Linear Wave Dynamics Research Articles

Difference between Upshear- and Downshear-Propagating Waves Associated with the Development of Squall Lines

Abstract During the development of squall lines, low-frequency gravity waves exhibit contrasting behaviors behind and ahead of the system, corresponding to its low-level upshear and downshear sides, respectively. This study employed idealized numerical simulations to investigate how low-level shear and tilted convective heating influence waves during two distinct stages of squall-line evolution. In the initial stage, low-level shear speeds up upshear waves, while it has contrasting effects on the amplitudes of different wave modes, distinguishing it from the Doppler effect. Downshear deep tropospheric downdraft (n = 1 wave) exhibits larger amplitudes, resulting in strengthened low-level inflow and upper-level outflow. However, n = 2 wave with low-level ascent and high-level descent has higher amplitude upshear and exhibits a higher altitude of peak w values downshear, leading to the development of a more extensive upshear low-level cloud deck and a higher altitude of downshear cloud deck. In the mature stage, as the convective updraft greatly tilts rearward (upshear), stronger n = 1 waves occur behind the system, while downshear-propagating n = 2 waves exhibit larger amplitudes. These varying wave behaviors subsequently contribute to the storm-relative circulation pattern. Ahead of the squall line, stronger n = 2 waves and weaker n = 1 waves produce intense outflow concentrated at higher altitudes, along with moderate midlevel inflow and weak low-level inflow. Conversely, behind the system, the remarkable high pressure in the upper troposphere and wake low are attributed to more intense n = 1 waves. Additionally, the cloud anvil features greater width and depth rearward and is situated at higher altitudes ahead of the system due to the joint effects of n = 1 and n = 2 waves. Significance Statement Squall lines are a significant source of high-impact weather events, and their development has been partially explained through linear wave dynamics. While the recurrent generation of waves during squall-line evolution has been found, the differentiation of wave behavior behind and ahead of the system, as well as its implications for storm circulation, has remained unclear. This study employs idealized simulations to reveal that during different stages of convection, low-level shear and the tilting of convective heating exert contrasting effects on wave behaviors. Moreover, various wave modes exhibit distinct responses to specific factors, and their combined effect elucidates the structural discrepancies observed both rearward and forward of the convective updraft. These findings could allow a step toward a better understanding of the intricate interaction between waves and convections.

Controls of Topographic Rossby Wave Properties and Downslope Transport in Dense Overflows

Abstract Antarctic Bottom Water is primarily formed via overflows of dense shelf water (DSW) around the Antarctic continental margins. The dynamics of these overflows therefore influence the global abyssal stratification and circulation. Previous studies indicate that dense overflows can be unstable, energizing topographic Rossby waves (TRW) over the continental slope. However, it remains unclear how the wavelength and frequency of the TRWs are related to the properties of the overflowing DSW and other environmental conditions, and how the TRW properties influence the downslope transport of DSW. This study uses idealized high-resolution numerical simulations to investigate the dynamics of overflow-forced TRWs and the associated downslope transport of DSW. It is shown that the propagation of TRWs is constrained by the geostrophic along-slope flow speed of the DSW and by the dynamics of linear plane waves, allowing the wavelength and frequency of the waves to be predicted a priori. The rate of downslope DSW transport depends nonmonotonically on the slope steepness: steep slopes approximately suppress TRW formation, resulting in steady, frictionally dominated DSW descent. For slopes of intermediate steepness, the overflow becomes unstable and generates TRWs, accompanied by interfacial form stresses that drive DSW downslope relatively rapidly. For gentle slopes, the TRWs lead to the formation of coherent eddies that inhibit downslope DSW transport. These findings may explain the variable properties of TRWs observed in oceanic overflows, and they imply that the rate at which DSW descends to the abyssal ocean depends sensitively on the manifestation of TRWs and/or nonlinear eddies over the continental slope.

