Vertical Dissipation Research Articles

Stability for the 2D magnetic Bénard system with partial dissipation and thermal damping near an equilibrium

In this paper, we focus on the Boussinesq equations with magnetohydrodynamics convection, in which the temperature obeys degenerate damped wave equations. Under the influence of an equilibrium, we prove that the 2D magnetic Bénard system remains stable in the whole space . In particular, we obtain the decay rate and large‐time behavior. Without the coupling, the 2D MHD system with only vertical dissipation is not known to be stable. It is revealed that both the thermal damping and the horizontal background magnetic field are indispensable.

Insights on Lateral Gravity Wave Propagation in the Extratropical Stratosphere From 44 Years of ERA5 Data

AbstractThe study presents (a) a 44‐year wintertime climatology of resolved gravity wave (GW) fluxes and forcing in the extratropical stratosphere using ERA5, and (b) their composite evolution around gradual (final warming) and abrupt (sudden warming) transitions in the wintertime circulation, focusing on lateral fluxes. The transformed Eulerian mean equations are leveraged to provide a glimpse of the importance of GW lateral propagation (i.e., horizontal propagation) toward driving the wintertime stratospheric circulation by analyzing the relative contribution of the vertical versus meridional flux dissipation. The relative contribution from lateral propagation is found to be notable, especially in the Austral winter stratosphere where lateral (vertical) momentum flux convergence provides a peak climatological forcing of up to −0.5 (−3.5) m/s/day around 60°S at 40–45 km altitude. Prominent lateral propagation in the wintertime midlatitudes also contributes to the formation of belts of GW activity in both hemispheres.

Investigation of piezocone dissipation test interpretation in clay accounting for vertical and horizontal porewater pressure dissipation with a large deformation axisymmetric penetration model

Investigation of piezocone dissipation test interpretation in clay accounting for vertical and horizontal porewater pressure dissipation with a large deformation axisymmetric penetration model

Shallow- and deep-convection characteristics in the greater Houston, Texas, area using cell tracking methodology

Abstract. The convective lifecycle, from initiation to maturity and dissipation, is driven by a combination of kinematic, thermodynamic, microphysical, and radiative processes that are strongly coupled and variable in time and space. Weather radars have been traditionally used to provide various convective-cloud characteristics. Here, we analyzed climatological convective-cell radar characteristics to obtain and assess the diurnal cycles of three convective-cell types – shallow, modest deep, and vigorous deep convective cells – that formed in the greater Houston area, using the National Weather Service radar from Houston, Texas, and a multi-cell identification and tracking algorithm. The examined dataset spans 4 years (2018–2021) and covers the warm-season months (June to September) in those years. The analysis showed clear diurnal cycles in cell initiation (CI) consistent with the sea breeze circulation and showed diurnal and normalized lifetime relationships in cell evolution parameters (e.g., maximum reflectivity, echo-top height, Geostationary Operational Environmental Satellite-16 (GOES-16) channel 13 brightness temperature, and the height of maximum reflectivity). The cell evolution is well represented by relationships between (1) the height and value of the maximum radar reflectivity, (2) the minimum GOES-16 channel 13 brightness temperature and the maximum vertically integrated liquid, (3) the maximum reflectivity and columnar-average reflectivity, and (4) the echo-top ascent rate and cell lifetime. The relationships presented herein help to identify the cell lifecycle stages such as early shallow convection, vigorous vertical development, anvil development, and convective core dissipation. GOES-16 Aerosol Optical Depth values are also used as a proxy for cell initiation aerosol concentrations to investigate any potential relationships between initiation location and aerosol concentration. Overall, no significant relationships between initiation location and aerosol concentration were found for the three cell types investigated, but there are some minor differences in the pre-CI aerosol optical depth for vigorous deep convective cells.

Comparison of Fat Transfer Combined with Plasma Energy and Only Fat Transfer Methods for Genital Rejuvenation.

