Internal Forcing Research Articles

On the energy decay of a viscoelastic piezoelectric beam model with nonlinear internal forcing terms and a nonlinear feedback

In this paper, we consider a piezoelectric beam model with nonlinear source terms and investigate the interaction between a viscoelastic damping and a nonlinear frictional damping. Under general assumptions on the relaxation function and the nonlinear feedback, we establish explicit formulae for the energy decay rates of this system and prove that the energy decays at a rate dictated by the weaker damping. Our results substantially improve some earlier related results in the literature.

Stratified inclined duct: direct numerical simulations

The stratified inclined duct (SID) experiment consists of a zero-net-volume exchange flow in a long tilted rectangular duct, which allows the study of realistic stratified shear flows with sustained internal forcing. We present the first three-dimensional direct numerical simulations (DNS) of SID to explore the transitions between increasingly turbulent flow regimes first described by Meyer & Linden (J. Fluid Mech., vol. 753, 2014, pp. 242–253). We develop a numerical set-up that faithfully reproduces the experiments and sustains the flow for arbitrarily long times at minimal computational cost. We recover the four qualitative flow regimes found experimentally in the same regions of parameter space: laminar flow, waves, intermittent turbulence and fully developed turbulence. We find good qualitative and quantitative agreement between DNS and experiments and highlight the added value of DNS to complement experimental diagnostics and increase our understanding of the transition to turbulence, both temporally (laminar/turbulent cycles) and parametrically (as the tilt angle of the duct and the Reynolds number are increased). These results demonstrate that numerical studies of SID – and deeper integration between simulations and experiments – have the potential to lead to a better understanding of stratified turbulence.

Decreasing surface chlorophyll in the tropical ocean as an indicator of anthropogenic greenhouse effect during 1998–2020

Abstract Available satellite data reveal a decreasing trend in surface chlorophyll (SChl) over the entire tropical ocean until 2020. Where contributions by internal variability and external forcing remain unclear. Here, state-of-the-art climate model simulations are analyzed to show that external forcing significantly contributes to the decreasing SChl trend. In contrast, internal variability plays a weak or even offsetting role. As for the underlying processes, anthropogenic greenhouse emissions lead to a remarkable reduction in SChl over the tropical oceans, whereas industrial aerosol load facilitates a considerable increase in SChl in the western tropical Pacific. In addition, the negative phase of the interdecadal Pacific variability during 1998–2020 contributes to an increase in SChl, while the impact from the Atlantic multidecadal variability is relatively weak in facilitating a decrease in SChl. Overall, these results imply that the impact of anthropogenic forcing has emerged as indicated in the tropical marine ecosystem.

Ensemble Spread Behavior in Coupled Climate Models: Insights From the Energy Exascale Earth System Model Version 1 Large Ensemble

AbstractAssessing uncertainty in future climate projections requires understanding both internal climate variability and external forcing. For this reason, single‐model initial condition large ensembles (SMILEs) run with Earth System Models (ESMs) have recently become popular. Here we present a new 20‐member SMILE with the Energy Exascale Earth System Model version 1 (E3SMv1‐LE), which uses a “macro” initialization strategy choosing coupled atmosphere/ocean states based on inter‐basin contrasts in ocean heat content (OHC). The E3SMv1‐LE simulates tropical climate variability well, albeit with a muted warming trend over the twentieth century due to overly strong aerosol forcing. The E3SMv1‐LE's initial climate spread is comparable to other (larger) SMILEs, suggesting that maximizing inter‐basin ocean heat contrasts may be an efficient method of generating ensemble spread. We also compare different ensemble spread across multiple SMILEs, using surface air temperature and OHC. The Community Earth system Model version 1, the only ensemble which utilizes a “micro” initialization approach perturbing only atmospheric initial conditions, yields lower spread in the first ∼30 years. The E3SMv1‐LE exhibits a relatively large spread, with some evidence for anthropogenic forcing influencing spread in the late twentieth century. However, systematic effects of differing “macro” initialization strategies are difficult to detect, possibly resulting from differing model physics or responses to external forcing. Notably, the method of standardizing results affects ensemble spread: control simulations for most models have either large background trends or multi‐centennial variability in OHC. This spurious disequlibrium behavior is a substantial roadblock to understanding both internal climate variability and its response to forcing.

