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J. Weinstock

Bio: J. Weinstock is an academic researcher from National Oceanic and Atmospheric Administration. The author has contributed to research in topics: Gravity wave & Turbulence. The author has an hindex of 8, co-authored 10 publications receiving 722 citations.

Papers
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Journal ArticleDOI
TL;DR: In this article, the vertical turbulent diffusion coefficient in a stably stratified fluid is derived analytically, without requiring that the flux Richardson number be known or specified, and the resulting expression for the diffusion coefficient is compared with the previous stratospheric results of Lilly et al.
Abstract: The vertical turbulent diffusion coefficient in a stably stratified fluid is derived analytically. This derivation does not require that the flux Richardson number be known or specified. The resulting expression for the diffusion coefficient is compared with the previous stratospheric results of Lilly et al. (1974) and its applicability to atmospheric diffusion and clear air turbulence is discussed.

167 citations

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TL;DR: In this article, the spectrum of gravity wave at each height is calculated directly from the wave equation and wave dissipation is approximately accounted for by a diffusion term, assuming that many wave dissipations can be approximately described by a scale-dependent diffusion process.
Abstract: For a highly idealized condition, the spectrum of saturated and unsaturated gravity waves at each height is calculated directly from the wave equation. A principal feature of this wave equation is the inclusion of wave dissipation, although in an approximate form. In the absence of wave absorption, reflection, radiation, wind shears, resonant wave–wave interactions and other sources and sinks, this dissipation at each height is determined solely by the “turbulent” or chaotic state caused by off-resonant wave–wave interactions and instability of the (broad) wave spectrum at that height. The dissipation is approximately accounted for by a diffusion term. The appropriate diffusivity is self-consistent with the continuum of spectral waves that cause the chaotic state and is argued to be scale dependent. An inverse calculation is also made of what the observed spectra imply for wave dissipation—again assuming that many wave dissipations can be approximately described by a scale-dependent diffusion pro...

146 citations

Journal ArticleDOI
TL;DR: In this article, a theoretical analysis of turbulence in the buoyancy subrange of stably stratified sheer flows is made based on a new calculation of buoyancy flux spectrum B (k), which was assumed that B(k) had a universal form which could be determined by a simple dimensional consideration.
Abstract: A theoretical investigation is made of turbulence in the buoyancy subrange of stably stratified sheer flows. This theory is based on a new calculation of the buoyancy flux spectrum B (k). In the Lumley-Shur theory, it was assumed that B (k) had a universal form which could be determined by a simple dimensional consideration. That assumption is shown to be incorrect. One new result of the present calculation is that B (k) has a fairly sharp transition at a wavenumber kB = 0.8½ωB/vm, where ωB is the Brunt-Vaisala frequency and vm the root-mean-square velocity in the equilibrium range. Physically, this transition is “interpreted” as an emission of incoherent gravity waves fed by the kinetic energy of vertically fluctuating air particles. When k kB, the gravity waves are strongly damped and consequently contain very little energy. The transition of the energy spectrum E(k) at kB is foun...

123 citations

Journal ArticleDOI
TL;DR: For stable stratification, it is pointed out that there exists a strong correlation between the intensity of atmospheric turbulence and the energy dissipation rate ϵ as discussed by the authors, which is given in terms of the variance of vertical velocity σw2 and the Brunt-Vaisala frequency ωB by ϵ = 0.4 σ w2ωB.
Abstract: For stable stratification, it is pointed out that there exists a strong correlation between the intensity of atmospheric turbulence and the energy dissipation rate ϵ. It is given in terms of the variance of vertical velocity σw2 and the Brunt-Vaisala frequency ωB by ϵ = 0.4 σw2ωB. This relation is argued to have a wider range of applicability in the stratosphere than the previous relation ϵ = β σw2, where β is taken to be constant.