To compare the fat transfer combined with plasma energy and only fat transfer methods for genital rejuvenation and to investigate the efficacy enhancing properties of plasma energy. Forty-six patients were equally divided into two groups according to the surgical method as the group A (n = 23) and the group B (n = 23). The patients in the group A received only fat transfer, while the patients in the group B received fat transfer combined with plasma energy. Both groups were scheduled for postoperative follow-up at 1, 3, 6, and 12 months. The lifting effect on the labia majora after the procedure was evaluated with photographs and patient satisfaction questionnaires including the female genital self-image scale (FGSIS). The mean age of all participants was 32.8 ± 5.1 years, and the mean body mass index (BMI) was 24.7 ± 3.4kg/m2. The mean preoperative FGSIS scores were similar between the groups (p = 0.542). The mean total FGSIS score was 18.8 ± 1.4 in the group A and 18.3 ± 1.5 in the group B in the preoperative period. However, the mean FGSIS scores at 1, 3, and 6 months were significantly higher in the group B than the group A (p = 0.032, p = 0.012, and p = 0.009, respectively). At 6 months of follow-up, the mean total FGSIS score was 20.7 ± 1.4 in the group A and 22.3 ± 1.5 in the group B, indicating a statistically significant difference (p = 0.028). This novel technique is a more minimally invasive technique compared to other energy modalities with lower lateral and vertical energy dissipation than other conventional methods, and labia majora fat filling augmentation application can be performed with more permanent and longer-lasting outcomes than fat transfer only. This journal requires that authors assign a level of evidence to each article. For a full description of these Evidence-Based Medicine ratings, please refer to the Table of Contents or the online Instructions to Authors www.springer.com/00266.

The two-and-a-half-dimensional incompressible Hall-MHD system with partial dissipation

In this paper, we investigate the Cauchy problem for the two-and-a-half-dimensional incompressible Hall-magnetohydrodynamic equations with partial dissipation. We prove the global regularity of a certain system of equations with horizontal or vertical dissipation and magnetic hyper-diffusion for large initial data.

Substrate dependence of the self-heating in lead zirconate titanate (PZT) MEMS actuators

Lead zirconate titanate (PZT) thin films offer advantages in microelectromechanical systems (MEMSs) including large motion, lower drive voltage, and high energy densities. Depending on the application, different substrates are sometimes required. Self-heating occurs in the PZT MEMS due to the energy loss from domain wall motion, which can degrade the device performance and reliability. In this work, the self-heating of PZT thin films on Si and glass and a film released from a substrate were investigated to understand the effect of substrates on the device temperature rise. Nano-particle assisted Raman thermometry was employed to quantify the operational temperature rise of these PZT actuators. The results were validated using a finite element thermal model, where the volumetric heat generation was experimentally determined from the hysteresis loss. While the volumetric heat generation of the PZT films on different substrates was similar, the PZT films on the Si substrate showed a minimal temperature rise due to the effective heat dissipation through the high thermal conductivity substrate. The temperature rise on the released structure is 6.8× higher than that on the glass substrates due to the absence of vertical heat dissipation. The experimental and modeling results show that the thin layer of residual Si remaining after etching plays a crucial role in mitigating the effect of device self-heating. The outcomes of this study suggest that high thermal conductivity passive elastic layers can be used as an effective thermal management solution for PZT-based MEMS actuators.

Stability for a system of the 2D incompressible magneto-micropolar fluid equations with partial mixed dissipation

This paper focuses on the 2D incompressible anisotropic magneto-micropolar fluid equations with vertical dissipation, horizontal magnetic diffusion, and horizontal vortex viscosity. The goal is to investigate the stability of perturbations near a background magnetic field in the 2D magneto-micropolar fluid equations. Two main results are obtained. The first result is based on the linear system. Global existence for any large initial data and asymptotic linear stability are established. The second result explores stability for the nonlinear system. It is proven that if the initial data are sufficiently small, then the solution for some perturbations near a background magnetic field remains small. Additionally, the long-time behaviour of the solution is presented. The most challenging terms in the proof are the linear terms in the velocity equation and the micro-rotation equation that will grow with respect to time t. We are able to find some background fields to control the growth of the linear terms. Our results reveal that some background fields can stabilise electrically conducting fluids.