Similarity and variability of blocked weather-regime dynamics in the Atlantic–European region

Abstract. Weather regimes govern an important part of the sub-seasonal variability of the mid-latitude circulation. Due to their role in weather extremes and atmospheric predictability, regimes that feature a blocking anticyclone are of particular interest. This study investigates the dynamics of these “blocked” regimes in the North Atlantic–European region from a year-round perspective. For a comprehensive diagnostic, wave activity concepts and a piecewise potential vorticity (PV) tendency framework are combined. The latter essentially quantifies the well-established PV perspective of mid-latitude dynamics. The four blocked regimes (namely Atlantic ridge, European blocking, Scandinavian blocking, and Greenland blocking) during the 1979–2021 period of ERA5 reanalysis are considered. Wave activity characteristics exhibit distinct differences between blocked regimes. After regime onset, Greenland blocking is associated with a suppression of wave activity flux, whereas Atlantic ridge and European blocking are associated with a northward deflection of the flux without a clear net change. During onset, the envelope of Rossby wave activity retracts upstream for Greenland blocking, whereas the envelope extends downstream for Atlantic ridge and European blocking. Scandinavian blocking exhibits intermediate wave activity characteristics. From the perspective of piecewise PV tendencies projected onto the respective regime pattern, the dynamics that govern regime onset exhibit a large degree of similarity: linear Rossby wave dynamics and nonlinear eddy PV fluxes dominate and are of approximately equal relative importance, whereas baroclinic coupling and divergent amplification make minor contributions. Most strikingly, all blocked regimes exhibit very similar (intra-regime) variability: a retrograde and an upstream pathway to regime onset. The retrograde pathway is dominated by nonlinear PV eddy fluxes, whereas the upstream pathway is dominated by linear Rossby wave dynamics. Importantly, there is a large degree of cancellation between the two pathways for some of the mechanisms before regime onset. The physical meaning of a regime-mean perspective before onset can thus be severely limited. Implications of our results for understanding predictability of blocked regimes are discussed. Further discussed are the limitations of projected tendencies in capturing the importance of moist-baroclinic growth, which tends to occur in regions where the amplitude of the regime pattern, and thus the projection onto it, is small. Finally, it is stressed that this study investigates the variability of the governing dynamics without prior empirical stratification of data by season or by type of regime transition. It is demonstrated, however, that our dynamics-centered approach does not merely reflect variability that is associated with these factors. The main modes of dynamical variability revealed herein and the large similarity of the blocked regimes in exhibiting this variability are thus significant results.

Role of odd viscosity in falling viscous fluid

The aim of the present study is to investigate the linear and nonlinear wave dynamics of a falling incompressible viscous fluid when the fluid undergoes an effect of odd viscosity. In fact, such an effect arises in classical fluids when the time-reversal symmetry is broken. The motivation to study this dynamics was raised by recent studies (Ganeshan & Abanov, Phys. Rev. Fluids, vol. 2, 2017, p. 094101; Kirkinis & Andreev, J. Fluid Mech., vol. 878, 2019, pp. 169–189) where the odd viscosity coefficient suppresses thermocapillary instability. Here, we explore the linear surface wave and shear wave dynamics for the isothermal case by solving the Orr–Sommerfeld eigenvalue problem numerically with the aid of the Chebyshev spectral collocation method. It is found that surface and shear instabilities can be weakened by the odd viscosity coefficient. Furthermore, the growth rate of the wavepacket corresponding to the linear spatio-temporal response is reduced as long as the odd viscosity coefficient increases. In addition, a coupled system of a two-equation model is derived in terms of the fluid layer thickness $h(x,t)$ and the flow rate $q(x,t)$. The nonlinear travelling wave solution of the two-equation model reveals the attenuation of maximum amplitude and speed in the presence of an odd viscosity coefficient, which ensures the delay of transition from the primary parallel flow with a flat surface to secondary flow generated through the nonlinear wave interactions. This physical phenomenon is further corroborated by performing a nonlinear spatio-temporal simulation when a harmonic forcing is applied at the inlet.

Direct observation of edge modes in zigzag granular chains

As a new class of artificial elastic materials, granular crystals are mechanical structures of elastic beads arranged in contact through a lattice. One important feature of wave dynamics in granular crystals is that it highly relies on the contact mechanics, allowing for exotic wave transport properties such as rotational waves, solitary waves, slow edge waves, topological edge waves, etc. Realizing granular structures with well-predicted wave physics not only renders these new properties to mechanical systems, but provides also significant possibilities for advanced elastic wave control scenarios. Here, we theoretically and experimentally study the linear wave dynamics in one-dimensional (1D) zigzag granular chains constructed with macroscopic spherical stainless steel/tungsten beads. A spring–mass model including normal, shear and bending mechanical couplings between beads is proposed to characterize the wave dynamics in the chain, which turns out to exhibit remarkable agreement with the experimental measurements. Our work confirms the existence of localized translational–rotational coupled modes at the ends of granular chains, and it might motivate future studies for novel topological wave effects in granular structures.

