Phase Speed Of Waves Research Articles

Measurements of the solar coronal magnetic field based on coronal seismology with propagating Alfvénic waves: forward modeling

Abstract Recent observations have demonstrated the capability of mapping the solar coronal magnetic field using the technique of coronal seismology based on the ubiquitous propagating Alfv'{e}nic/kink waves through imaging spectroscopy. We established a magnetohydrodynamic (MHD) model of a gravitationally stratified open magnetic flux tube, exciting kink waves propagating upwards along the tube. Forward modeling was performed to synthesize the Fe \textsc{xiii} 1074.7 and 1079.8 nm spectral line profiles, which were then used to determine the wave phase speed, plasma density, and magnetic field with seismology method. A comparison between the seismologically inferred results and the corresponding input values verifies the reliability of the seismology method. In addition, we also identified some factors that could lead to errors during magnetic field measurements. Our results may serve as a valuable reference for current and future coronal magnetic field measurements based on observations of propagating kink waves.

Propagation speed model of mode-2 internal solitary waves in the northern South China Sea based on multi-source optical remote sensing

The phase speed of internal solitary waves (ISWs) is an essential dynamical parameter for the study of their generation, propagation, and evolution. In this study, a model based on multi-source optical remote sensing data was developed to calculate the phase speed of mode-2 ISWs in the northern South China Sea (NSCS). A total of 430 mode-2 ISWs were identified from optical remote sensing images acquired by Terra/Aqua, Gaofen-1/6 (GF-1/6), Huanjing-2A/B (HJ-2A/B), and China-Brazil Earth Resources Satellite 04 (CBERS-04) between 2014 and 2024. These waves are primarily distributed in areas with a total water depth of 150–500 m near Dongsha Atoll and Shenhu-Yitong Shoals, propagating perpendicular to the local isobaths. The phase speeds of the mode-2 ISWs were estimated using the multiple images comparison (MIC) method, and a depth-based phase speed model was developed. The model was validated using field measurements and theoretical phase speeds. The results were within the reasonable range of theoretical predictions and showed a mean relative error (MRE) of 7.64% compared to the annual average data from field measurements. Further analysis of the spatial and interval distribution of the phase speeds of mode-2 ISWs on the NSCS continental shelf revealed that the phase speeds ranged from 0.42 to 0.75 m/s, with the highest proportion occurring in the interval 0.60–0.65 m/s.

Love wave along the corrugated interface between an elastic half-space and the corrugated porous layer containing two fluids

This article presents a comprehensive analysis of Love wave propagation along the interface between a porous layer saturated with two immiscible fluids and an underlying elastic half-space. The study places particular emphasis on the corrugated nature of both the interface and the upper boundary of the porous layer. A complex dispersion relation, governed by appropriate boundary conditions, is derived and subsequently simplified into four distinct subcases. The effects of corrugation parameters at the upper boundary of the porous layer and the interface between the layer and the elastic half-space are investigated. The influence of the undulation parameter, which represents the combined effects of wave number and porous layer thickness is also analyzed on the phase speed of the Love wave. In the numerical discussion, a geological structure analogous to oil-contaminated sandstone aquifers in contact with sedimentary bedrock, a common formation in coastal regions, is considered as a realistic example. The key findings reveal that the phase speed of Love waves is highly sensitive to both the corrugation and undulation parameters. Increased corrugation at the upper boundary of the layer enhances phase speed, while corrugation at the interface decreases it. An increase in the undulation parameter decreases the phase speed of the Love wave. Additionally, the presence of oil and water within the porous sandstone significantly reduces phase speed, particularly at lower frequencies, due to higher viscosity and internal friction. This study provides valuable insights into wave propagation dynamics in complex geological settings, with implications for hydrogeology, environmental monitoring, and seismic risk assessment.

Development of a Two-Step EOF Statistical Postprocessing Algorithm to Identify Patterns of Systematic Error and Variance within GEFSv12 Reforecasts