Field observations of the wake from a full-scale tidal turbine array

Wake measurements are critical for quantifying the hydrodynamic effects of tidal energy extraction and for designing arrays of tidal turbines. In this investigation field measurements from the wake of PLAT-I, a commercial-scale floating array of four tidal turbines, are presented. Instrumented surface-following drifters are used to measure velocity and turbulence in the wake of PLAT-I while deployed in Grand Passage, an energetic tidal channel in the Bay of Fundy, NS, Canada. Field measurements were obtained when the turbines where fully operational under optimal conditions during spring tides. The collected data are used to construct tridimensional maps of acoustic backscatter, mean velocity, vertical velocity variance and turbulent kinetic energy dissipation rate downstream of the platform at different stages of the tide. The operational turbine array wake was captured for ebb and flood tides. For both ebb and flood, reduced velocities are observed in the upper water column at the depths spanned by the turbine rotors. Vertical profiles of velocity mix quickly during flood tide but velocities remain slower than the undisturbed flow outside of the wake up to 20 effective diameters downstream of the platform. In contrast, during ebb, the velocity deficit persists farther downstream, and the reduced velocity increases slightly. Elevated turbulence levels peak at 2 effective diameters downstream of the turbines and recover to undisturbed flow levels at approximately 10 effective diameters downstream of the platform for both ebb and flood tides. Total energy dissipated through turbulence within the wake is estimated to be less than 10% of the energy extracted for electricity production.

Stability threshold of Couette flow for 2D Boussinesq equations in Sobolev spaces

Consider the nonlinear stability of the Couette flow in the Boussinesq equations with vertical dissipation on T×R. We prove that if the initial perturbations uin and θin to the Couette flow vs=(y,0)⊤ and θs=1, respectively, satisfy ‖uin‖HN+1+ν−12‖θin‖HN+ν−13‖|∂x|13θ‖HN≪ν13, N>7, then the resulting solution remains close to the Couette flow in L2 at the same order for all time.

Vertical migration and dissipation of oxytetracycline induces the recoverable shift in microbial community and antibiotic resistance

Antibiotic resistance gene (ARG) spread in anthropogenic polluted soils is believed to be accelerated by the incidental inputs of antibiotics via fertilizing and irrigation, and endangering food and human health. However, due to the complex nature of substrates and uncertain microbial responses, the primary drivers of ARG dissemination remain unclear. To address this concern, the effects of antibiotic inputs on soil microbes and antibiotic resistance under simulated natural conditions was investigated in this study. Specifically, four flow-through reactors with gravity flow were established, and the oxytetracycline (OTC) a typical antibiotic in agricultural soils was studied at environmental concentrations (i.e. 0.1, 1 and 10 mg/kg) for 31 days. The vertical distribution and dissipation of OTC were profiled by measuring the residuals in layers over time. Correspondingly, the effects of antibiotic exposure on microbial communities and ARG abundances were studied. The results showed that the average exposure intensity of OTC in different soil layers ranged in 0.03–6.45 mg/kg, and resulted in different dissipation kinetics. In addition, top layer was found to be the main site of OTC reduction, where OTC dissipated at magnitude of 74.0–96.6 %, depending on the initial OTC concentration. OTC migration and dissipation resulted in the shift of community composition to the extent of 0.25–0.33 in terms of Bray-Curtis distance, which partially recovered over time. And the achievement of alternative community compositions was supposed to be largely affected by the microbial interaction. Along with the community changes, a short-term accumulation of resistance genes was detected, while the relative abundance of indicator ARGs, i.e. tetG and mexB, rising up to 10-fold higher than the initial, although eventually decayed. Collective findings of this study indicated that antibiotics at environmental concentrations might trigger extra microbial interactions and thereby reducing the demand for ARGs accumulation. It provided valuable understandings in the risk of antibiotic spillage, especially for the incident exposure at the environmentally relevant concentrations.

