Carl H. Gibson

Alignment of vorticity and scalar gradient with strain rate in simulated Navier–Stokes turbulence

The alignment between vorticity and eigenvectors of the strain‐rate tensor in numerical solutions of Navier–Stokes turbulence is studied. Solutions for isotropic flow and homogeneous shear flow from pseudospectral calculations using 1283 grid points have been examined. The Taylor Reynolds number is 83 or greater. In both flows there is an increased probability for the vorticity to point in the intermediate strain direction and at three‐fourths of the sample points this strain is positive (extensive). This propensity for vorticity alignment with a positive intermediate strain is a consequence of angular momentum conservation, as shown by a restricted Euler model of the coupling between strain and vorticity. Probability distributions for intermediate strain, conditioned on total strain, change from a symmetric triangular form at small strain to an asymmetric one for large strain. The most probable value of the asymmetric distribution gives strains in the ratios of 3:1: −4. The evolution of the distribution ...

The universal equilibrium spectra of turbulent velocity and scalar fields

Kolmogoroff’s (1941) theory of local isotropy and universal similarity predicts that all turbulent velocity spectra are reducible to a single universal curve for the highest wave-numbers and that under certain conditions dimensional analysis may be used to predict spectral shapes. Identical arguments predict that the fine structure of conserved dynamically passive scalar fields mixed by turbulence will also be universally similar. A single-electrode conductivity probe in a bridge circuit was used to measure the spectra and decay of a random homogeneous field of concentration and temperature behind a grid, and a Lintronic constant-temperature hot-film anemometer was used to measure the decay of velocity field. These experimental measurements of absolute turbulent velocity, temperature, and concentration spectra in salt water are here compared with the general predictions of universal similarity and local isotropy theories, as well as a prediction by Batchelor (1959) of the exact large wave-number spectral form for scalar mixing at high Schmidt number (v D). The spectral shapes are found to have the predicted similarity forms, and the data are consistent with Batchelor’s predicted spectrum of the scalar field.

Effects of small-scale turbulence on microalgae*

Turbulence flows are characterized by their viscous dissipation rates ɛ and the kinematic viscosity of the fluid ν, but the effects of turbulence on organisms such as microalgae smaller than the Kolmogorov inertial-viscous length scale LK ≡ (ν3/ε)/14 depend on the stress τ ≡ µγ, where µ = ϱν is the dynamic viscosity, ρ is the density, and the rate-of-strain γ ≡ (ε/ν)/12. While various workers have shown qualitatively that turbulence affects several microalgal physiological processes, these effects have not been quantified in terms of ε, τ or γ. Various microalgal groups seem to have different sensitivities to inhibition by turbulence. The relative sensitivities aregreen algae < blue-green algae < diatoms < dinoflagellates with dinoflagellates being most sensitive. We have quantified the growth sensitivity to turbulence for a red tide dinoflagellate,Gonyaulax polyedra Stein, by imposing constant γ values on cultures placed within a gap between rotating outer and fixed inner concentric cylinders. Threshold turbulence values for growth inhibition are consistent with turbulence parameters near the sea surface with light winds, suggesting turbulence may be the reason that high winds inhibit red tides. For ɛ > 0.18 cm2s−3, τ > 0.04 dynes cm−2 (0.002 N M−2 or Pa), γ > 4.4 rad s−1, cell numbers and chlorophyll fluorescence declined, and cells lost their longitudinal flagella and the ability to swim forward. At lower ε, τ and γ values growth rates and cell morphology were the same as in unsheared control cultures. High turbulence may affect other algae, such asSpirulina, which are commonly mass cultured.

Sampling Turbulence in the Stratified Ocean: Statistical Consequences of Strong Intermittency

Abstract Turbulence and turbulent mixing in the ocean are strongly intermittent in amplitude, space and time. The degree of intermittency is measured by the “intermittency factor” σ2, defined as either σ2lnϵ, the variance of the logarithm of the viscous dissipation rate ϵ, or σ2lnχ, the variance of the logarithm of the temperature dissipation rate χ. Available data suggest that the cumulative distribution functions of ϵ and χ in stratified layers are approximately lognormal with large σ2 values in the range 3–7. Departures from lognormality are remarkably similar to those for Monte Carlo generated lognormal distributions contaminated with simulated noise and undersampling effects. Confidence limits for the maximum likelihood estimator of the mean of a lognormal random variable are determined by Monte Carlo techniques and by theoretical modeling. They show that such large σ2 values cause large uncertainty in estimates of the mean unless the number of data samples is extremely large. To obtain estimates of ...