Abstract Analysis of seasonally varying signals of model error biases, as well as the diagnosis of space–time patterns of synoptic error, here is accomplished through the development of a statistical postprocessing algorithm based on time-extended empirical orthogonal functions (EEOFs) built on patterns of variance. This work analyzes GEFSv12 200-hPa geopotential height (Z200) model error against ERA5 reanalysis data. The mean-square error variance between GEFSv12 reforecast and ERA5 grows rapidly after day 7 of a forecast and continues to increase through the end of the 16-day forecast period. At lead time 16, the largest variance occurs in mid- to high-latitude oceanic storm tracks. Variance is highest during hemispheric winter when baroclinic energy is abundant. The seasonal cycle of error shows largest anomalies in the high latitudes during hemispheric winter. After running the titular two-step, space–time EEOF algorithm, a standardized spatial eigenspectrum shows that eigenvalues increase at longer lead times after decreasing in the medium range, demonstrating that the algorithm extracts large-scale signals of systematic error in the long range. Leading wintertime space–time eigenmode pairs include high-latitude blocking structures and Rossby wave trains. Results suggest that the large-scale systematic errors in GEFSv12 Z200 initiate in part from inaccurate representations of phase speeds of atmospheric waves in the polar jet.

Estimating the In Situ Stratification via Remotely Sensed Internal Wave Speeds

Abstract This work tests a methodology for estimating the ocean stratification gradient using remotely sensed, high temporal and spatial resolution field measurements of internal wave propagation speeds. The internal wave (IW) speeds were calculated from IW tracks observed using a shore-based, X-band marine radar deployed at a field site on the south-central coast of California. An inverse model, based on the work of Kar and Guha, utilizes the linear internal wave dispersion relation, assuming a constant vertical density gradient is the basis for the inverse model. This allows the vertical gradient of density to be expressed as a function of the internal wave phase speed, local water depth, and a background average density. The inputs to the algorithm are the known cross-shore bathymetry, the background ocean density, and the remotely sensed cross-shore profiles of IW speed. The estimated density gradients are then compared to the synchronously measured vertical density profiles collected from an in situ instrument array. The results show a very good agreement offshore in deeper water (∼50–30 m) but more significant discrepancies in shallow water (20–10 m) closer to shore. In addition, a sensitivity analysis is conducted that relates errors in measured speeds to errors in the estimated density gradients. Significance Statement The propagation speed of ocean internal waves inherently depends on the vertical structure of the water density, which is termed stratification. In this work, we evaluate and test with real field observations a technique to infer the ocean density stratification from internal wave propagation speeds collected from remote sensing images. Such methods offer a way to monitor ocean stratification without the need for extensive in situ measurements.

Upper mantle structure beneath the Mongolian region from multimode surface waves: Implications for the western margin of Amurian plate

Multimode phase speeds of surface waves are used to build a new radially anisotropic S wave model in the eastern Eurasian and Mongolian regions. Our dataset includes seismic waveforms of over 1655 teleseismic events (Mw≥5.8) from 2009 to 2021, recorded at permanent and temporary stations in and around Mongolia. The multimode dispersion curves of Love and Rayleigh waves were extracted using the nonlinear waveform fitting method for individual seismograms. Then, we retrieved phase speed maps for each mode and frequency, incorporating finite-frequency effects. Finally, localized multimode dispersion curves extracted from the phase speed maps were inverted for local 1-D SV and SH wave profiles, which are combined into a radially anisotropic 3-D shear wave model. Our new model exhibits significant lateral variations of S wave speeds at 70–100 km depth beneath Mongolia, i.e., slow anomalies in the tectonically active western Mongolia in contrast to fast anomalies in stable eastern Mongolia. In the radial anisotropy model, SH waves are faster than SV waves in most areas of the Mongolian lithosphere above 100 km depth, except for the northeast of the Altay Mountains. The Hangay Dome region is characterized by significantly slower velocities that may relate to its uplifting. A large-scale low velocity beneath the northeast of the Hangay Dome with a slower SV wave speed than SH may indicate the existence of partially molten layers. This study also reveals distinct lateral variations of S wave speeds across the boundary between the Amurian and Eurasian plates, characterized by the fast anomaly in eastern Mongolia, corresponding to the lithosphere in the western Amurian plate.

Soliton interaction in a two-temperature electron plasma with trapping and superthermality effects

Head-on collision of the two small-amplitude electron-acoustic (EA) solitons is studied in an unmagnetized collisionless plasma in the presence of superthermal (hot) trapped electrons. For this purpose, using a well-known extended Poincare–Lighthill–Kuo (PLK) method, a pair of the trapped Korteweg–de Vries (tKdV) equations is derived to investigate the soliton trajectories and phase shifts. The latter are found dependent on amplitudes of the interacting solitons, effectively altering with hot-electron superthermality and plasma parameters. Typical parameters for the electron diffusion region (EDR) and day-side auroral zone have been selected to examine the impact of hot-electron superthermality, trapping parameter, hot-to-cold electron number density ratio, and cold-to-hot electron temperature ratio on the profiles of potential excitations and phase shifts of interacting solitons. It is found that phase speed of the EA waves becomes altered by varying the κ–parameter, strongly modifying the nonlinearity and dispersive coefficients in a superthermal trapped plasma. However, particle trapping phenomenon does not affect the linear phase speed but introduces a fractional nonlinearity in the tKdV equations of two interacting solitons. The impact of the adiabatic and isothermal pressures is also highlighted to show new modifications in the propagation characteristics of two interacting solitons.

