Large Horizontal Velocity Research Articles

Kinetic Energy Exchanges between a Two-Dimensional Front and Internal Waves

Abstract Fronts and near-inertial waves (NIWs) are energetic motions in the upper ocean that have been shown to interact and provide a route for kinetic energy (KE) dissipation of balanced oceanic flows. In this paper, we study these KE exchanges using an idealized model consisting of a two-dimensional geostrophically balanced front undergoing strain-induced semigeostrophic frontogenesis and internal wave (IW) vertical modes. The front–IW KE exchanges are quantified separately during two frontogenetic stages: an exponential sharpening stage that is characterized by a low Rossby number and is driven by the imposed strain (i.e., mesoscale frontogenesis), followed by a superexponential sharpening stage that is characterized by an Rossby number and is driven by the convergence of the secondary circulation (i.e., submesoscale frontogenesis). It is demonstrated that high-frequency IWs quickly escape the frontal zone and are very efficient at extracting KE from the imposed geostrophic strain field through the deformation shear production (DSP). Part of the extracted KE is then converted to wave potential energy. On the contrary, NIWs remain locked to the frontal zone and readily exchange energy with the ageostrophic frontal circulation. During the exponential stage, NIWs extract KE from the geostrophic strain through DSP and transfer it to the frontal secondary circulation via the ageostrophic shear production (AGSP) mechanism. During the superexponential stage, a newly identified mechanism, convergence production (CP), plays an important role in the NIW KE budget. The CP transfers KE from the convergent ageostrophic secondary circulation to the NIWs and largely cancels out the KE loss due to the AGSP. This CP may explain previous findings of KE transfer enhancement from balanced motions to IWs in frontal regions of realistic ocean models. We provide analytical estimates for the aforementioned energy exchange mechanisms that match well the numerical results. This highlights that the strength of the exchanges strongly depends on the frontal Rossby and Richardson numbers. Significance Statement Fronts with large horizontal density and velocity gradients are ubiquitous in the upper ocean. They are generated by a process known as frontogenesis, which is often initialized by straining motions of mesoscale balanced circulations. Here we examine the energy exchanges between fronts and internal waves in an idealized configuration, aiming to elucidate the mechanisms that can drain energy from oceanic balanced circulations. We identify a new mechanism for energy transfers from the frontal circulation to near-inertial internal waves called convergence production. This mechanism is especially effective during the later stages of frontogenesis when the convergent ageostrophic secondary circulation that develops is strong.

Enhancing one-way wave equation-based migration with deep learning

One advantage of one-way wave equation-based migration is its low computational cost. However, due to the limited wavefield propagation angle, it is difficult to use one-way wave equation-based migration for high-precision imaging of structures with large inclinations due to issues such as inaccurate amplitudes and migration image artifacts. In addition, when the model has large horizontal velocity differences, it is difficult for the one-way wave propagator to calculate an accurate wavefield phase. Reverse time migration (RTM) based on the two-way wave propagator has a high resolution and avoids the issues associated with one-way wave propagators; however, it has a high computational cost in practical applications. We develop a convolutional neural network (CNN) application mode that improves one migration method by learning from another one and design a CNN with a structure similar to U-net that combines the advantages of both migration methods. The CNN label is the RTM result, and the corresponding input is the result of one-way wave migration with a generalized screen propagator (GSP). The trained CNN model improves the amplitude in the one-way wave migration image and removes the errors caused by large lateral velocity perturbations. Moreover, by maintaining the high migration calculation efficiency, our CNN model allows for a high resolution, few artifacts, and accurate images of steep structures in the one-way wave migration result. With our method, the accuracy of the one-way wave migration result is close to that of the RTM result. The use of GSP-based migration in our CNN model rather than conventional RTM to generate prospecting images can considerably reduce the calculation costs.