The uniqueness of global solution for the 2D Boussinesq equations with partial dissipation

In this paper, we prove the uniqueness of the global solution for a two-dimensional Boussinesq system with only vertical dissipation and horizontal thermal diffusion. This settles a uniqueness problem remarked in O. Said, et al. [12].

Stability and decay rate of smooth solutions for the 3D Boussinesq equation with partial horizontal dissipation and thermal damping

In this paper, we investigate the stability and large time behavior of some three dimensional Boussinesq equations with the horizontal dissipation in the horizontal velocity components and thermal damping. Due to the lack of vertical dissipation in the horizontal velocity components and full dissipation in the vertical velocity component, these problems becomes very challenging. Combining the higher order Sobolev norm of the velocity and the temperature and decay estimates of the lower order Sobolev norm of the velocity and the temperature, the stability issue and precise decay rates have been built. The most difficulty is to estimate L1-norm of ‖∇hu‖L∞ in time variable t.

Stabilizing Effect of the Magnetic Field and Large-Time Behavior of 2D Incompressible MHD System with Vertical Dissipation

Stabilizing Effect of the Magnetic Field and Large-Time Behavior of 2D Incompressible MHD System with Vertical Dissipation

The Global Well-Posedness and Decay Estimates for the 3D Incompressible MHD Equations With Vertical Dissipation in a Strip

Abstract The three-dimensional incompressible magnetohydrodynamic (MHD) system with only vertical dissipation arises in the study of reconnecting plasmas. When the spatial domain is the whole space $\mathbb R^3$, the small data global well-posedness remains an extremely challenging open problem. The one-directional dissipation is simply not sufficient to control the nonlinearity in $\mathbb R^3$. This paper solves this open problem when the spatial domain is the strip $\Omega := \mathbb R^2\times [0,1]$ with Dirichlet boundary conditions. By invoking suitable Poincaré type inequalities and designing a multi-step scheme to separate the estimates of the horizontal and the vertical derivatives, we are able to establish the global well-posedness in the Sobolev setting $H^3$ as long as the initial horizontal derivatives are small. We impose no smallness condition on the vertical derivatives of the initial data. Furthermore, the $H^3$-norm of the solution is shown to decay exponentially in time. This exponential decay is surprising for a system with no horizontal dissipation. This large-time behavior reflects the smoothing and stabilizing phenomenon due to the interaction within the MHD system and with the boundary.

Stability of the 3D MHD equations without vertical dissipation near an equilibrium

<abstract><p>Important progress has been made on the standard Laplacian case with mixed partial dissipation and diffusion. The stability problem of the 3D incompressible magnetohydrodynamic (MHD) equations without vertical dissipation but with the fractional velocity dissipation $ (-\Delta)^\alpha u $ and magnetic diffusion $ (-\Delta)^\beta b $ is unfortunately not often well understood for many ranges of fractional powers. This paper discovers that there are new phenomena with the case $ \alpha, \beta \leq 1 $. We establish that, if an initial datum ($ u_0, b_0 $) in the Sobolev space $ H^3(\mathbb{R}^3) $ is close enough to the equilibrium state, and we replace the terms $ (-\Delta)^\alpha u $ and $ (-\Delta)^\beta b $ by $ (-\Delta_h)^\alpha u $ and $ (-\Delta_h)^\beta b $, respectively, the resulting equations with $ \alpha, \beta \in(\frac{1}{2}, 1] $ then always lead to a steady solution, where $ \Delta_h = \partial_{x_1}^2+\partial_{x_2}^2 $.</p></abstract>

Stability of hydrostatic equilibrium in a uniform magnetic field with mixed partial dissipation

This paper intend to study the BMHD system in the whole space $ \mathbb{R}^{2} $ with vertical dissipation, horizontal magnetic dissipation and vertical temperature dissipation.Under the perturbation of hydrostaticequilibrium in a uniform magnetic field, we prove the nonlinear stability by introducing two additional functionals of the horizontalderivative of the velocity and the temperature.Simultaneously, the large-time behavior is also obtained.