The effect of vertical temperature gradient on the equivalent depth in thin atmospheric layers

AbstractThe equivalent depth of an atmospheric layer is of importance in determining the phase speed of gravity waves and characterizing wave phenomena. The value of the equivalent depth can be obtained from the eigenvalues of the vertical structure equation (the vertical part of the primitive equations) where the mean temperature profile is a coefficient. Both numerical solutions of the vertical structure equation and analytical considerations are employed to calculate the equivalent depth, , as a function of the atmospheric layer's thickness, . Our solutions for layers of thickness 100 2000 m show that for baroclinic modes, can be over two orders of magnitudes smaller than . Analytic expressions are derived for in layers of uniform temperature and numerical solutions are derived for layers in which the temperature changes linearly with height. A comparison between the two cases shows that a slight temperature gradient (of say 0.65 K across a 100 m layer) decreases by a factor of 3 (but can reach a factor of 10 for larger gradients) compared with its value in a layer of uniform temperature, while a change of 10 K in the layer's uniform temperature hardly changes . The baroclinic mode exists in all combinations of boundary conditions top and bottom while the barotropic mode only exists when the vertical velocity vanishes at both boundaries of the layer.

Phase and group speeds of airborne surface waves over porous layers and periodically rough hard surfaces.

Sound fields above porous layers or rough acoustically hard boundaries may include airborne surface waves. The surface wave properties depend on the effective surface admittance. Analytical expressions for surface wave speeds are derived from models for the acoustical properties of rigid porous media. Surface wave effects on measurements of level difference spectra over porous asphalt are investigated and predictions of phase, group speeds, and vertical attenuation of the surface waves over externally reacting hard backed layers corresponding to a porous asphalt are compared. Predictions of surface wave characteristics above an identical vertical slit medium are compared with data obtained over arrays of parallel aluminum strips on an acoustically hard surface. Group speeds of surface waves over lattices, parallel regularly spaced strips, and snow obtained by numerical differentiation of the phase speed spectra corresponding to admittance spectra deduced from complex excess attenuation are found to compare well with those estimated from time domain data. An effective admittance, deduced from a boundary element method simulation of the excess attenuation spectrum over regularly spaced ribs so that the frequency of the peak corresponds with that in the measured spectrum, is used to estimate the group speed of the associated surface wave.

Heatwave Location Changes in Relation to Rossby Wave Phase Speed

AbstractSurface anticyclones connected to the ridge of an upper‐tropospheric Rossby wave are the main dynamical drivers of mid‐latitude summer heatwaves. It is, however, unclear to what extent an anomalously low zonal phase speed of the wave in the upper troposphere is necessary for persistent temperature extremes at the surface. Here, we use spectral decomposition to separate fast and slow synoptic‐scale waves. A composite analysis of ERA5 reanalysis data reveals that, while in some regions heatwaves become more frequent during episodes of weak or no phase propagation, temperature extremes in other regions are commonly associated with more rapidly eastward propagating Rossby waves. Reflected in the mean heatwave duration as well, this relationship is possibly linked to a longitudinal phase preference of slow and fast waves or a meridional storm track shift. These findings open up new questions about the influence of mid‐latitude dynamics on temperature extremes.

