convection on large scales. This shows that the role of dimensionality is secondary to correctly accounting for the basic physics of the explosion. We also analyze information provided by particle tracers embedded in the flow, and find that the unbound material has relatively long residency times in two-dimensional models, while in three dimensions a significant fraction of the explosion energy is carried by particles with relatively short residency times.

Simulation of three dimensional double-diffusive throughflow in internally heated anisotropic porous media

A model for double-diffusive convection in an anisotropic porous layer with a constant throughflow is explored, with penetrative convection being simulated via an internal heat source. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using three dimensional simulation. Our results show that the linear threshold accurately predicts on the onset of instability in the steady state throughflow. However, the required time to arrive at the steady state increases significantly as the Rayleigh number tends to the linear threshold.

Study of formation process of cold intermediate layer based on reanalysis of Black Sea hydrophysical fields for 1971–1993

A reanalysis of hydrophysical fields for 1971–1993 is used to study the formation mechanisms of the cold intermediate layer (CIL): the advective mechanism (associated with the advection of cold waters formed in the northwestern shelf (NWS)) and the convective mechanism (caused by wintertime convection inside cyclonic gyres in the central part of the sea). We consider the periods of alternating atmospheric conditions: the mild winter of 1980–1981, normal winter of 1987–1988, and cold winter of 1992–1993. Interannual features of replenishment and renewal of “old” CIL waters caused by these mechanisms are identified. In particular, cooled shelf waters sink along the continental slope and merge with “old” CIL waters during the mild winter of 1980–1981 more than 1 month later than during the cold winter 1992–1993 and more than 3 weeks later than during the normal winter of 1987–1988. The Sevastopol anticyclonic gyre and the northwest branch of the Black Sea Rim Current markedly influence the transformation of entrained cold NWS waters transported to the southwest and the central part of the water area. The local formation process of cold intermediate waters is found to be caused by the wintertime penetrating convection over domelike isosurfaces of temperature and salinity arising due to rising constant halocline (pycnocline) at the centers of cyclonic gyres because of the intensification of the wintertime circulation. Anomalously cold surface water, characterized by increased density, gradually sinks. An analysis of TS indices indicates that the transformed cold water spreads out over isopycnic surfaces with time, being entrained in cyclonic circulation and spreading throughout the sea, thus renewing “old” CIL waters.

EFFECTS OF PENETRATIVE CONVECTION ON SOLAR DYNAMO

Spherical solar dynamo simulations are performed. Self-consistent, fully compressible magnetohydrodynamic system with a stably stratified layer below the convective envelope is numerically solved with a newly developed simulation code based on the Yin-Yang grid. The effects of penetrative convection are studied by comparing two models with and without the stable layer. The differential rotation profile in both models is reasonably solar-like with equatorial acceleration. When considering the penetrative convection, a tachocline-like shear layer is developed and maintained beneath the convection zone without assuming any forcing. While turbulent magnetic field becomes predominant in the region where the convective motion is vigorous, mean-field component is preferentially organized in the region where the convective motion is less vigorous. Especially in the stable layer, the strong large-scale field with a dipole symmetry is spontaneously built up. The polarity reversal of the mean-field component takes place globally and synchronously throughout the system regardless the presence of the stable layer. Our results suggest that the stably stratified layer is a key component for organizing the large-scale strong magnetic field, but is not essential for the polarity reversal.

Analysis of available data from liquefied natural gas rollover incidents to determine critical stability ratios

