Lvov Yuri V.

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Lvov

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Yuri V.

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On the origins of the oceanic ultraviolet catastrophe

(American Meteorological Society, 2022-03-25) Dematteis, Giovanni ; Polzin, Kurt L. ; Lvov, Yuri V.

We provide a first-principles analysis of the energy fluxes in the oceanic internal wave field. The resulting formula is remarkably similar to the renowned phenomenological formula for the turbulent dissipation rate in the ocean, which is known as the finescale parameterization. The prediction is based on the wave turbulence theory of internal gravity waves and on a new methodology devised for the computation of the associated energy fluxes. In the standard spectral representation of the wave energy density, in the two-dimensional vertical wavenumber–frequency (m–ω) domain, the energy fluxes associated with the steady state are found to be directed downscale in both coordinates, closely matching the finescale parameterization formula in functional form and in magnitude. These energy transfers are composed of a “local” and a “scale-separated” contributions; while the former is quantified numerically, the latter is dominated by the induced diffusion process and is amenable to analytical treatment. Contrary to previous results indicating an inverse energy cascade from high frequency to low, at odds with observations, our analysis of all nonzero coefficients of the diffusion tensor predicts a direct energy cascade. Moreover, by the same analysis fundamental spectra that had been deemed “no-flux” solutions are reinstated to the status of “constant-downscale-flux” solutions. This is consequential for an understanding of energy fluxes, sources, and sinks that fits in the observational paradigm of the finescale parameterization, solving at once two long-standing paradoxes that had earned the name of “oceanic ultraviolet catastrophe.”
Oceanic internal-wave field : theory of scale-invariant spectra

(American Meteorological Society, 2010-12) Lvov, Yuri V. ; Polzin, Kurt L. ; Tabak, Esteban G. ; Yokoyama, Naoto

Steady scale-invariant solutions of a kinetic equation describing the statistics of oceanic internal gravity waves based on wave turbulence theory are investigated. It is shown in the nonrotating scale-invariant limit that the collision integral in the kinetic equation diverges for almost all spectral power-law exponents. These divergences come from resonant interactions with the smallest horizontal wavenumbers and/or the largest horizontal wavenumbers with extreme scale separations. A small domain is identified in which the scale-invariant collision integral converges and numerically find a convergent power-law solution. This numerical solution is close to the Garrett–Munk spectrum. Power-law exponents that potentially permit a balance between the infrared and ultraviolet divergences are investigated. The balanced exponents are generalizations of an exact solution of the scale-invariant kinetic equation, the Pelinovsky–Raevsky spectrum. A small but finite Coriolis parameter representing the effects of rotation is introduced into the kinetic equation to determine solutions over the divergent part of the domain using rigorous asymptotic arguments. This gives rise to the induced diffusion regime. The derivation of the kinetic equation is based on an assumption of weak nonlinearity. Dominance of the nonlocal interactions puts the self-consistency of the kinetic equation at risk. However, these weakly nonlinear stationary states are consistent with much of the observational evidence.
Toward regional characterizations of the oceanic internal wavefield

(American Geophysical Union, 2011-11-10) Polzin, Kurt L. ; Lvov, Yuri V.

Many major oceanographic internal wave observational programs of the last 4 decades are reanalyzed in order to characterize variability of the deep ocean internal wavefield. The observations are discussed in the context of the universal spectral model proposed by C. J. R. Garrett and W. H. Munk. The Garrett and Munk model is a good description of wintertime conditions at Site D on the continental rise north of the Gulf Stream. Elsewhere and at other times, significant deviations in terms of amplitude, separability of the 2-D vertical wavenumber-frequency spectrum, and departure from the model's functional form are reported. Specifically, the Garrett and Munk model overestimates annual average frequency domain spectral levels both at Site D and in general. The bias at Site D is associated with the Garrett and Munk model being a fit to wintertime data from Site D and the presence of an annual cycle in high-frequency energy in the western subtropical North Atlantic having a maximum in winter. The wave spectrum is generally nonseparable, with near-inertial waves typically having greater bandwidth (occupying smaller vertical scales) than continuum frequency waves. Separability is a better approximation for more energetic states, such as wintertime conditions at Site D. Subtle geographic differences from the high-frequency and high vertical wavenumber power laws of the Garrett and Munk spectrum are apparent. Such deviations tend to covary: whiter frequency spectra are partnered with redder vertical wavenumber spectra. We review a general theoretical framework of statistical radiative balance equations and interpret the observed variability in terms of the interplay between generation, propagation, and nonlinearity. First, nonlinearity is a fundamental organizing principle in this work. The observed power laws lie close to the induced diffusion stationary states of the resonant kinetic equation describing the lowest-order nonlinear transfers. Second, eddy variability and by implication wave mean interactions are also an organizing principle. Observations from regions of low eddy variability tend to be outliers in terms of their parametric spectral representation; other data tend to cluster in two regions of parameter space. More tentatively, the seasonal cycle of high-frequency energy is in phase with the near-inertial seasonal cycle in regions of significant eddy variability. In regions of low eddy variability, the seasonal cycle in high-frequency energy lags that of near-inertial energy. The induced diffusion stationary states are approximate analytic solutions to the resonant kinetic equation, and the Garrett and Munk spectrum represents one such analytic solution. We present numerical solutions of the resonant kinetic equation, however, that are inconsistent with the Garrett and Munk model representing a stationary state, either alone or in combination with other physical mechanisms. We believe this to be the case for other regional characterizations as well. We argue that nonstationarity of the numerical solutions is related to local transfers in horizontal wavenumber, whereas the analytic induced diffusion stationary states consider only nonlocal transfers in vertical wavenumber. Consequences for understanding the pathways by which energy is transferred from sources to sinks are considered. Further progress likely requires self-consistent solutions to a broadened kinetic equation.
An oceanic ultra-violet catastrophe, wave-particle duality and a strongly nonlinear concept for geophysical turbulence

(MDPI AG, 2017-06-29) Polzin, Kurt L. ; Lvov, Yuri V.