Opposite spectral properties of Rossby waves during weak and strong stratospheric polar vortex events

Abstract. In this study we provide a systematic characterization of Rossby wave activity during the 25 sudden stratospheric warming (SSW) and 31 strong polar vortex (SPV) events that occurred in the period 1979–2021, identifying the specific tropospheric and stratospheric waves displaying anomalous behaviour during such events. Space–time spectral analysis is applied to ERA5 data for this purpose, so that both the wavenumber and the zonal phase speed of the waves can be assessed. We find that SSW events are associated with a reduction in the phase speed of Rossby waves, first in the stratosphere and then in the troposphere; SPV events are tied to a simultaneous increase of phase speed across vertical levels. Phase speed anomalies become significant around the event and persist for 2–3 weeks afterwards. Changes of Rossby wave properties in the stratosphere during SSW and SPV events are dominated by changes in the background flow, with a systematic reduction or increase, respectively, in eastward propagation of the waves across most wavenumbers. In the troposphere, on the other hand, the effect of the background flow is also complemented by changes in wave properties, with a shift towards higher wavenumbers during SSW events and towards lower wavenumbers for SPV events. The opposite response between SSW and SPV events is also visible in the meridional heat and momentum flux co-spectra, which highlight from a novel perspective the connection between stratospheric Rossby waves and upward propagation of waves.

Application of fluctuations in the sound field in inversion of internal solitary wave phase speed

Internal solitary waves propagation perturbing the sound velocity field, causes fluctuations in the sound field. This paper proposes to process the sound pressure data by the Product of the Slope and the even square of the Difference between two points of the acoustic parameter-time curve (PSD). The PSD processed data are processed to time-frequency analysis to extract the frequencies of the fluctuations in sound field. In this paper, numerical simulations and laboratory experiments are carried out on the process of internal solitary wave propagation in the sound field, and the characteristics of the sound field perturbation by internal solitary waves of different amplitudes are investigated. Results are both showing that the method can extract the dominant frequency of fluctuations in the sound field caused by internal solitary waves in real conditions. The method can be applied to the inversion of internal solitary wave phase speed which related to other parameters such as amplitude and characteristic width by theory. It is anticipated that this method can help realize the monitoring of internal solitary waves using acoustic paths.

Evolution of wind-induced wave groups in water of finite depth

The generation of water waves by wind is a fundamental and much-studied problem of scientific and operational concern. One mechanism that has obtained a wide degree of acceptance and use is the Miles air shear flow instability theory in which water waves grow due to energy transfer from the air at a critical level where the wave phase speed matches the wind speed. In this paper we revisit and extend this theory by examining how the predicted wave growth rate depends on the water depth and the wind shear parameters. At the same time we include frictional effects due to water bottom stress and at the water surface, and add an additional driving term due to wave stress in the air near the sea surface, using a turbulent parametrisation. The theory is developed using a frictional modification of the usual potential flow theory for water waves, the modified Euler equations, coupled to linearised air-flow equations. To assist our analysis we develop a long-wave approximation for the key Miles growth parameter, which explicitly shows how this depends on the water depth and the wind shear parameters. Since our focus is on the development of wave groups, we present a forced nonlinear Schrödinger equation in which the forcing term describes wave growth or decay. For very shallow water the modified Euler equations are reduced to their shallow-water counterpart, which are briefly discussed using Riemann invariants.

Modulation of Annual Rossby Waves on the Formation of Basin‐Wide Salinity Fronts

AbstractThis study reveals the formation mechanisms of a group of salinity fronts across the Arabian Sea (AS) and explores their associations with annual Rossby waves, utilizing Soil Moisture Active Passive (SMAP) satellite data and other relevant data sets. As low‐salinity water is transported westward and northward at varying rates between 6°N ∼ 20°N, substantial basin‐wide northeast‐southwest oriented salinity fronts emerge at its leading edge from March to May. Further analysis indicates a strong correlation between the transport of low‐salinity water and the westward‐propagating Rossby waves. The salinity fronts are primarily influenced by the geostrophic circulation, which significantly contributes to the transport of low‐salinity water. As a result, the low‐salinity water closely aligns with positive sea level anomaly (SLA), representing westward propagating downwelling Rossby waves. A continuously stratified linear ocean model (LOM) analysis suggests second mode baroclinic Rossby waves dominate seasonal sea level changes, surpassing the influence of the first mode. The spatial mean standard deviation of the first mode within the region of 56 ∼ 75°E, 9 ∼ 11°N is approximately 60% that of the second mode. Positive SLA is mainly caused by the annual downwelling Rossby waves radiating from the eastern boundary. Due to the latitudinal decrease in the phase speed of the annual Rossby waves, the sea level fronts manifest the northeast‐southwest direction, resembling the location of the sea surface salinity fronts. The salinity fronts highlight the crucial role of Rossby waves in shaping upper ocean water mass distribution in the AS, potentially impacting the broader Indian Ocean climate.