Stochastic estimation of Green’s functions with application to diffusion and advection-diffusion-reaction problems

A stochastic method is described for estimating Green’s functions (GF’s), appropriate to linear advection-diffusion-reaction transport problems, evolving in arbitrary geometries. By allowing straightforward construction of approximate, though high-accuracy GF’s, within any geometry, the technique solves the central challenge in obtaining Green’s function solutions. In contrast to Monte Carlo solutions of individual transport problems, subject to specific sets of conditions and forcing, the proposed technique produces approximate GF’s that can be used: a) to obtain (infinite) sets of solutions, subject to any combination of (random and deterministic) boundary, initial, and internal forcing, b) as high fidelity direct models in inverse problems, and c) as high quality process models in thermal and mass transport design, optimization, and process control problems. The technique exploits an equivalence between the adjoint problem governing the transport problem Green’s function, G(x,t|x′,t′), and the backward Kolmogorov problem governing the transition density, p(x,t|x′,t′), of the stochastic process used in Green’s function construction. We address nonspecialists and report four contributions. First, a recipe is outlined for diagnosing when stochastic Green’s function estimation can be used, and for subsequently estimating the transition density and associated Green’s function. Second, a naive estimator for the transition density is proposed and tested. Third, Green’s function estimation error produced by random walker absorption at Dirichlet boundaries is suppressed using a simple random walker splitting technique. Last, spatial discontinuity in estimated GF’s, produced by the naive estimator, is suppressed using a simple area averaging method. The paper provides guidance on choosing key numerical parameters, and the technique is tested against two simple unsteady, linear heat conduction problems, and an unsteady groundwater dispersion problem, each having known, exact GF’s.

A 2000-year temperature reconstruction on the East Antarctic plateau from argon–nitrogen and water stable isotopes in the Aurora Basin North ice core

Abstract. The temperature of the Earth is one of the most important climate parameters. Proxy records of past climate changes, in particular temperature, represent a fundamental tool for exploring internal climate processes and natural climate forcings. Despite the excellent information provided by ice core records in Antarctica, the temperature variability of the past 2000 years is difficult to evaluate from the low-accumulation sites in the Antarctic continent interior. Here we present the results from the Aurora Basin North (ABN) ice core (71∘ S, 111∘ E, 2690 m a.s.l.) in the lower part of the East Antarctic plateau, where accumulation is substantially higher than other ice core drilling sites on the plateau, and provide unprecedented insight into East Antarctic past temperature variability. We reconstructed the temperature of the last 2000 years using two independent methods: the widely used water stable isotopes (δ18O) and by inverse modelling of borehole temperature and past temperature gradients estimated from the inert gas stable isotopes (δ40Ar and δ15N). This second reconstruction is based on three independent measurement types: borehole temperature, firn thickness, and firn temperature gradient. The δ18O temperature reconstruction supports stable temperature conditions within 1 ∘C over the past 2000 years, in agreement with other ice core δ18O records in the region. However, the gas and borehole temperature reconstruction suggests that surface conditions 2 ∘C cooler than average prevailed in the 1000–1400 CE period and supports a 20th century warming of 1 ∘C. A precipitation hiatus during cold periods could explain why water isotope temperature reconstruction underestimates the temperature changes. Both reconstructions arguably record climate in their own way, with a focus on atmospheric and hydrologic cycles for water isotopes, as opposed to surface temperature for gas isotopes and boreholes. This study demonstrates the importance of using a variety of sources for comprehensive paleoclimate reconstructions.