Liquefied natural gas (LNG) rollover refers to the sudden mixing of stratified LNG layers, which can cause the generation of significant amounts of boil‐off gas. Such events are a significant safety concern in LNG storage but there are no reliable models for its description at industrial scales available in the open literature. In this article, the data and models for LNG rollover existing in the open literature are reviewed and a new framework for quantitatively analyzing the limited available data is presented. We extended the definition of the hydrostatic stability ratio for binary mixtures to allow its estimation for multicomponent mixtures, either from the reported LNG layer compositions or measurements of the LNG layer densities. By analyzing the graphical data of Bates and Morrison (Int J. Heat Mass Transfer. 1997;40:8) the critical value of the stability ratio, Rc, separating the diffusive phase of LNG rollover from the penetrative convection phase was estimated to be 3.8 ± 0.5. This is significantly larger than the critical ratio of 2 reported for saline solutions and is also larger than the initial stability ratio of 1.7 estimated from the best documented LNG rollover incident at La Spezia in 1971. Lumped‐parameter models for LNG rollover reported in the literature have successfully described the La Spezia incident by using the Reynolds analogy to estimate mass transfer rates from heat transfer correlations. However, these same models are unsuccessful when applied to other reported LNG rollover incidents, with the predicted rollover time being too short because the mass‐transfer coefficient is overestimated. The results presented here suggest that these limitations could be overcome by using a smaller mass‐transfer coefficient (estimated, e.g., from the Chilton‐Colburn analogy) and by tracking the multicomponent system's stability ratio until the critical value is reached whereupon the mass transfer regime changes. © 2013 American Institute of Chemical Engineers AIChE J, 60: 362–374, 2014

On the structure of the Lofoten Basin Eddy

A small anticyclonic eddy of extraordinary intensity sits in the center of the Lofoten Basin near 69°40′N, 3°E. This paper gives a first detailed description of its kinematics and lowest‐order dynamic balances. Using a 75 kHz vessel‐mounted acoustic Doppler current profiler, hydrography, and six RAFOS floats to probe the eddy, we document a solid body core with 7–8 km radius and relative vorticity very close to –f, where f is the local Coriolis parameter. Maximum orbital velocities close to 0.8 ms−1 were observed at 18 km radius. One float, trapped in the core of the eddy for 9 months, indicated undiminished strength throughout that period, possibly even intensifying in winter. Hydrography revealed adiabatic conditions from the bottom of a shallow seasonal thermocline to 1000 m depth in early July 2010. Thermal convection in winter maintains an already deep pycnostad, and may also play a key role in intensifying the eddy, quite possibly through penetrative convection that deepens and sharpens the underlying pycnocline. Heat lost to the atmosphere has to be replenished from warm anticyclonic eddies shed off the eastern branch of the Norwegian Atlantic Current, but the mechanism(s) by which it is added to the eddy remains to be studied. Examination of historical data sets suggests the eddy is a permanent feature of the Lofoten Basin. Two hydrocasts from the 1960s also show a similar adiabatic mixed layer albeit 1°C cooler than in 2010, perhaps reflecting the generally cold winter conditions that prevailed then.

Tropopause analysis over the Iranian region using GPS radio occultation data

Near-tropopause phenomena like upper level fronts and cyclones, penetrative cumulus convection and mesoscale mechanisms of exchange make important contributions to the mixing processes in the atmosphere. Spatio-temporal monitoring of the tropopause height, temperature and pressure is an appropriate tool to show the running processes in the atmosphere. In this study, GPS radio occultation data is used to investigate the tropopause height fluctuations and the relation between the stratosphere–troposphere exchange and the aforementioned phenomena over the Iranian region. The paper shows how the position of the sub-tropical jet has changed with time, using GPS radio occultation observations. The tropopause height changes latitudinally, and three different bimodal probability distribution functions are observed. The results also show that the mixing region in the south of Iran is associated with the subtropical jet in winter. However, this region shifts north of Iran due to changes in the position of the subtropical jet during the summer. Consistency of the mixing region from the radio occultation data and the total ozone of TOMS over the Iranian region is also observed.