Formation and heating of chromospheric fibrils in a radiation-MHD simulation

Aims. We examine the movements of mass elements within dense fibrils using passive tracer particles (corks) in order to understand the creation and destruction processes of fibrils. Methods. Simulated fibrils were selected at times when they were visible in a Hα image proxy. The corks were selected within fibril Hα formation regions. From this set, we selected a cork and constructed the field line passing through it. Other fibrilar corks close to this field line were also selected and pathlines were constructed, revealing the locations of the mass elements forwards and backwards in time. Finally, we analysed the forces acting on these mass elements. Results. The main process of fibrilar loading in the simulation is different to the mass loading scenario in which waves steepen into shocks and push material upwards along the field lines from locations near their footpoints. The twisted, low-lying field lines were destabilised and then they untwisted, lifting the material trapped above their apexes via the Lorentz force. Subsequently, the majority of the mass drained down the field lines towards one or both footpoints under the influence of gravity. Material with large horizontal velocities could also be elevated in rising field lines, creating somewhat parabolic motions, but the material was not generally moving upward along a stationary magnetic field line during loading. Conclusions. The processes observed in the simulation are additional scenarios that are plausible. The criteria for observing such events are described in this work. We note that it is desirable for our simulations to also be able to form more densely packed fibrils from material fed from the base of field footpoints. The experimental parameters required to achieve this are also discussed in this paper.

Interference effect on tsunami generation by segmented seafloor deformations

Most tsunamis are triggered by seismic events, involving an underwater earthquake with a sharp vertical displacement of the seafloor. Generally, seabed deformations are not unipolar, but instead bipolar or even more complex. To model tsunamis generated by segmented seafloor deformations, an analytical model and a numerical model including source kinematics are presented. Specifically, a parametric analysis, varying the number of segments and the relative sizes of each segment, is performed to investigate their influence on the wave generation process. Destructive interference is observed between the free surface waves generated by adjacent segments moving in opposite directions. The relatively large horizontal velocities compared to vertical velocities within the rotating flow generated in the case with two opposing segments correspond to relatively low wave amplitudes and the shift in the location of the largest wave. When the net uplift or subsidence volume is smaller, the associated destructive interference is more pronounced. In addition, a larger number of opposing segments produce a more complex velocity field within the tsunamigenic region, causing more destructive interference on the free surface. The role of destructive interference induced by segmented seabed deformations should be considered in assessing tsunami hazards caused by complex fault ruptures.

Structure of Submesoscale Fronts of the Mississippi River Plume

AbstractSubmesoscale currents (SMCs), in the forms of fronts, filaments, and vortices, are studied using a high-resolution (~150 m) Regional Oceanic Modeling System (ROMS) simulation in the Mississippi River plume system. Fronts and filaments are identified by large horizontal velocity and buoyancy gradients, surface convergence, and cyclonic vertical vorticity with along-coast fronts and along-plume-edge filaments notably evident. Frontogenesis and arrest/destruction are two fundamental phases in the life cycle of fronts and filaments. In the Mississippi River plume region, the horizontal advective tendency induced by confluence and convergence plays a primary role in frontogenesis. Confluent currents sharpen preexisting horizontal buoyancy gradients and initiate frontogenesis. Once the fronts and filaments are formed and the Rossby number reaches O(1), they further evolve frontogenetically mainly by convergent secondary circulations, which can be maintained by different cross-front momentum balance regimes. Confluent motions and preexisting horizontal buoyancy gradients depend on the interaction between wind-induced Ekman transport and the spreading plume water. Consequently, the direction of wind has a significant effect on the temporal variability of SMCs, with more active SMCs generated during a coastally downwelling-favorable wind and fewer SMCs during an upwelling-favorable wind. Submesoscale instabilities (~1–3 km) play a primary role in the arrest and fragmentation of most fronts and filaments. These instabilities propagate along the fronts and filaments, and their energy conversion is a mixed barotropic–baroclinic type with horizontal-shear instabilities dominating.

Flight Maneuver of a Damselfly with Phase Modulation of the Wings

We developed a numerical model for four-wing self-propulsion to calculate effectively the flight velocity generated with varied wing motions, which satisfactorily verified biological experiments. Through this self-propulsion model, we analyzed the flight velocity of a damselfly (Matrona cyanoptera) at varied phases. The results show that after phase modulation of the wings, the aerodynamic performance of the forewing (FW) is affected by the incoming flow and an effective angle of attack, whereas that of the hindwing (HW) is dominated by the vortex interaction and induced flow generated by the shed vortex of the FW. Cooperating with the flow interaction, in stable flight, the HW in the lead phase has a larger vertical velocity, whereas the FW in the lead phase has a larger horizontal velocity. Regarding the aerodynamic efficiency, the FW in the lead phase has greater horizontal efficiency, whereas the HW in the lead phase has greater vertical efficiency; the overall efficiency does not vary with the phase. This work interprets that a dragonfly adopts the HW in the lead phase to generate a larger lift, thus supporting the larger body weight, whereas a damselfly adopts the FW in the lead phase to have a greater forward velocity, which can supplement the lack of flapping frequency.