External Dynamic Mechanisms Controlling the Periodic Offshore Blooms in Beibu Gulf

AbstractSince offshore waters are less affected by human activities and nutrient‐rich water masses, existing theories on periodic offshore blooms (POB) consider that the POB is proportional to the intensity of ocean fronts (nutrient supply from enhancing vertical mixing), ignoring external nutrient supply and external forcing (climatic oscillations). This study proposes an external dynamic mechanism of the POB on the basis of field observations and long‐term satellite remote sensing data (1981–2022) in Beibu Gulf, which is influenced by remarkable external forcing. A strong thermal front with an inverted‐V structure occurred in the central gulf every winter due to the strong wind stress. The intensity of the front on the east side is weaker due to the intrusion of the west‐Guangdong coastal current (WGCC). However, nutrient supply variation resulted in the POB's different intensity in different areas of the inverted‐V front. Chlorophyll a concentrations in the eastern (nutrients supplied by WGCC) and northern (nutrients supplied by vertical mixing) were obviously higher than that in the western front (limited nutrient supply) in winter. On an interannual scale, the intensity of POB in La Niña years is remarkably stronger than in El Niño years due to the stronger WGCC supplying more nutrients in La Niña. This study suggests that the intensity and range of POB are not proportional to the frontal intensity in the gulf, but are directly driven by the internal forcing (fronts and nutrient supply from WGCC), which is controlled by the external forcing.

Influence of solar forcing on multidecadal variability in the Atlantic meridional overturning circulation (AMOC)

There is a growing debate regarding the influence of solar activity on climate change as the solar forcing signal on decadal/multidecadal timescales is not robust in long-term reconstructed climate data or numerical simulations. However, solar forcing could be amplified by ocean–atmosphere coupling in sensitive regions, including the North Atlantic Ocean (N.A.). This study assessed the influence of varied total solar irradiance (TSI) due to the effects of solar activity on Atlantic Meridional Overturning Circulation (AMOC) based on an Earth System model with intermediate complexity (PLASIM-GENIE). Three groups of experiments with different TSI series; i.e., constant (NS), decadal varied (DS), and reconstructed whole (AS) for 1610–2000, were conducted and the AMOC response was investigated. The results showed that the internal forcing of the climate system led to quasi-35-year and quasi-65-year AMOC cycles and a significant and stable negative correlation between TSI and AMOC on a multidecadal timescale. The period was significantly extended due to solar forcing. The declining AMOC trend occurred in simulations after 1800. Thus, solar forcing contributed to a weakening AMOC at a rate of 0.41 Sv per century. The decadal variation in TSI was the main contributor to this decline due to solar forcing.

A direct N-body integrator for modelling the chaotic, tidal dynamics of multibody extrasolar systems: TIDYMESS

ABSTRACT Tidal dissipation plays an important role in the dynamical evolution of moons, planets, stars, and compact remnants. The interesting complexity originates from the interplay between the internal structure and external tidal forcing. Recent and upcoming observing missions of exoplanets and stars in the galaxy help to provide constraints on the physics of tidal dissipation. It is timely to develop new N-body codes, which allow for experimentation with various tidal models and numerical implementations. We present the open-source N-body code TIDYMESS, which stands for ‘TIdal DYnamics of Multibody ExtraSolar Systems’. This code implements a Creep deformation law for the bodies, parametrized by their fluid Love numbers and fluid relaxation times. Due to tidal and centrifugal deformations, we approximate the general shape of a body to be an ellipsoid. We calculate the associated gravitational field to quadruple order, from which we derive the gravitational accelerations and torques. The equations of motion for the orbits, spins and deformations are integrated directly using a fourth-order integration method based on a symplectic composition. We implement a novel integration method for the deformations, which allows for a time-step solely dependent on the orbits, and not on the spin periods or fluid relaxation times. This feature greatly speeds up the calculations, while also improving the consistency when comparing different tidal regimes. We demonstrate the capabilities and performance of TIDYMESS, particularly in the niche regime of parameter space where orbits are chaotic and tides become non-linear.