Energy growth in subcritical viscoelastic pipe flows

This work studies the dynamics of linear non-modal waves in viscoelastic pipe flows of FENE-P fluids using transient growth and resolvent analyses. We particularly focus on the time evolution of the amplification of the disturbance energy (using the 4th-order Runge–Kutta method) and discuss the dynamical traits of the Orr and the critical-layer mechanisms in the conformation tensor field when the transient energy increases. The helical mode undergoes a larger energy growth than the axisymmetric mode. The effects of various flow parameters have been investigated on the growth rate and energy amplification of the non-modal waves and the optimal flow structures. It is found that when the elastic effect is stronger, the amplitude of the optimal conformation tensor in the pipe centre region becomes greater from a non-modal perspective. • Orr mechanism in the conformation tensor is at play when transient energy increases. • Conformation tensor in the pipe centre becomes greater when elasticity is stronger. • Helical modes, though stable, undergo larger energy growth than the axisymmetric mode.

Parameterizing Nonpropagating Form Drag over Rough Bathymetry

AbstractSlowly evolving stratified flow over rough topography is subject to substantial drag due to internal motions, but often numerical simulations are carried out at resolutions where this “wave” drag must be parameterized. Here we highlight the importance of internal drag from topography with scales that cannot radiate internal waves, but may be highly nonlinear, and we propose a simple parameterization of this drag that has a minimum of fit parameters compared to existing schemes. The parameterization smoothly transitions from a quadratic drag law () for low Nh/u0 (linear wave dynamics) to a linear drag law () for high Nh/u0 flows (nonlinear blocking and hydraulic dynamics), where N is the stratification, h is the height of the topography, and u0 is the near-bottom velocity; the parameterization does not have a dependence on Coriolis frequency. Simulations carried out in a channel with synthetic bathymetry and steady body forcing indicate that this parameterization accurately predicts drag across a broad range of forcing parameters when the effect of reduced near-bottom mixing is taken into account by reducing the effective height of the topography. The parameterization is also tested in simulations of wind-driven channel flows that generate mesoscale eddy fields, a setup where the downstream transport is sensitive to the bottom drag parameterization and its effect on the eddies. In these simulations, the parameterization replicates the effect of rough bathymetry on the eddies. If extrapolated globally, the subinertial topographic scales can account for 2.7 TW of work done on the low-frequency circulation, an important sink that is redistributed to mixing in the open ocean.

Spatially Quasi-Periodic Water Waves of Infinite Depth

We formulate the two-dimensional gravity-capillary water wave equations in a spatially quasi-periodic setting and present a numerical study of solutions of the initial value problem. We propose a Fourier pseudo-spectral discretization of the equations of motion in which one-dimensional quasi-periodic functions are represented by two-dimensional periodic functions on a torus. We adopt a conformal mapping formulation and employ a quasi-periodic version of the Hilbert transform to determine the normal velocity of the free surface. Two methods of time-stepping the initial value problem are proposed, an explicit Runge–Kutta (ERK) method and an exponential time-differencing (ETD) scheme. The ETD approach makes use of the small-scale decomposition to eliminate stiffness due to surface tension. We perform a convergence study to compare the accuracy and efficiency of the methods on a traveling wave test problem. We also present an example of a periodic wave profile containing vertical tangent lines that is set in motion with a quasi-periodic velocity potential. As time evolves, each wave peak evolves differently, and only some of them overturn. Beyond water waves, we argue that spatial quasi-periodicity is a natural setting to study the dynamics of linear and nonlinear waves, offering a third option to the usual modeling assumption that solutions either evolve on a periodic domain or decay at infinity.

Linear wave dynamics and intrinsic axisymmetric thermoacoustic instability in swirling flame combustors

This paper investigates the intrinsic thermoacoustic (ITA) feedback and its possible interaction with the cavity acoustic resonance in swirling flame combustors under the configuration of axisymmetric perturbations. The dynamics of acoustic-vortical-entropic perturbations due to the unsteady heat release rate by a swirling flame are given in the presence of azimuthal and axial base flow velocities. The critical gain of ITA oscillations is given meanwhile parametric analysis show that the phase shift between acoustic and vortical waves plays an important role on the ITA critical gain. Applied to the configuration of a plenum-swirler-chamber combustor with the presence of swirling flames, the present work predicts correctly the thermoacoustic oscillations. Meanwhile, the criterion of ITA modes is given in matrix form. Analysis on the interaction between the ITA feedback and the cavity acoustic resonant feedback shows that the thermoacoustic modes of the whole system are composed of both ITA-oriented modes and the cavity-oriented resonant modes. Increasing the transit time difference between the acoustic and vortical waves reduces frequencies of ITA and ITA-oriented modes and worsens their stabilities. The cavity-oriented thermoacoustic mode, on the other hand, forms a spiral orbit and approaches to an attractor, which is independent of the transit time difference.