There is no theoretical underpinning that successfully explains how turbulent mixing is fed by wave breaking associated with nonlinear wave-wave interactions in the background oceanic internal wavefield. We address this conundrum using one-dimensional ray tracing simulations to investigate interactions between high frequency internal waves and inertial oscillations in the extreme scale separated limit known as “Induced Diffusion”. Here, estimates of phase locking are used to define a resonant process (a resonant well) and a non-resonant process that results in stochastic jumps. The small amplitude limit consists of jumps that are small compared to the scale of the resonant well. The ray tracing simulations are used to estimate the first and second moments of a wave packet’s vertical wavenumber as it evolves from an initial condition. These moments are compared with predictions obtained from the diffusive approximation to a self-consistent kinetic equation derived in the ‘Direct Interaction Approximation’. Results indicate that the first and second moments of the two systems evolve in a nearly identical manner when the inertial field has amplitudes an order of magnitude smaller than oceanic values. At realistic (oceanic) amplitudes, though, the second moment estimated from the ray tracing simulations is inhibited. The transition is explained by the stochastic jumps obtaining the characteristic size of the resonant well. We interpret this transition as an adiabatic ‘saturation’ process which changes the nominal background wavefield from supporting no mixing to the point where that background wavefield defines the normalization for oceanic mixing models.
Resonant and near-resonant internal wave interactions

(American Meteorological Society, 2012-05) Lvov, Yuri V. ; Polzin, Kurt L. ; Yokoyama, Naoto

The spectral energy density of the internal waves in the open ocean is considered. The Garrett and Munk spectrum and the resonant kinetic equation are used as the main tools of the study. Evaluations of a resonant kinetic equation that suggest the slow time evolution of the Garrett and Munk spectrum is not in fact slow are reported. Instead, nonlinear transfers lead to evolution time scales that are smaller than one wave period at high vertical wavenumber. Such values of the transfer rates are inconsistent with the viewpoint expressed in papers by C. H. McComas and P. Müller, and by P. Müller et al., which regards the Garrett and Munk spectrum as an approximate stationary state of the resonant kinetic equation. It also puts the self-consistency of a resonant kinetic equation at a serious risk. The possible reasons for and resolutions of this paradox are explored. Inclusion of near-resonant interactions decreases the rate at which the spectrum evolves. Consequently, this inclusion shows a tendency of improving of self-consistency of the kinetic equation approach.
Interacting internal waves explain global patterns of interior ocean mixing

(Nature Research, 2024-08-29) Dematteis, Giovanni ; Le Boyer, Arnaud ; Pollmann, Friederike ; Polzin, Kurt L. ; Alford, Matthew H. ; Whalen, Caitlin B. ; Lvov, Yuri V.

Across the stable density stratification of the abyssal ocean, deep dense water is slowly propelled upward by sustained, though irregular, turbulent mixing. The resulting mean upwelling determines large-scale oceanic circulation properties like heat and carbon transport. In the ocean interior, this turbulent mixing is caused mainly by breaking internal waves: generated predominantly by winds and tides, these waves interact nonlinearly, transferring energy downscale, and finally become unstable, break and mix the water column. This paradigm, long parameterized heuristically, still lacks full theoretical explanation. Here, we close this gap using wave-wave interaction theory with input from both localized and global observations. We find near-ubiquitous agreement between first-principle predictions and observed mixing patterns in the global ocean interior. Our findings lay the foundations for a wave-driven mixing parameterization for ocean general circulation models that is entirely physics-based, which is key to reliably represent future climate states that could differ substantially from today’s.
A one-dimensional model for investigating scale-separated approaches to the interaction of oceanic internal waves

(American Meteorological Society, 2024-10-23) Polzin, Kurt L. ; Lvov, Yuri V.

High-frequency wave propagation in near-inertial wave shear has, for four decades, been considered fundamental in setting the spectral character of the oceanic internal wave continuum and for transporting energy to wave breaking. We compare idealized ray-tracing numerical results with metrics derived using a wave turbulence derivation for the kinetic equation and a path integral to study this specific process. Statistical metrics include the time-dependent ensemble mean vertical wavenumber, referred to as a mean drift; dispersion about the mean drift; time-lagged correlation estimates of wavenumber; and phase locking of the wave packets with the background. The path integral permits us to identify the mean drift as a resonant process and dispersion about that mean drift as nonresonant. At small inertial wave amplitudes, ray tracing, wave turbulence, and the path integral provide consistent descriptions for the mean drift of wave packets in the spectral domain and dispersion about the mean drift. Extrapolating these results to the background internal wavefield overpredicts downscale energy transports by an order of magnitude. At oceanic amplitudes, however, the numerics support diminished transport and dispersion that coincide with the mean drift time scale becoming similar to the lagged correlation time scale. We parse this as the transition to a non-Markovian process. Despite this decrease, numerical estimates of downscale energy transfer are still too large. We argue that residual differences result from an unwarranted discard of Bragg scattering resonances. Our results support replacing the long-standing interpretive paradigm of extreme scale-separated interactions with a more nuanced slate of “local” interactions in the kinetic equation.

Lvov Yuri V.

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