Kinematic comparison of support and swing techniques between elite and sub-elite athletes during the 30-m acceleration of sprint running

ABSTRACT The support and swing techniques of accelerative sprint were compared at different acceleration phases between different athlete groups using high-speed photography. Performance distinction between elite and sub-elite athletes (n = 16) was measured at steps 3, 4, 8, and 9 during a 30-m sprint run. The integral kinematic parameters of hip and knee joints were then compared between the groups. The results indicated that, in elite athletes, integral kinematic parameters such as larger step length, lower step frequency, shorter support time, and longer support distance resulted in larger horizontal velocity of the centre of gravity during the acceleration phase. However, as distance increased, this horizontal velocity increased with step length, support distance, and support time. For various kinematic parameters, the superior performance of elite athletes was mainly based on larger hip angle range and smaller knee angle of touch down. Hip angle of touchdown and toe-off of the supporting leg were important for sub-elite athletes, but training knee angle of touchdown was more suitable for improving performance in elite athletes. The present study provided theoretical reference for beginners and coaches of accelerative running technique.

Stable extension of the unified model into the mesosphere and lower thermosphere

A coupled Sun-to-Earth model is the goal for accurate forecasting of space weather. A key component of such a model is a whole atmosphere model – a general circulation model extending from the ground into the upper atmosphere – since it is now known that the lower atmosphere also drives variability and space weather in the upper atmosphere, in addition to solar variability. This objective motivates the stable extension of The Met Office’s Unified Model (UM) into the Mesosphere and Lower Thermosphere (MLT), acting as a first step towards a whole atmosphere model. At the time of performing this research, radiation and chemistry schemes that are appropriate for use in the MLT had not yet been implemented. Furthermore, attempts to run the model with existing parameterizations and a raised upper boundary led to an unstable model with inaccurate solutions. Here, this instability is examined and narrowed down to the model’s radiation scheme – its assumption of Local Thermodynamic Equilibrium (LTE) is broken in the MLT. We subsequently address this issue by relaxation to a climatological temperature profile in this region. This provides a stable extended UM which can be used as a developmental tool for further examination of the model performance. The standard vertical resolution used in the UM above 70 km is too coarse (approx. 5 km) to represent waves that are important for MLT circulation. We build on the success of the nudging implementation by testing the model at an improved vertical resolution. Initial attempts to address this problem with a 3 km vertical resolution and a 100 km lid were successful, but on increasing the resolution to 1.5 km the model becomes unstable due to large horizontal and vertical wind velocities. Increasing the vertical damping coefficient, which damps vertical velocities near the upper boundary, allows a successful year long climatology to be produced with these model settings. With the goal of a whole atmosphere model we also experiment with an increased upper boundary height. Increasing the upper model boundary to 120 and 135 km also leads to stable simulations. However, a 3 km resolution must be used and it is necessary to further increase the vertical damping coefficient. This is highly promising initial work to raise the UM into the MLT, and paves the way for the development of a whole atmosphere model.

Distribution of phosphorus in bed sediment at confluences responding to hydrodynamics

Knowledge of the distribution of contaminants at channel confluences is critical for understanding their transport and dwelling at river networks where flow confluences constitute the key nodes. Flume experiments were conducted to study the distribution of phosphorus adsorption in surface sediment under complex hydrodynamics at channel confluences. The influence of the discharge ratio of the tributary discharge to the main stream discharge was also investigated. The results showed that the horizontal velocity and vertical velocity of flow are the dominant factors affecting the distribution of phosphorus adsorption. Flows with a larger horizontal velocity are not beneficial to phosphorus adsorption on sediment and thus low- and high-adsorption strips of phosphorus occur in the maximum velocity zone and the flow separation zone, respectively. Downwelling flows are beneficial to phosphorus adsorption on sediment as they can enhance phosphorus exchange between overlying water and the bed sediment. A small flow penetration with a small discharge ratio causes a decrease in vertical velocity in the separation zone as well as the strong intrusion of a helical cell into the bottom of this zone, which results in an increase in horizontal velocity near the bed and consequently the phosphorus adsorption is largely restricted.