Horizontal convection dynamics: insights from transient adjustment

AbstractThe dynamics of horizontal convection are revealed by examining transient adjustment toward thermal equilibrium. We restrict attention to high Rayleigh numbers (of $O(1{0}^{12} )$) and a Prandtl number ${\sim }5$ that characterize many practical applications, and consider responses to small changes in the thermal boundary conditions, using laboratory experiments, three-dimensional direct numerical simulations (DNS) and simple theoretical models. The experiments and the mechanical energy budget from the DNS demonstrate that unsteady forcing can produce flow dramatically more active than horizontal convection under steady forcing. The physical mechanisms at work are indicated by the time scales of approach to the new equilibrium, and we show that these can range over two orders of magnitude depending on the imposed change in boundary conditions. Changes that lead to a net destabilizing buoyancy flux give rapid adjustments: for applied heat flux conditions the whole of the circulation is controlled by conduction through the stable portion of the boundary layer, whereas for applied temperature difference the circulation is controlled by small-scale convection within the unstable part of the boundary layer. The experiments, DNS and models are in close agreement and show that the time scale under applied temperatures is as small as 0.01 vertical diffusion time scales, a factor of four smaller than for imposed flux. Both cases give adjustments too rapid for diffusion in the interior to play a significant role, at least through 99 % of the adjustment, and we conclude that diffusion through the full depth is not significant in setting the equilibrium state. Boundary changes leading to a net stabilizing buoyancy flux give a very different response, causing the convection to quickly form a shallow circulation cell, followed eventually by a return to full-depth overturning through a combination of penetrative convection and conduction. The time scale again varies by orders of magnitude, depending on the boundary conditions and the location of the imposed boundary perturbation.

Solar-like oscillations in distant stars as seen by CoRoT : the special case of HD 42618, a solar sister

We report the observations of a main-sequence star, HD 42618 (Teff = 5765 K, G3V) by the space telescope CoRoT. This is the closest star to the Sun ever observed by CoRoT in term of its fundamental parameters. Using a preliminary version of CoRoT light curves of HD 42618, p modes are detected around 3.2 mHz associated to ℓ = 0, 1 and 2 modes with a large spacing of 142 μHz. Various methods are then used to derive the mass and radius of this star (scaling relations from solar values as well as comparison between theoretical and observationnal frequencies) giving values in the range of (0.80 − 1.02)M⊙ and (0.91 − 1.01)R⊙. A preliminary analysis of ℓ = 0 and 1 modes allows us also to study the amount of penetrative convection at the base of the convective envelope.

VARIABLE GRAVITY FIELD AND THROUGHFLOW EFFECTS ON PENETRATIVE CONVECTION IN A POROUS LAYER

The effect of vertical throughflow and variable gravity field on the onset of penetrative convection simulated via internal heating in a porous medium is studied. Flow in the porous medium is governed by Forchheimer-extended Darcy equation. The boundaries are considered to be rigid, however permeable, and insulated to temperature perturbations. The eigen value problem is solved using a regular perturbation technique with wave number as a perturbation parameter. The variable gravity parameter, the direction of throughflow and the presence of volumetric internal heat source in a porous layer play a decisive role on the stability characteristics of the system. In addition, the influence of Prandtl number arising due to throughflow is also emphasized on the stability of the system. It is observed that both stabilizing and destabilizing factors can be enhanced due to the simultaneous presence of a volumetric source, gravity field and vertical throughflow so that a more precise control (suppress or augment) of thermal convective instability in a layer of porous medium is possible.

The penetrative mixing in the Laptev Sea coastal polynya pycnocline layer

The large recurrent areas of open water and/or thin ice (polynyas) producing cold brine-enriched waters off the fast-ice edge are evident in the Laptev Sea in winter time. A number of abrupt positively correlated transitions in temperature and salinity were recorded in the bottom and intermediate layers at a mooring station in the West New Siberian (WNS) polynya in February–March 2008. Being in the range of ∼0.5°C and ∼1.6psu these changes are induced by horizontal motions across the polynya and correspond to temperature and salinity horizontal gradients in the range of 0.3–1.0°C/10km and 1.4–3.5psu/10km, respectively. The events of distinct freshening and temperature decrease coincide with a northward current off the fast-ice edge, while southward currents brought saltier and warmer waters at intermediate depths. We suggest that the observed transitions are connected to altering pycnocline depths across the polynya. The source of relatively fresher waters at the intermediate depths in polynya is supposed to originate from penetrative mixing of surface low salinity waters to intermediate water depth. Several forcing processes that could be responsible for a penetrative mixing through the density interface in polynya are discussed. These are penetrative convection and shear-driven mixing that originates from two-layer water dynamics and/or baroclinic tidal motions. The heavily ridged seaward fast-ice edge could produce an additional source of turbulent mixing even through a shear-free density interface due to the increased roughness at the ice–water interface.