A statistical perspective on the signal‐to‐noise paradox

AbstractAn anomalous signal‐to‐noise ratio (also called the signal‐to‐noise paradox) present in climate models has been widely reported, affecting predictions and projections from seasonal to centennial timescales and encompassing prediction skill from internal processes and external climate forcing. An anomalous signal‐to‐noise ratio describes a situation where the mean of a forecast ensemble correlates better with the corresponding verification than with its individual ensemble members. This situation has severe implications for climate science, meaning that large ensembles might be required to extract prediction signals. Although a number of possible physical mechanisms for this paradox have been proposed, none has been universally accepted. From a statistical point of view, an anomalous signal‐to‐noise ratio indicates that forecast ensemble members are not statistically interchangeable with the verification, and an apparent paradox arises only if such an interchangeability is assumed. It will be demonstrated in this study that an anomalous signal‐to‐noise ratio is a consequence of the relative magnitudes of the variance of the observations, the ensemble mean, and the error of the ensemble mean. By analysing the geometric triangle formed by these three quantities, and given that for typical seasonal forecasting systems both the correlation and the forecast signal are relatively small, it is concluded that an anomalous signal‐to‐noise ratio should, in fact, be expected in such circumstances.

A 1.5-million-year record of orbital and millennial climate variability in the North Atlantic

Abstract. Climate during the last glacial period was marked by abrupt instability on millennial timescales that included large swings of temperature in and around Greenland (Daansgard–Oeschger events) and smaller, more gradual changes in Antarctica (AIM events). Less is known about the existence and nature of similar variability during older glacial periods, especially during the early Pleistocene when glacial cycles were dominantly occurring at 41 kyr intervals compared to the much longer and deeper glaciations of the more recent period. Here, we report a continuous millennially resolved record of stable isotopes of planktic and benthic foraminifera at IODP Site U1385 (the “Shackleton Site”) from the southwestern Iberian margin for the last 1.5 million years, which includes the Middle Pleistocene Transition (MPT). Our results demonstrate that millennial climate variability (MCV) was a persistent feature of glacial climate, both before and after the MPT. Prior to 1.2 Ma in the early Pleistocene, the amplitude of MCV was modulated by the 41 kyr obliquity cycle and increased when axial tilt dropped below 23.5∘ and benthic δ18O exceeded ∼3.8 ‰ (corrected to Uvigerina), indicating a threshold response to orbital forcing. Afterwards, MCV became focused mainly on the transitions into and out of glacial states (i.e. inceptions and terminations) and during times of intermediate ice volume. After 1.2 Ma, obliquity continued to play a role in modulating the amplitude of MCV, especially during times of glacial inceptions, which are always associated with declining obliquity. A non-linear role for obliquity is also indicated by the appearance of multiples (82, 123 kyr) and combination tones (28 kyr) of the 41 kyr cycle. Near the end of the MPT (∼0.65 Ma), obliquity modulation of MCV amplitude wanes as quasi-periodic 100 kyr and precession power increase, coinciding with the growth of oversized ice sheets on North America and the appearance of Heinrich layers in North Atlantic sediments. Whereas the planktic δ18O of Site U1385 shows a strong resemblance to Greenland temperature and atmospheric methane (i.e. Northern Hemisphere climate), millennial changes in benthic δ18O closely follow the temperature history of Antarctica for the past 800 kyr. The phasing of millennial planktic and benthic δ18O variation is similar to that observed for MIS 3 throughout much of the record, which has been suggested to mimic the signature of the bipolar seesaw – i.e. an interhemispheric asymmetry between the timing of cooling in Antarctica and warming in Greenland. The Iberian margin isotopic record suggests that bipolar asymmetry was a robust feature of interhemispheric glacial climate variations for at least the past 1.5 Ma despite changing glacial boundary conditions. A strong correlation exists between millennial increases in planktic δ18O (cooling) and decreases in benthic δ13C, indicating that millennial variations in North Atlantic surface temperature are mirrored by changes in deep-water circulation and remineralization of carbon in the abyssal ocean. We find strong evidence that climate variability on millennial and orbital scales is coupled across different timescales and interacts in both directions, which may be important for linking internal climate dynamics and external astronomical forcing.