Global well-posedness of 3-D inhomogeneous Navier–Stokes system with initial velocity being a small perturbation of 2-D solenoidal vector field

Motivated by [21], we consider the global wellposedness to the 3-D incompressible inhomogeneous Navier–Stokes equations with large horizontal velocity. In particular, we proved that when the initial density is close enough to a positive constant, then given divergence free initial velocity field of the type (v0h,0)(xh)+(w0h,w03)(xh,x3), we shall prove the global wellposedness of (1.1). The main difficulty here lies in the fact that we will have to obtain the L1(R+;Lip(R3)) estimate for convection velocity in the transport equation of (1.1). Toward this and due to the strong anisotropic properties of the approximate solutions, we will have to work in the framework of anisotropic Littlewood–Paley theory here.

Sensitivity to modelling and design of curved surface sliding bearings in the nonlinear seismic analysis of base-isolated r.c. framed buildings

The main object of this study is to investigate the influence that different modelling assumptions of the curved surface sliding (CSS) bearings may have on the lateral-torsional response of irregular base-isolated structures located in near-fault area, characterized by fling-step and directivity effects with large amplitudes and long period horizontal velocity pulses. The second aim is to evaluate the effects of different design assumptions of the CSS system. To this end, a six-storey base-isolated reinforced concrete (r.c.) framed building, with an L-shaped plan and setbacks in elevation, is designed assuming low- and medium-type friction properties, both with two in-plan distributions of the dynamic-fast friction coefficient, corresponding to: (i) the same value for all isolators; (ii) a different value for each isolator. Four additional cases are compared reducing the friction coefficient in accordance with a temperature increase up to 250°C during ground motions. A computer code for the nonlinear dynamic analysis is developed, in order to compare five models of the CSS bearings that consider constant and variable axial loads combined with constant and variable friction coefficients as function of sliding velocity, axial pressure and stick-slip effect. A lumped plasticity model is used to describe the inelastic behaviour of the superstructure, including a 26-flat surface modelling of the axial load-biaxial bending moment elastic domain at the end sections of r.c. frame members. Near-fault ground motions with significant horizontal components are selected and scaled in line with the design hypotheses adopted for the test structure.

Anticyclonic Eddy Sheddings from Kuroshio Loop and the Accompanying Cyclonic Eddy in the Northeastern South China Sea

AbstractSheddings of Kuroshio Loop Current (KLC) eddies in the northeastern South China Sea (SCS) are investigated using mooring arrays, multiple satellite data, and data-assimilative HYCOM products. Based on altimeter sea surface heights between 1992 and 2014, a total of 19 prominent KLC eddy shedding (KLCES) events were identified, among which four events were confirmed by the concurrent moored and satellite observations. Compared to the leaping behavior of Kuroshio, KLCES is a relatively short-duration phenomenon that primarily occurs in boreal autumn and winter. The KLC and its shedding anticyclonic eddy (AE) trap a large amount of Pacific water with high temperature–salinity and low chlorophyll concentration in the upper layer. The corresponding annual-mean transport caused by KLCES reaches 0.24–0.38 Sv (1 Sv ≡ 106 m3 s−1), accounting for 6.8%–10.8% of the upper-layer Luzon Strait transport. Altimeter-based statistics show that among ~90% of the historical KLCES events, a cyclonic eddy (CE) is immediately generated behind the AE southwest of Taiwan. Both energetics and stability analyses reveal that because of its large horizontal velocity shear southwest of Taiwan, the northern branch of KLC is strongly unstable and the barotropic instability of KLC constitutes the primary generation mechanism for the CE. After CE is generated, it quickly grows and gradually migrates southward, which in turn facilitates the detachment of AE from KLC. The intrinsic relationship between KLC and CE explains well why eddy pairs are commonly observed in the region southwest of Taiwan.

Two Dimensional Subsonic Euler Flows Past a Wall or a Symmetric Body

The existence and uniqueness of two dimensional steady compressible Euler flows past a wall or a symmetric body are established. More precisely, given positive convex horizontal velocity in the upstream, there exists a critical value \({\rho_{\rm cr}}\) such that if the incoming density in the upstream is larger than \({\rho_{\rm cr}}\), then there exists a subsonic flow past a wall. Furthermore, \({\rho_{\rm cr}}\) is critical in the sense that there is no such subsonic flow if the density of the incoming flow is less than \({\rho_{\rm cr}}\). The subsonic flows possess large vorticity and positive horizontal velocity above the wall except at the corner points on the boundary. Moreover, the existence and uniqueness of a two dimensional subsonic Euler flow past a symmetric body are also obtained when the incoming velocity field is a general small perturbation of a constant velocity field and the density of the incoming flow is larger than a critical value. The asymptotic behavior of the flows is obtained with the aid of some integral estimates for the difference between the velocity field and its far field states.