Rotation induced mixing in stellar interiors

The standard model of stellar structure is unable to account for various observational facts, such as anomalies in the surface composition, and there is now a broad consensus that some extra mixing must occur in the radiation zones, in addition to the always present convective overshoot or penetration. The search for the causes of this extra mixing started in the late seventies, and it was quickly realized – in particular by Sylvie Vauclair and her co-workers – that some mild turbulence must be present to counteract the effect of gravitational settling and radiative levitation. What could be responsible for this turbulence? One suggestion was the internal gravity waves emitted at the boundary of convection zones, but it is still not established whether these waves will lead to true mixing. However they transport angular momentum, and therefore they generate differential rotation, which may be shear-unstable and thus lead to turbulence. Another way to transport angular momentum and produce an unstable rotation profile is through the large-scale circulation which is induced by the structural adjustments as the star evolves, or by the torques applied to it (due to stellar wind, accretion, tides). These processes participate in what is called the “rotational mixing”; their implementation in stellar evolution codes – again under Sylvie's impulse – has given birth to a new generation of stellar models, which agree much better with the observational constraints, although there is still room for improvement.

An alternative scaling for unsteady penetrative free convection

The daytime evolution of the atmospheric boundary layer under high pressure, anticyclonic synoptic systems over a homogeneous terrain can be successfully described by a penetrative free convection model, evolving from an initially stably stratified environment. In this article dimensional analysis has been employed to derive a new set of scaling parameters, which are functions of external, time‐dependent, fluid properties and boundary conditions. This novel theoretical framework has been adopted to compare laboratory scale experiments, performed using a thermally controlled water tank and a Large Eddy Simulation (LES) numerical model. Both these have been developed for the characterization of the instabilities associated with the development of the Convective Boundary Layer (CBL). The characteristic length and time scales of the thermal plumes, their spatial distribution and interaction with the overlying stable layer are analyzed. The proposed scaling parameters appear to be representative of the bulk and turbulent properties of the CBL, as confirmed by both numerical and laboratory results.

Triply resonant penetrative convection

A thermal convection model is considered that consists of a layer of viscous incompressible fluid contained between two horizontal planes. Gravity is acting vertically downward, and the fluid has a density maximum in the active temperature range. A heat source/sink that varies with vertical height is imposed. It is shown that in this situation there are three possible (different) sub-layers that may induce convective overturning instability. The possibility of resonance between the motion in these layers is investigated. A region is discovered where a very sharp increase in Rayleigh number is observed. In addition to a linearized instability analysis, two global (unconditional) nonlinear stability thresholds are derived.

Structural stability for the resonant porous penetrative convection

We study the structural stability of a problem in a porous medium when the density of saturating liquid is a nonlinear function of temperature and an internal heat source is present. We prove a convergence result for the Forchheimer coefficient. That is to say, when λ → 0, the solution of the non-isothermal flow in a porous medium of the Forchheimer type, see (1.1), can converge to the solution of the equivalent Darcy type.

Seismic signature of envelope penetrative convection: the CoRoT star HD 52265

Aims: We aim at characterizing the inward transition from convective to radiative energy transport at the base of the convective envelope of the solar-like oscillator HD 52265 recently observed by the CoRoT satellite. Methods: We investigated the origin of one specific feature found in the HD 52265 frequency spectrum. We modelled the star to derive the internal structure and the oscillation frequencies that best match the observations and used a seismic indicator sensitive to the properties of the base of the envelope convection zone. Results: The seismic indicators clearly reveal that to best represent the observed properties of HD 52265, models must include penetrative convection below the outer convective envelope. The penetrative distance is estimated to be $\sim0.95 H_P$, which corresponds to an extent over a distance representing 6.0 per cents of the total stellar radius, significantly larger than what is found for the Sun. The inner boundary of the extra-mixing region is found at $0.800\pm0.004 R$ where $R=1.3 R_\odot$ is the stellar radius. Conclusions: These results contribute to the tachocline characterization in stars other than the Sun.

Structural stability in resonant penetrative convection in a Forchheimer porous material

Structural stability is studied in the problem of a fluid saturating a porous medium of Forchheimer type when the density of the fluid has a cubic temperature dependence. This problem allows the possibility of resonance between internal layers in thermal convection. In this paper we investigate continuous dependence on the heat source, this source being an important quantity in the resonance problem.