A weak-form spectral Chebyshev technique for nonlinear vibrations of rotating functionally graded beams

This study presents the spectral Chebyshev technique (SCT) for nonlinear vibrations of rotating beams based on a weak formulation. In addition to providing a fast-converging and precise solution for linear vibrations of structures with complex geometry, material, and physics, this method is further advanced to be able to analyze the nonlinear vibration behavior of continuous systems. Rotational motion and material gradation further complicate this nonlinear behavior. Accordingly, the beam is considered to be axially functionally graded (FG) and a model representing the forced nonlinear vibrations of the beam about steady-state equilibrium deformations (SSEDs) is developed. The model includes Coriolis, centrifugal softening, and nonlinear stiffening effects caused by coupling of the axial, chordwise, and flapwise motions, and large amplitude deformations. The integral boundary value problem for the rotating structure is discretized using the SCT and element-wise multiplication definition. As a result, mass, damping, and stiffness matrices, as well as internal nonlinear forcing functions and external forcing vectors, are obtained for a given rotating beam. This formulation provides a general representation of nonlinear strain relations in matrix form and circumvents the complexity rising from obtaining and solving the partial differential equations directly. In addition, nonlinear forcing functions are obtained in matrix form which facilitates the application of harmonic balance method easier to obtain the forced nonlinear response.

The dry and hot American Southwest under the present and future climates

The American Southwest is undergoing alarming climate crises, suffering from the on-going mega drought, frequent flash flooding, heat waves, and wildfires that cause air pollution. The climate crises are mainly associated with hydroclimatic processes and particularly water fluxes across the different components of the climate system. This study serves to discuss where the author stand in terms of scientific understanding of hydroclimatic systems in this region and their physical drivers (e.g., the North American Summer monsoon and Pacific North American teleconnections). This work highlights the relative contributions of precipitation and temperature to droughts through the lens of theories and modeling tools. More importantly, it is crucial to characterize the relative roles of internal variability and external forcing in shaping the hydroclimatic system in the southwestern United States. Future pathways are also described including high-resolution global modeling system, advancing understanding relative roles of precipitation and temperature in modulating hydroclimate system, further understanding the role of external forcing, as well as the partnership between scientists and other stakeholders.摘要由于正在持续的特⼤⼲旱, 更频繁的洪⽔, 热浪以及导致空⽓污染的⼭⽕, 美国西南部⽬前正在 经历⽓候危机. 这些⽓候危机主要与⽔⽂⽓候过程相关, 尤其是⽓候系统各圈层之间的⽔汽通量. 本研究主要讨论⽬前⼀些⽔⽂系统的科学基站以及物理驱动因素, ⽐如北美夏季风以及太平洋北美遥相关. 本研究指出降⽔以及⽓温对于⼲旱的相对作⽤的理论和⼯具. 确定内部变率和外部强迫对于美国西南部⽔⽂⽓候系统的相对作⽤尤为重要. 展望未来, 需要研究⾼分辨率模拟系统, 加强降⽔以及温度对于⽔⽂⽓候系统相对作⽤的理解, 外部强迫的作⽤以及通过科学家以及 其他利益相关者之间的合作.

Small-scale spatiotemporal thermal regimes drive patterns of zooplankton abundance in a kelp forest

During internal tidal forcing, high-frequency water column temperatures and zooplankton abundances were measured within and at the outer edge of a Giant Kelp Forest at two depths. Although the sampling sites were only separated by 300m, differences occurred in their thermal regimes and in their zooplankton abundance, distribution, and temperature relationships. Dominant organisms at both sites included copepods and bryozoan cyphonautes. Outside of the kelp forest, the water column was more stratified, with distinct alternating cold and warm periods defined by abrupt thermal fronts indicative of internal wave phases. Lower zooplankton abundances and fewer taxa (only 31) were detected, with more cyphonautes and copepods found in the deeper strata and during the cold phase of internal waves. Inside the kelp forest, on the other hand, the water column was less stratified and less variable over time, with no clear alternating internal wave phases. An order of magnitude greater zooplankton abundance occurred with more taxa (54) identified and more cyphonatues and copepods found in the surface strata. At both sites, abundances of copepods increased with high frequency cooling in the deeper strata, whereas near the surface they showed the reverse pattern, increasing during warming. Across sites, cyphonautes decreased outside of the kelp forest while they increased within the kelp forest. The patterns detected across depths, across sites, and related with high frequency thermal variability suggest complex forcing of zooplankton abundances by alternating shoaling and sinking of the thermocline related with internal waves. These results emphasize the small-scale spatiotemporal biophysical complexity in nearshore waters and contribute to the understanding of nearshore plankton dynamics related with internal wave forcing mechanisms in Giant Kelp Forest environments.