Near-inertial waves in the wake of 2011 Typhoon Nesat in the northern South China Sea

In September 2011, Typhoon Nesat passed over a moored array of instruments recording current and temperature in the northern South China Sea (SCS). Awake of baroclinic near-inertial waves (NIWs) commenced after Nesat passed the array. The associated near-inertial currents are surface-intensified and clockwise-polarized. The vertical range of NIWs reached 300 m, where the vertical range is defined as the maximum depth of the horizontal near-inertial velocity 5 cm/s. The current oscillations have a frequency of 0.7099 cycles per day (cpd), which is 0.025f higher than the local inertial frequency. The NIWs have an e-folding time-scale of 10 d based on the evolution of the near-inertial kinetic energy. The depth-leading phase of near-inertial currents indicates downward group velocity and energy flux. The estimated vertical phase velocity and group velocity are 0.27 and 0.08 cm/s respectively, corresponding to a vertical wavelength of 329 m. A spectral analysis reveals that NIWs act as a crucial process to redistribute the energy injected by Typhoon Nesat. A normal mode and an empirical orthogonal function analysis indicate that the second mode has a dominant variance contribution of 81%, and the corresponding horizontal phase velocity and wavelength are 3.50 m/s and 420 km respectively. The remarkable large horizontal phase velocity is relevant to the rotation of the earth, and a quantitative analysis suggests that the phase velocity of the NIWs with a blue-shift of 0.025f overwhelms that of internal gravity waves by a factor of 4.6.

Propagation and Inundation Characteristics of the 2011 Tohoku Tsunami on the Central Sanriku Coast

Propagation and inundation characteristics of the 2011 Tohoku tsunami on the central Sanriku coast are investigated through field surveys and numerical simulations using offshore wave recordings as incident wave conditions. The numerical model successfully reproduces the extent of flood areas as well as the distribution of tsunami heights along the intricate coastline except for run-up of extreme heights over steep slopes. The survey and computed results suggest significant variations of tsunami heights along the coastline. Their positive dependency on topographic slopes implies that the incoming tsunami propagates in standing wave mode to precipitous sites while in progressive wave mode accompanied by wave breaking over gentle slopes. Temporal-spatial analysis of wave properties in different bays reveals that the inner bay topography provides a clear contrast to inundation characteristics. The impacting waves have extreme heights due to the funnel effect and local wave resonances causing highly transient flooding in narrow V-shaped bays whereas tsunami surges over longer periods across innermost shores of U-shaped bays to produce large horizontal velocities during both run-up and backwash phases.

Turbulence and diapycnal mixing over the East Pacific Rise crest near 10°N

Turbulent mixing plays an important role in the return path of the global overturning circulation of the ocean. Previous measurements indicate that much of the mixing takes place near topography, in particular near seamounts and mid‐ocean ridges. Here we report on the first microstructure data set collected over the crest and flanks of a fast‐spreading ridge. The data indicate that in spite of weak tidally modulated background turbulence levels (ε ≈ 10−10 W kg−1) diapycnal diffusivity is elevated above 10−4 m2 s−1 below crest depth of the ridge throughout the entire region because of the weak density stratification. Near the peaks and in the narrow deep passages of a chain of seamounts, where large horizontal velocities have been observed, turbulence levels are elevated by up to an order of magnitude above background. We conclude that topographic organization plays an important role in determining spatial patterns of turbulence in this region and that both tidal and subinertial energy contribute to the mixing.

Biot-Savart law and the formation mechanism of Somali low-level jet

Firstly, we investigate the impact of cross-equatorial Somali low-level jet on the atmospheric circulation in the east of Tibet Plateau using lattice Boltzmann model simulation. Secondly, we study the relationship between thermal conditions on the bottom boundary and the formation of Somali jet based on Biot-Savart law using the data from National Centres for Environmental Prediction (NCEP). As the radiation from the Sun gradually moves from the southern meridian, the temperature on the ground surface of Somali Peninsular and Arabic Peninsular gradually increases. During the same period the surface temperature of the Northern Indian Ocean increases much slower. It is shown that this increase in the temperature difference between the land and sea is inductive to the formation and development of Rayleigh-Benard convection and leads to the increasing relative vorticity strength between positive and negative vertical vortices over the land and sea. According to Biot-Savart law, the increase in vorticity strength will induce correspondingly a large horizontal velocity. The pair of positive and negative vorticity fields over the two Peninsulars and the sea surface is effective in forming and maintaining this current. This mechanism is referred to as "Somali suction pump". It draws air continually from the Southern hemisphere and releases it at the coastal area of Somali.