EVOLUTION OF LINEAR WAVES IN A POROUS MEDIUM SATURATED WITH A BUBBLE LIQUID

Background The study of the processes of propagation of pressure waves in liquid-saturated porous media is associated not only with solving practical problems of underwater acoustics, seismics, object protection, non-destructive testing, etc., but it is also necessary to understand the fundamental foundations of wave processes. in such environments. Aims and Objectives Investigation of the evolution of a pulse of finite duration in a porous medium saturated with a gas-liquid mixture. Analysis of two situations of the location of bubbles in a porous medium. The first, when the bubble envelopes several pores, and the second situation - gas bubbles are much smaller than the pore sizes and are located on the pore walls. Results The dynamics of linear waves in a porous medium filled with a gas-liquid mixture has been studied. The influence of the determining factors of a bubbly liquid (volumetric content, dispersion of bubbles) and a porous medium on the shape and decay of impulse disturbances is analyzed.

Observed Eddy–Internal Wave Interactions in the Southern Ocean

AbstractThe physical mechanisms that remove energy from the Southern Ocean’s vigorous mesoscale eddy field are not well understood. One proposed mechanism is direct energy transfer to the internal wave field in the ocean interior, via eddy-induced straining and shearing of preexisting internal waves. The magnitude, vertical structure, and temporal variability of the rate of energy transfer between eddies and internal waves is quantified from a 14-month deployment of a mooring cluster in the Scotia Sea. Velocity and buoyancy observations are decomposed into wave and eddy components, and the energy transfer is estimated using the Reynolds-averaged energy equation. We find that eddies gain energy from the internal wave field at a rate of −2.2 ± 0.6 mW m−2, integrated from the bottom to 566 m below the surface. This result can be decomposed into a positive (eddy to wave) component, equal to 0.2 ± 0.1 mW m−2, driven by horizontal straining of internal waves, and a negative (wave to eddy) component, equal to −2.5 ± 0.6 mW m−2, driven by vertical shearing of the wave spectrum. Temporal variability of the transfer rate is much greater than the mean value. Close to topography, large energy transfers are associated with low-frequency buoyancy fluxes, the underpinning physics of which do not conform to linear wave dynamics and are thereby in need of further research. Our work suggests that eddy–internal wave interactions may play a significant role in the energy balance of the Southern Ocean mesoscale eddy and internal wave fields.

Effect of the North Pacific Tropospheric Waveguide on the Fidelity of Model El Niño Teleconnections

AbstractIn a free-running climate model, DJF tropical–extratropical teleconnections are assessed and compared to observed teleconnections in reanalysis data. From reanalysis, the leading mode of covariability between tropical outgoing longwave radiation (OLR) and Northern Hemisphere extratropical geopotential height (Z500) is identified using maximum covariance analysis (MCA). This mode relates closely to the El Niño pattern. The GCM captures the tropical OLR well but the associated extratropical Z500 less well. The GCM climatology has an equatorward shifted North Pacific jet bias. We examine whether the difference in the teleconnection pattern is related to the GCM’s jet bias. In both a ray-tracing analysis and a barotropic model, this jet bias is shown to affect the Rossby wave propagation from the tropical Pacific into the North Pacific. These idealized model results suggest qualitatively that the MCA difference is largely consistent with linear Rossby wave dynamics. While the basic state has a larger effect on the North Pacific MCA, a Rossby wave source (RWS) bias in the Caribbean has a larger effect on the North Atlantic MCA. The North Pacific jet bias is also proposed to affect the downstream propagation of waves from North America into the Caribbean, where it affects tropical RWS and the triggering of secondary waves into the North Atlantic. We propose that climatological biases in the tropics are one underlying cause of the jet bias. Our study may also help understand the results of other climate models with similar jet biases.

Speed-of-light pulses in a massless nonlinear Dirac equation.