Well-posedness and applications of classical elastohydrodynamics for a swimming filament

We consider a classical elastohydrodynamic model of an inextensible filament undergoing planar motion in . The hydrodynamics are described by resistive force theory, and the fibre elasticity is governed by Euler–Bernoulli beam theory. Our aim is twofold: (1) Serve as a starting point for developing the mathematical analysis of filament elastohydrodynamics, particularly the analytical treatment of an inextensibility constraint, and (2) As an application, prove conditions on internal fibre forcing that allow a free-ended filament to swim. Our analysis of fibre swimming speed is supplemented with a numerical optimization of the internal fibre forcing, as well as a novel numerical method for simulating an inextensible swimmer.

Soil moisture-constrained East Asian Monsoon meridional patterns over China from observations

As an internal forcing of the earth climate system, soil moisture (SM) significantly influences the water and energy cycle by controlling evapotranspiration and terrestrial solar energy. The current study used observed precipitation, remotely sensed SM, and reanalysis of atmosphere and land parameters to assess the East Asian Monsoon (EAM) precipitation variability due to meridional SM oscillations across China. A generalized linear method, namely coupled manifold technique (CMT) for assessing the reciprocal forcing between two climate fields and numerical simulations are applied to SM and EAM precipitation. We find that the EAM precipitation interannual variability between north and south China significantly correlates with SM meridional oscillation. The CMT results further showed that SM forcing has a significant (99% confidence) influence on the EAM precipitation explaining about 0.40 of the variance ratio in north and south China. The EAM and SM composite analysis show that the wetter (drier) north (south) oscillates the EAM precipitation over the north (south) of China and vice versa due to SM thermal controls. We then used control and sensitivity simulations with SM observations to further validate the findings implying that SM can potentially improve the interannual EAM forecast skills. The model results show that a wetter (drier) north (south) results in negative (positive) sensible heat (latent heat) anomalies that impact the boundary layer and propagate to change the meridional atmospheric heating profile. When positive (negative) SM anomalies exist over northern (southern) China, the zonal easterlies and extratropical westerlies move to north China causing above-normal precipitation that descends into southern China, suppressing subtropical westerlies and precipitation in southern China. On the contrary, a dry (wet) north (south) favors intensified subtropical westerlies and precipitation in southern China. The findings have dire implications for the water and energy cycle of the region in the projected wetting and drying patterns of the north (south).

Causes and evolution of winter polynyas north of Greenland

Abstract. During the 42-year period (1979–2020) of satellite measurements, four major winter (December–March) polynyas have been observed north of Greenland: one in December 1986 and three in the last decade, i.e., February of 2011, 2017, and 2018. The 2018 polynya was unparalleled in its magnitude and duration compared to the three previous events. Given the apparent recent increase in the occurrence of these extreme events, this study aims to examine their evolution and causality, in terms of forced versus natural variability. The limited weather station and remotely sensed sea ice data are analyzed combining with output from the fully coupled Regional Arctic System Model (RASM), including one hindcast and two ensemble simulations. We found that neither the accompanying anomalous warm surface air intrusion nor the ocean below had an impact (i.e., no significant ice melting) on the evolution of the observed winter open-water episodes in the region. Instead, the extreme atmospheric wind forcing resulted in greater sea ice deformation and transport offshore, accounting for the majority of sea ice loss in all four polynyas. Our analysis suggests that strong southerly winds (i.e., northward wind with speeds greater than 10 m s−1) blowing persistently over the study region for at least 2 d or more were required over the study region to mechanically redistribute some of the thickest Arctic sea ice out of the region and thus to create open-water areas (i.e., a latent heat polynya). To assess the role of internal variability versus external forcing of such events, we carried out and examined results from the two RASM ensembles dynamically downscaled with output from the Community Earth System Model (CESM) Decadal Prediction Large Ensemble (DPLE) simulations. Out of 100 winters in each of the two ensembles (initialized 30 years apart: one in December 1985 and another in December 2015), 17 and 16 winter polynyas were produced north of Greenland, respectively. The frequency of polynya occurrence had no apparent sensitivity to the initial sea ice thickness in the study area pointing to internal variability of atmospheric forcing as a dominant cause of winter polynyas north of Greenland. We assert that dynamical downscaling using a high-resolution regional climate model offers a robust tool for process-level examination in space and time, synthesis with limited observations, and probabilistic forecasts of Arctic events, such as the ones being investigated here and elsewhere.