Global regularity for the 3D axisymmetric incompressible Hall-MHD system with partial dissipation and diffusion

In this paper, we study the Cauchy problem for the 3D incompressible axisymmetric Hall-MHD system with horizontal velocity dissipation and vertical magnetic diffusion.We obtain a unique global smooth solution of which in the cylindrical coordinate system the swirl velocity fields, the radial and the vertical components of the magnetic fields are trivial. This type of solution has been studied for the MHD system in [17][16] and [15] and for the Hall-MHD system with total dissipation and diffusion in [11]. Some new and fine estimates are obtained in this paper to overcome the difficulties raised from the Hall term and the loss of vertical velocity dissipation and horizontal magnetic diffusion. Finally we can show that the estimates $\int_0^T \ \nabla u(t)\ _{L^\infty} dt$ and $\int_0^T \ \nabla b(t)\ _{L^\infty} dt$ are finite in a priori way and hence obtain the global well-posedness to the system under considered.

Using dissolved oxygen variance to investigate the influence of nonextreme wind events on hypoxia in Mobile Bay, a shallow stratified estuary

Wind forcing plays an important role in determining spatial patterns of estuarine bottom water hypoxia, defined as dissolved oxygen (DO) concentration< 2 mg L-1, by driving coastal circulation patterns and by intensifying mixing of the water column. However, the importance of these wind-driven mixing processes varies with space and time and are dynamically intermingled with biological processes like photosynthesis and respiration making it difficult to tease apart wind impacts on DO dynamics in estuarine systems. Using a high-resolution, three-dimensional numerical model, we studied the effect of a non-extreme southeast wind event on the DO dynamics of Mobile Bay during a hypoxic event in April-May of 2019. A new approach, called ‘vertical dissolved oxygen variance’ (VDOV) was developed to quantitatively separate all the physical and biogeochemical factors in the water column that control the development and dissipation of hypoxia events. The system-wide volume integrated values of VDOV tracked the changes in hypoxic area in the bay and the VDOV tendency term was dominated by contributions from sediment oxygen demand (DO loss via respiration) and vertical dissipation (DO gain via mixing). There was a notable inverse relationship between hypoxia area and wind speed. Further analysis of the local VDOV during a non-extreme southeast wind event showed the wind-induced vertical dissipation was the main factor in eliminating hypoxia from the bay. This enhanced dissipation accounted for both turbulent mixing from wind stress and negative straining of the vertical density gradient from wind induced circulation. The response of DO to the wind forcing prompted the development of two non-dimensional numbers, an advection-diffusion time-scale ratio and a demand-diffusion flux ratio, to better generalize the expected DO dynamics. Overall, this work showed that wind effects are critical for understanding hypoxia variability in a shallow stratified estuary.

Stability and exponential decay of the magnetic Bénard system with horizontal dissipation

This article is concerned with the global stability problem for the two-dimensional magnetic Bénard system. The focus here involves only horizontal dissipation, horizontal magnetic diffusion, and horizontal thermal diffusivity. The lack of vertical dissipation makes it difficult to study the stability and long-time behavior of the magnetic Bénard system. To handle these, we use a new method to decompose the velocity u, magnetic field b, and temperature Θ into the horizontal average (u‾,b‾,Θ‾) and the oscillation part (u˜,b˜,Θ˜). Then we establish the global stability by using several anisotropic inequalities when the initial data are small in H2(Ω). Moreover, we mathematically show that the H1-norm of the oscillation part eventually decays exponentially to zero. Furthermore, the solution (u,b,Θ) approaches the horizontal average (u‾,b‾,Θ‾) asymptotically.