In this work, we explore a massless nonlinear Dirac equation, i.e., a nonlinear Weyl equation. We study the dynamics of its pulse solutions and find that a localized one-hump initial condition splits into a localized two-hump pulse, while an associated phase structure emerges in suitable components of the spinor field. For times larger than a transient time t_{s} this pulse moves with the speed of light, effectively featuring linear wave dynamics and maintaining its shape (both in two and three dimensions). We show that for the considered nonlinearity, this pulse represents an exact solution of the nonlinear equation. Finally, we briefly comment on the generalization of the results to a broader class of nonlinearities.

Linear and nonlinear spin-wave dynamics in ultralow-damping microstructured Co2FeAl Heusler waveguide

We report on the investigation of linear and nonlinear spin-wave dynamics of a microstructured Co2FeAl Heusler waveguide using the microfocus Brillouin light scattering technique. A significantly increased decay length of 19.55 μm owing to decreased Gilbert damping has been observed for waves propagating in the linear regime. Furthermore, the localized edge mode caused by the demagnetizing field leads to the nonlinear generation of high-order harmonics at double and triple excitation frequencies at high powers. The obtained results provide valuable insights into the linear and nonlinear spin wave dynamics of the Heusler waveguide and could potentially be applied in the implementation of spin wave frequency multipliers for magnonic applications.

The Impact of Tropical Precipitation on Summertime Euro-Atlantic Circulation via a Circumglobal Wave Train

AbstractThe influence of tropical precipitation variability on summertime seasonal circulation anomalies in the Euro-Atlantic sector is investigated. The dominant mode of the maximum covariance analysis (MCA) between the Euro-Atlantic circulation and tropical precipitation reveals a cyclonic anomaly over the extratropical North Atlantic, contributing to anomalously wet conditions over western Europe and dry conditions over eastern Europe and Scandinavia (in the positive phase). The related mode of tropical precipitation variability is associated with tropical Pacific SST anomalies and is closely linked to the El Niño–Southern Oscillation (ENSO). The second MCA mode consists of weaker tropical precipitation anomalies but with a stronger extratropical signal that reflects internal atmospheric variability. The teleconnection mechanism is tested in barotropic model simulations, which indicate that the observed link between the dominant mode of tropical precipitation and the Euro-Atlantic circulation anomalies is largely consistent with linear Rossby wave dynamics. The barotropic model response consists of a circumglobal wave train in the extratropics that is primarily forced by divergence anomalies in the eastern tropical Pacific. Both the eastward and westward group propagation of the Rossby waves are found to be important in determining the circulation response over the Euro-Atlantic sector. The mechanism was also analyzed in an operational seasonal forecasting system, ECMWF’s System 4. While System 4 is well able to reproduce and skillfully forecast the tropical precipitation, the extratropical circulation response is absent over the Euro-Atlantic region, which is likely related to biases in the Asian jet stream.

Linear Stability of Moist Convecting Atmospheres. Part I: From Linear Response Functions to a Simple Model and Applications to Convectively Coupled Waves

Abstract A procedure is presented to systematically construct simple models for the linear stability of moist convecting atmospheres. First, linear response functions of a cumulus ensemble constructed from cloud-system-resolving models are coupled with matrices expressing two-dimensional large-scale linear wave dynamics. For a radiative–convective equilibrium reference state, this model gives two branches of unstable modes: a propagating convectively coupled wave branch and a stationary branch related to storage of column-integrated moist static energy (MSE). The stationary branch is unstable only when radiative feedback is included, while the convectively coupled wave branch is less affected by radiative feedback. With a modular order-reduction procedure from control theory, the linear-response-function-based model is reduced to a system of six ordinary differential equations while still capturing the essential features of the unstable modes (eigenvalues and structures). The six-dimensional system is then split into a slow and a fast manifold. The slow manifold (again, reflecting column MSE storage) is essential for the stationary mode but not for the convectively coupled waves. The fast manifold is then transformed into a form similar to that of prior simple models of convectively coupled waves, thus placing those models and the insights derived from them on a firmer footing. The procedure also better quantifies the parameters of such simple models and allows the stability difference between different reference states to be better understood.

An adiabatic foehn mechanism

Atmospheric mountain flows, produced when the incoming wind is small near the surface and continuously increases with altitude, are evaluated with models of increasing complexity. All models confirm that foehn can be produced by a mountain gravity wave critical level mechanism, where the critical level is located below the surface. This mechanism does not involve humidity, upper‐level wave breaking, upstream blocking, downward wave reflections or hydraulic control, as often suggested by popular theories. The first model used is a theoretical one which combines linear gravity wave dynamics with a nonlinear boundary condition: in this model the wave breaking does not feed back onto the dynamics by construction. Partial linear wave reflections are also minimized by using smooth profiles of the incident wind and a uniform stratification N2 = constant, and can even be suppressed when the incident wind shear is also constant, Uz = constant. The second model is a numerical mesoscale model (Weather Research and Forecasting), and we show that it predicts mountain wave fields which can be reproduced by the theoretical model, provided that we specify an adequate boundary‐layer depth in the theoretical model.