Experimental study on flow kinematics of breaking wave impinging and overtopping on a deck structure

The present study experimentally investigates the flow kinematics due to breaking waves impinging and overtopping on a simplified deck structure. Several breaking-wave impinging scenarios in relation to the model deck are conducted. The resulting flow velocities in the aerated regions are measured using bubble image velocimetry (BIV). A wave focusing method is employed to generate plunging breakers. Repeated measurements are performed to obtain mean flow and turbulence characteristics. Two distinguished flow behaviors are observed among all seven scenarios. For the cases of a fully developed plunging breaker interacting with the deck structure, the maximum horizontal velocities above and below the structure are both around 1.2C, with C being the phase speed of the breaking wave; for the cases of a non-fully-developed plunging breaker impingement, the flow velocity below the deck is surprisingly large, with a value of 1.8C below the deck against 1.2C above the deck. Furthermore, the use of a dam-break flow to model the overtopping horizontal velocities on the deck is performed with satisfactory agreements for all the impinging scenarios. Moreover, the temporal and spatial varying prediction equation proposed by Ryu et al. (2007b) is used to model overtopping flow velocities, showing the applicability of this simplified methodology.

The Dynamics of Magnetic Rossby Waves in the Quasigeostrophic Shallow Water Magnetohydrodynamic Theory

The dynamics of magnetic Rossby waves are investigated by applying a quasigeostrophic shallow water magnetohydrodynamic system, which is linearized with respect to both uniform background flow and uniform magnetic field. Due to the influence of the free surface divergence, the phase speed for magnetic Rossby waves can be either a monotonically increasing or a monotonically decreasing function, and the resulting difference between the group velocity and the phase speed can be either positive or negative. This is determined by whether the corresponding Alfvén wave speed is the upper limit or not. Differently, the phase speed is always a monotonically increasing function and the difference between the group velocity and the phase speed is always positive for incompressible magnetic Rossby waves. Multiplying a factor, the wavenumber vector shares the same endpoint with the group velocity vector. The endpoint moves on a cycle that has a center at the k-axis and is tangent to the l-axis in the wavenumber space. The circle is quite similar to the Longuet-Higgins circle for Rossby waves on Earth’s atmosphere and ocean. The fundamental dynamics is the theoretical basis for deeply understanding the meridional energy transport by waves and the interaction between waves and the background states.

Strong diffraction of nonlinear surface acoustic waves in crystals

Nonlinear distortion and shock formation in planar surface acoustic waves in anisotropic crystals have been modeled without [Hamilton et al., JASA (1999)] and with [Cormack et al., JASA 2022] piezoelectricity. Weak diffraction has been included in the paraxial approximation for nonlinear surface wave beams in isotropic solids [Shull et al., JASA (1995)]. Here, a procedure for including strong diffraction, i.e., without the paraxial approximation, in the model for nonlinear surface waves in crystals is presented, which incorporates the angular spectrum approach described by Kharusi and Farnell (JASA 1970). Anisotropy is defined by expressing the phase speed of a plane wave, and therefore, the magnitude of the corresponding wavenumber, as a function of the direction of propagation. Next, an explicit expression relating the two wavenumber components in the planar surface along which the wave propagates must be obtained as a function of direction, requiring iterative solution of a transcendental relation. The beam is then propagated incrementally away from the source, advancing the angular spectrum in k-space and including nonlinear interactions in the spatial domain to characterize the combined effects of diffraction and nonlinearity. Preliminary results are presented for converging nonlinear surface waves in crystals. [Work supported by IR&D at ARL:UT.]

Assessment of climate biases in OpenIFS version 43r3 across model horizontal resolutions and time steps

Abstract. We examine the impact of horizontal resolution and model time step on the climate of the OpenIFS version 43r3 atmospheric general circulation model. A series of simulations for the period 1979–2019 are conducted with various horizontal resolutions (i.e. ∼100, ∼50, and ∼25 km) while maintaining the same time step (i.e. 15 min) and using different time steps (i.e. 60, 30, and 15 min) at 100 km horizontal resolution. We find that the surface zonal wind bias is significantly reduced over certain regions such as the Southern Ocean and the Northern Hemisphere mid-latitudes and in tropical and subtropical regions at a high horizontal resolution (i.e. ∼25 km). Similar improvement is evident too when using a coarse-resolution model (∼100 km) with a smaller time step (i.e. 30 and 15 min). We also find improvements in Rossby wave amplitude and phase speed, as well as in weather regime patterns, when a smaller time step or higher horizontal resolution is used. The improvement in the wind bias when using the shorter time step is mostly due to an increase in shallow and mid-level convection that enhances vertical mixing in the lower troposphere. The enhanced mixing allows frictional effects to influence a deeper layer and reduces wind and wind speed throughout the troposphere. However, precipitation biases generally increase with higher horizontal resolutions or smaller time steps, whereas the surface air temperature bias exhibits a small improvement over North America and the eastern Eurasian continent. We argue that the bias improvement in the highest-horizontal-resolution (i.e. ∼25 km) configuration benefits from a combination of both the enhanced horizontal resolution and the shorter time step. In summary, we demonstrate that, by reducing the time step in the coarse-resolution (∼100 km) OpenIFS model, one can alleviate some climate biases at a lower cost than by increasing the horizontal resolution.