120 citations

Journal ArticleDOI
TL;DR: In this paper, a nonlinear theory of internal gravity waves is extended to slowly varying mean winds u0.s. This theory determines the wave amplitudes, enhanced diffusion and momentum deposition, for a broad spectrum of waves as well as for a single wave.
Abstract: A nonlinear theory of internal gravity waves is extended to slowly varying mean winds u0. This theory determines the wave amplitudes, enhanced diffusion and momentum deposition, for a broad spectrum of waves as well as for a single wave. It is shown that the momentum deposition is not constant with altitude, even above the altitude where a wave saturates (breaks). The deposition is seen to decrease as a critical level is approached. The rate of decrease varies with spectral width. In general, the behavior of saturated waves near a critical level is shown to differ greatly from that of linearly growing waves. It is then proven that the momentum deposition is always related to the diffusion coefficient in a very simple and general way. Hence, knowledge of one implies knowledge of the other. Both quantities vary with altitude in nearly the same way. A feature of the theoretical momentum deposition is that it sometimes behaves like Rayleigh friction and sometimes not. It is referred to as “generalize...

95 citations


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TL;DR: In this article, a review of gravity wave sources and characteristics, the evolution of the gravity wave spectrum with altitude and with variations of wind and stability, the character and implications of observed climatologies, and the wave interaction and instability processes that constrain wave amplitudes and spectral shape are discussed.
Abstract: [1] Atmospheric gravity waves have been a subject of intense research activity in recent years because of their myriad effects and their major contributions to atmospheric circulation, structure, and variability. Apart from occasionally strong lower-atmospheric effects, the major wave influences occur in the middle atmosphere, between ∼ 10 and 110 km altitudes because of decreasing density and increasing wave amplitudes with altitude. Theoretical, numerical, and observational studies have advanced our understanding of gravity waves on many fronts since the review by Fritts [1984a]; the present review will focus on these more recent contributions. Progress includes a better appreciation of gravity wave sources and characteristics, the evolution of the gravity wave spectrum with altitude and with variations of wind and stability, the character and implications of observed climatologies, and the wave interaction and instability processes that constrain wave amplitudes and spectral shape. Recent studies have also expanded dramatically our understanding of gravity wave influences on the large-scale circulation and the thermal and constituent structures of the middle atmosphere. These advances have led to a number of parameterizations of gravity wave effects which are enabling ever more realistic descriptions of gravity wave forcing in large-scale models. There remain, nevertheless, a number of areas in which further progress is needed in refining our understanding of and our ability to describe and predict gravity wave influences in the middle atmosphere. Our view of these unknowns and needs is also offered.

2,206 citations

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TL;DR: In this paper, the influence of breaking gravity waves on the dynamics and chemical composition of the 60- to 110-km region has been investigated with a two-dimensional dynamical/chemical model that includes a parameterization of gravity wave drag and diffusion.
Abstract: The influence of breaking gravity waves on the dynamics and chemical composition of the 60- to 110-km region has been investigated with a two-dimensional dynamical/chemical model that includes a parameterization of gravity wave drag and diffusion. The momentum deposited by breaking waves at mesospheric altitudes reverses the zonal winds, drives a strong mean meridional circulation, and produces a very cold summer and warm winter mesopause, in general agreement with observations. The seasonal variations of the computed eddy diffusion coefficient are consistent with the behavior of mesospheric turbulence inferred from MST radar echoes. In particular, it is found that eddy diffusion is strong in summer and winter but much weaker at the equinoxes and that this seasonal behavior has important consequences for the distribution of chemical species. Comparison between computed atomic oxygen and ozone, and the abundances of these constituents inferred from the 557.7-nm and 1.27-μm airglow emissions, reveals excellent agreement. The consistency between model results and these diverse types of observations lends strong support to the hypothesis that gravity waves play a very important role in determining the zonally averaged structure of the mesosphere and lower thermosphere.