Role of Equatorial Basin-Mode Resonance for the Seasonal Variability of the Angola Current at 11°S

AbstractMultiyear moored velocity observations of the Angola Current near 11°S reveal a weak southward mean flow superimposed by substantial intraseasonal to seasonal variability, including annual and semiannual cycles with distinct baroclinic structures. In the equatorial Atlantic these oscillations are associated with basin-mode resonances of the fourth and second baroclinic modes, respectively. Here, the role of basin-mode resonance and local forcing for the Angola Current seasonality is investigated. A suite of linear shallow-water models for the tropical Atlantic is employed, each model representing a single baroclinic mode forced at a specific period. The annually and semiannually oscillating forcing is given by 1) an idealized zonally uniform zonal forcing restricted to the equatorial band corresponding to a remote equatorial forcing or 2) realistic, spatially varying Fourier components of wind stress data that include local forcing off Angola, particularly alongshore winds. Model-computed modal amplitudes are scaled to match moored velocity observations from the equatorial Atlantic. The observed annual cycle of alongshore velocity at 11°S is well reproduced by the remote equatorial forcing. Including local forcing slightly improves the agreement between observed and simulated semiannual oscillations at 11°S compared to the purely equatorial forcing. However, the model-computed semiannual cycle lacks amplitude at middepth. This could be the result of either underestimating the strength of the second equatorial basin mode of the fourth baroclinic mode or other processes not accounted for in the shallow-water models. Overall, the findings underline the importance of large-scale linear equatorial wave dynamics for the seasonal variability of the boundary circulation off Angola.

The Dynamics of Mesoscale Winds in the Upper Troposphere and Lower Stratosphere

Abstract Spectral analysis is applied to infer the dynamics of mesoscale winds from aircraft observations in the upper troposphere and lower stratosphere. Two datasets are analyzed: one collected aboard commercial aircraft and one collected using a dedicated research aircraft. A recently developed wave–vortex decomposition is used to test the observations’ consistency with linear inertia–gravity wave dynamics. The decomposition method is shown to be robust in the vicinity of the tropopause if flight tracks vary sufficiently in altitude. For the lower stratosphere, the decompositions of both datasets confirm a recent result that mesoscale winds are consistent with the polarization and dispersion relations of inertia–gravity waves. For the upper troposphere, however, the two datasets disagree: only the research aircraft data indicate consistency with linear wave dynamics at mesoscales. The source of the inconsistency is a difference in mesoscale variance of the measured along-track wind component. To further test the observed flow’s consistency with linear wave dynamics, the ratio between tropospheric and stratospheric mesoscale energy levels is compared to a simple model of upward-propagating waves that are partially reflected at the tropopause. For both datasets, the observed energy ratio is roughly consistent with the simple wave model, but wave frequencies diagnosed from the data draw into question the applicability of the monochromatic theory at wavelengths smaller than 10 km.

Internal swells in the tropics: Near‐inertial wave energy fluxes and dissipation during CINDY

AbstractA developing MJO event in the tropical Indian Ocean triggered wind disturbances that generated inertial oscillations in the surface mixed layer. Subsequent radiation of near‐inertial waves below the mixed layer produced strong turbulence in the pycnocline. Linear plane wave dynamics and spectral analysis are used to explain these observations, with the ultimate goal of estimating the wave energy flux in relation to both the energy input by the wind and the dissipation by turbulence. The results indicate that the wave packets carry approximately 30–40% of the wind input of inertial kinetic energy, and propagate in an environment conducive to the occurrence of a critical level set up by a combination of vertical gradients in background relative vorticity and Doppler shifting of wave frequency. Turbulent kinetic energy dissipation measurements demonstrate that the waves lose energy as they propagate in the transition layer as well as in the pycnocline, where approaching this critical level may have dissipated approximately 20% of the wave packet energy in a single event. Our analysis, therefore, supports the notion that appreciable amounts of wind‐induced inertial kinetic energy escape the surface boundary layer into the interior. However, a large fraction of wave energy is dissipated within the pycnocline, limiting its penetration into the abyssal ocean.