Generation and Evolution of Internal Solitary Waves in a Coastal Plain Estuary

Abstract Large-amplitude internal solitary waves were recently observed in a coastal plain estuary and were hypothesized to evolve from an internal lee wave generated at the channel–shoal interface. To test this mechanism, a 3D nonhydrostatic model with nested domains and adaptive grids was used to investigate the generation of the internal solitary waves and their subsequent nonlinear evolution. A complex sequence of wave propagation and transformation was documented and interpreted using the nonlinear wave theory based on the Korteweg–de Vries equation. During the ebb tide a mode-2 internal lee wave is generated by the interaction between lateral flows and channel–shoal topography. This mode-2 lee wave subsequently propagates onto the shallow shoal and transforms into a mode-1 wave of elevation as strong mixing on the flood tide erases stratification in the bottom boundary layer and the lower branch of the mode-2 wave. The mode-1 wave of elevation evolves into an internal solitary wave due to nonlinear steepening and spatial changes in the wave phase speed. As the solitary wave of elevation continues to propagate over the shoaling bottom, the leading edge moves ahead as a rarefaction wave while the trailing edge steepens and disintegrates into a train of rank-ordered internal solitary waves, due to the combined effects of shoaling and dispersion. Strong turbulence in the bottom boundary layer dissipates wave energy and causes the eventual destruction of the solitary waves. In the meantime, the internal solitary waves can generate elevated shear and dissipation rate in local regions. Significance Statement In the coastal ocean nonlinear internal solitary waves are widely recognized to play an important role in generating turbulent mixing, modulating short-term variability of nearshore ecosystem, and transporting sediment and biochemical materials. However, their effects on shallow and stratified estuaries are poorly known and have been rarely studied. The nonhydrostatic model simulations presented in this paper shed new light into the generation, propagation, and transformation of the internal solitary waves in a coastal plain estuary.

Direct Observation of Wave-Coherent Pressure Work in the Atmospheric Boundary Layer

Abstract Surface waves grow through a mechanism in which atmospheric pressure is offset in phase from the wavy surface. A pattern of low atmospheric pressure over upward wave orbital motions (leeward side) and high pressure over downward wave orbital motions (windward side) travels with the water wave, leading to a pumping of kinetic energy from the atmospheric boundary layer into the waves. This pressure pattern persists above the air–water interface, modifying the turbulent kinetic energy in the atmospheric wave-affected boundary layer. Here, we present field measurements of wave-coherent atmospheric pressure and velocity to elucidate the transfer of energy from the atmospheric turbulence budget into waves through wave-coherent atmospheric pressure work. Measurements show that the phase between wave-coherent pressure and velocity is shifted slightly above 90° when wind speed exceeds the wave phase speed, allowing for a downward energy flux via pressure work. Although previous studies have reported wave-coherent pressure, to the authors’ knowledge, these are the first reported field measurements of wave-coherent pressure work. Measured pressure work cospectra are consistent with an existing model for atmospheric pressure work. The implications for these measurements and their importance to the turbulent kinetic energy budget are discussed. Significance Statement Surface waves grow through a pattern of atmospheric pressure that travels with the water wave, acting as a pump against the water surface. The pressure pumping, sometimes called pressure work, or the piston pressure, results in a transfer of kinetic energy from the air to the water that makes waves grow larger. To conserve energy, it is thought that the pressure work on the surface must extract energy from the mean wind profile or wind turbulence that sets the shape of the wind speed with height. In this paper, we present direct measurements of pressure work in the atmosphere above surface waves. We show that the energy extracted by atmospheric pressure work fits existing models for how waves grow and a simple model for how waves reduce energy in the turbulent kinetic energy budget. To our knowledge, these are the first reported field measurements of wave-coherent pressure work.