Surprising behaviors in flapping locomotion with passive pitching

To better understand the role of wing and fin flexibility in flapping locomotion, we study through experiment and numerical simulation a freely moving wing that can “pitch” passively as it is actively heaved in a fluid. We observe a range of flapping frequencies corresponding to large horizontal velocities, a regime of underperformance relative to a clamped (nonpitching) flapping wing, and a surprising, hysteretic regime in which the flapping wing can move horizontally in either direction (despite left/right symmetry being broken by the specific mode of pitching). The horizontal velocity is shown to peak when the flapping frequency is near the immersed system’s resonant frequency. Unlike for the clamped wing, we find that locomotion is achieved by vertically flapped symmetric wings with even the slightest pitching flexibility, and the system exhibits a continuous departure from the Stokesian regime. The phase difference between the vertical heaving motion and consequent pitching changes continuously with the flapping frequency, and the direction reversal is found to correspond to a critical phase relationship. Finally, we show a transition from coherent to chaotic motion by increasing the wing’s aspect ratio, and then a return to coherence for flapping bodies with circular cross section.

Mobile lid convection beneath Enceladus' south polar terrain

Enceladus' south polar region has a large heat flux, 55–110 mW m−2, that is spatially associated with cryovolcanic and tectonic activity. Tidal dissipation and vigorous convection in the underlying ice shell are possible sources of heat, however, prior predictions of the heat flux carried by stagnant lid convection range from Fconv ∼ 15 to 30 mW m−2, too low to explain the observed heat flux. The high heat flux and increased cryovolcanic and tectonic activity suggest that near‐surface ice in the region has become rheologically and mechanically weakened enough to permit convective plumes to reach close to the surface. If the yield strength of Enceladus' lithosphere is less than ∼1–10 kPa, convection may instead occur in the “mobile lid” regime, which is characterized by large heat fluxes and large horizontal velocities in the near‐surface ice. I show that model ice shells with effective surface viscosities between 1016 and 1017 Pa s and basal viscosities between 1013 and 1015 Pa s have convective heat fluxes comparable to that observed by Composite Infrared Spectrometer. If this style of convection is occurring, the south polar terrain should be spreading horizontally with v ∼1–10 mm a−1 (where a is years) and should be resurfaced in ∼0.1–10 Ma. On the basis of Cassini imaging data, the south polar terrain is ∼0.5 Ma old, consistent with the mobile lid hypothesis. Maxwell viscoelastic tidal dissipation in such ice shells is not capable of generating enough heat to balance convective heat transport. However, tidal heat may also be generated in the near‐surface along faults as suggested by Nimmo et al. (2007) and/or viscous dissipation within the ice shell may occur by other processes not accounted for by the canonical Maxwell dissipation model.

Comparison of Solar Cycle Variations of Solarp‐Mode Frequencies from GONG and MDI

The solar p-mode frequencies change with the solar cycle. The horizontal phase velocity dependence of the relative frequency change scaled by mode mass provides depth information on the perturbations in the solar interior. Both GONG data and SOHO MDI data show that the horizontal phase velocity dependence of the scaled relative frequency change varies with solar cycle. Temporal variations of GONG and MDI frequency changes are qualitatively consistent despite some discrepancies. For both GONG and MDI, the smoothed scaled relative frequency change versus horizontal phase velocity is approximately constant at small horizontal phase velocities, but its value decreases for horizontal phase velocities higher than a critical value, as surface activities develop. This critical horizontal phase velocity corresponds to a depth near the base of the convection zone. The magnitude of the decrease in frequency change at large horizontal phase velocities approximately correlates with the sunspot number for both GONG and MDI, although the GONG magnitude is greater than the MDI one. If these signals are real, it suggests that the wave speed in a region near the base of the convection zone changes with the solar cycle. This change might relate to solar cycle variations of magnetic fields near the base of the convection zone.