On a nonlinear system of plate equations with variable exponent nonlinearity and logarithmic source terms: Existence and stability results

<abstract><p>In this paper, we consider a coupling non-linear system of two plate equations with logarithmic source terms. First, we study the local existence of solutions of the system using the Faedo-Galerkin method and Banach fixed point theorem. Second, we prove the global existence of solutions of the system by using the potential wells. Finally, using the multiplier method, we establish an exponential decay result for the energy of solutions of the system. Some conditions on the variable exponents that appear in the coupling functions and the involved constants that appear in the source terms are determined to ensure the existence and stability of solutions of the system. A series of lemmas and theorems have been proved and used to overcome the difficulties caused by the variable exponent and the logarithmic nonlinearities. Our result generalizes some earlier related results in the literature from the case of only constant exponent of the nonlinear internal forcing terms to the case of variable exponent and logarithmic source terms, which is more useful from the physical point of view and needed in several applications.</p></abstract>

Twelve-Year Cycle in the Cloud Top Winds Derived from VMC/Venus Express and UVI/Akatsuki Imaging

We present joint analysis of the UV (365 nm) images captured by the cameras on board ESA’s Venus Express and JAXA’s Akatsuki spacecraft. These observations enabled almost continuous characterization of the cloud top circulation over the longest period of time so far (2006–2021). More than 46,000 wind vectors were derived from tracking the UV cloud features and revealed changes in the atmospheric circulation with the period of 12.5 ± 0.5 years. The zonal wind component is characterized by an annual mean of −98.6 ± 1.3 m/s and an amplitude of 10.0 ± 1.6 m/s. The mean meridional wind velocity is −2.3 ± 0.2 m/s and has an amplitude of 3.4 ± 0.3 m/s. Plausible physical explanations of the periodicity include both internal processes and external forcing. Both missions observed periodical changes in the UV albedo correlated with the circulation variability. This could result in acceleration or deceleration of the winds due to modulation of the deposition of the radiative energy in the clouds. The circulation can be also affected by the solar cycle that has a period of approximately 11 years with a large degree of deviation from the mean. The solar cycle correlated with the wind observations can probably influence both the radiative balance and chemistry of the mesosphere. The discovered periodicity in the cloud top circulation of Venus, and especially its similarity with the solar cycle, is strongly relevant to the study of exoplanets in systems with variable “suns”.

Remote internal wave forcing of regional ocean simulations near the U.S. West Coast

Low mode internal waves are able to propagate across ocean basins and modulate ocean dynamics thousands of kilometers away from their generation sites. In this study, the impact of remotely generated internal waves on the internal wave energetics near the U.S. West Coast is investigated with realistically forced regional ocean simulations. At the open boundaries, we impose high-frequency oceanic state variables obtained from a global ocean simulation with realistic atmospheric and astronomical tidal forcing. We use the Discrete Fourier Transform (DFT) technique in separating ingoing and outgoing internal tide energy fluxes at the open boundaries in order to quantify internal tide reflections. Although internal tide reflections are reduced with increasing sponge viscosity and/or sponge layer width, reflection coefficients (λ) can be as high as 73%. In the presence of remote internal waves, the model variance and spatial correlations become more in agreement with both mooring and altimetry datasets. The results confirm that an improved internal wave continuum can be achieved in regional models with remote internal wave forcing at the open boundaries. However, care should be taken to avoid excessive reflections of internal waves from the interior at these boundaries.