805 citations

Journal ArticleDOI
TL;DR: In this paper, a simple eddy kinetic energy parameterization of the oceanic vertical mixing is presented, which is designed to simulate vertical mixing at all depths, from the upper boundary layer down to the abyss.
Abstract: A simple eddy kinetic energy parameterization of the oceanic vertical mixing is presented. The parameterization scheme is based on recent works on atmospheric turbulence modeling. It is designed to simulate vertical mixing at all depths, from the upper boundary layer down to the abyss. This scheme includes a single prognostic equation for the turbulent kinetic energy. The computation of the turbulent length scales is diagnostic, rather than prognostic. In weakly turbulent regions the simulated vertical diffusivity is inversely proportional to the Brunt-Vaisala frequency. In the first validation experiments presented here, the vertical mixing scheme is embedded into a simple one-dimensional model and used for upper ocean simulations at two very different test sites: the station Papa in the Gulf of Alaska and the Long-Term Upper Ocean Study (LOTUS) mooring in the Sargasso Sea. At station Papa the model successfully simulates the seasonal evolution of the upper ocean temperature field. At LOTUS the focus is on a short 2-week period. A detailed analysis of the oceanic heat budget during that period reveals a large bias in the bulk-derived surface heat fluxes. After correction of the fluxes the model does well in simulating the evolution of the temperature and wind-driven current. In particular, the large observed diurnal cycles of the sea surface temperature are well reproduced. During the second (windy) week of the selected period the model accounts for about two thirds of the kinetic energy of the observed upper ocean currents at periods larger than 6 hours. The local wind forcing thus appears to be the dominant generation mechanism for the near-inertial motions, which are the most energetic. The velocity simulation is especially good at the low frequencies. During the second simulated week the model accounts for as much as 78% of the kinetic energy at subinertial frequencies. The simulated mean velocity profile is reminiscent of an Ekman spiral, in agreement with the observations.

697 citations

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TL;DR: A review of recent advances in the understanding of gravity wave saturation in the middle atmosphere can be found in this article, where a brief discussion of the studies leading to the identification of the gravity wave effects and their role in middle atmosphere dynamics is presented.
Abstract: This paper provides a review of recent advances in our understanding of gravity wave saturation in the middle atmosphere. A brief discussion of those studies leading to the identification of gravity wave effects and their role in middle atmosphere dynamics is presented first. This is followed by a simple development of the linear saturation theory to illustrate the principal effects. Recent extensions to the linear saturation theory, including quasi-linear, nonlinear, and transient effects, are then described. Those studies addressing the role of gravity wave saturation in the mean circulation of the middle atmosphere are also discussed. Finally, observations of gravity wave motions, distribution, and variability and those measurements specifically addressing gravity wave saturation are reviewed.

575 citations

Journal ArticleDOI
TL;DR: In this paper, the authors estimate time and space scales for 3D displacements of phytoplankton caused by turbulent mixing, internal waves, Langmuir circulations, and double diffusive processes.
Abstract: The dependence of phytoplankton photosynthesis on light intensity may be altered by the range and frequency of variations in light intensity recentlv experienced by the organisms. A major source of the fluctuations in light intensity experienced by phytoplankton in the upper ocean is vertical motion. We estimate time and space scales for \\Tertical displacements of phytoplankton caused by turbulent mixing, internal waves, Langmuir circulations, and double diffusive processes. In the surface layer, depending on windspeed, current shear and stratification, we find that time scales for cycling of phytoplankton by turbulent eddies and mixing vary from about 0.5 h to hundreds of hours for vertical displacements of the order of 10 m. In the seasonal thermocline, turbulent diffusive time scales for displacements as small as several meters are weeks to months, whereas similar displacements by internal waves occur over periods of several minutes to several hours, according to the strength of the density stratification, and are then dominant. Langmuir cells seem to scale as the large turbulent eddies and need not be treated separately, and double diffusive processes seem to be of minor importance. The formulation used here of a vertical turbulent diffusion coefficient K, as a function of observable quantities-e the rate of dissipation of turbulent kinetic energy, and N the local buoyancy frequency-should also be us&d for estimating vertical fluxes of nutrients. In addition, this formulation is reversible in time and can be used to estimate the recent depth and light history of phytoplankton taken from the upper ocean. Traditionally the dependence of the photosynthetic production rate of phytoplankton on light intensity has been described by “P vs. I” curves relating the rate of photosynthetic production, P, to increasing light intensity, I, determined usually from experiments where portions of the same sample are incubated at several different constant light intensities for the same period. The uptake of labeled carbon over that period is measured and considered to be an index of the photosynthetic production (Peterson 1980). Division by the time interval gives the photosynthetic rate. A smooth curve fitted through the data resembles one of the family of curves shown in Fig. 1 (which, for illustration, has been generated from the model equation of Platt et al. 1980): P(I) = aem”‘( 1 eeVr). (1) Several problems exist: different curves are often found at different times of day (provided the incubation period is sufficiently brief, say 2-4 h), at different depths, during different seasons, and with different organisms (Harris 1973; MacCaull and Platt 1977; Platt et al. 1980). Furthermore, time-course measurements of varying photosynthetic production P(t)

495 citations