Fine Structure of Scalar Fields Mixed by Turbulence. I. Zero‐Gradient Points and Minimal Gradient Surfaces

Turbulent mixing of passive scalar properties such as temperature or concentration is discussed. From physical and geometrical considerations it is concluded that the smallest scale features of a steady‐state turbulent scalar distribution are primarily determined by the number and distribution of points in the fluid for which the scalar gradient vector is zero, and surfaces for which the gradient magnitude is minimal. Mechanisms for the production, destruction, and motion of such “zero gradient points” and “minimal gradient surfaces” are examined. Initially, zero gradient points must be produced from regions of uniform scalar gradient, but the vast majority result from secondary splitting due to strain induced eccentricities of the closed isoscalar surfaces surrounding maximum or minimum points. An expression for the velocity of surfaces of constant scalar value is derived and used to interpret the Obukhov‐Corrsin length scale (D3/e)14 as the minimum size eddy capable of generating a zero gradient point f...

Statistics of the fine structure of turbulent velocity and temperature fields measured at high Reynolds number

Derivatives of velocity and temperature in the wind over the ocean were found to be quite variable. Probability distribution functions of squared derivatives were consistent with lognormality predictions by Kolmogoroff, Obukhoff and Yaglom. Kurtosis values for velocity derivatives ranged from 13 to 26 and from 26 to 43 for temperature derivatives. Universal inertial subrange constants were evaluated from dissipation spectra and were found to be 40 to 300% larger than most values reported previously. Evidence for local anisotropy of the temperature field is provided by non-zero values of the measured derivative skewness.

Quantified small-scale turbulence inhibits a red tide dinoflagellate, Gonyaulax polyedra Stein

Abstract The development of marine dinoflagellate red tides off southern California requires optimal temperature and light regimes, a source of nutrients that may be supplied by wind-induced upwelling and upmixing, and vertical migration by cells to this source. Red tides occur after the winds decrease and the water becomes highly stratified with a shallow mixed layer. This implies low turbulence levels may be an additional requirement for red tide development. Because dinoflagellates with sizes about 35 μm are much smaller than the inertial-viscous, or Kolmogorov scales L κ ≡ (ν 3 /ϵ) 1 4 = (ν/γ) 1 2 of oceanic turbulence, the important flow parameters are the viscous dissipation rate per unit mass ϵ (cm2s−3 or ergs g−1s−1), the rate-of-strain γ ≡ (ϵ/ν) 1 2 ( rad s −1 ) , and the stress τ ≡ μγ (dyne cm−2), where ν is the kinematic viscosity and μ is the dynamic viscosity. In the present work we have cultured the red tide dinoflagellate, Gonyaulax polyedra Stein, under conditions of known ϵ, γ and τ. Growth was inhibited at ϵ values from 0.18 to 164 cm2 s−3 (γ from 4.4 to 132 rad s−1) but not at 0.05 (γ = 2.2) so the threshold stress τ for growth inhibition was 0.02–0.04 dyne cm−2 (0.002–0.004 Pa). This is in the expected range for light winds at the sea surface, suggesting small-scale scale turbulence is the reason higher winds inhibit red tides. Threshold turbulence levels are related to calculated surface levels at various wind speeds and to postulated subsurface euphotic zone levels under incipient red tide conditions. Motile cells in shear-inhibited cultures lost their ability to swim forward vigorously but rather spun in place due to the loss of longitudinal (trailing) flagella, observed microscopically, without loss of girdle flagella.

Fossil Temperature, Salinity, and Vorticity Turbulence in the Ocean

Abstract Small scale fluctuations of temperature, salinity, and vorticity in the ocean occur in isolated patches apparently caused by bursts of active turbulence. After the turbulence has been dampened by stable stratification the fluctuations persist as “fossil turbulence”. The persistence times and internal structure of fossil turbulence are investigated by considering the evolution of a patch of very strong turbulence in a stratified fluid after the source of turbulent kinetic energy has been removed. A variety of parameters, scales, and spectral properties are inferred from this model. Comparison with observations reveals that oceanic temperature microstructure below the mixing layer is fossil temperature turbulence or a combination of active and fossil temperature turbulence; fully turbulent patches are not observed. Even though the mixing rate is greatest in the most active temperature patches, the degree of fossilization is also greatest. The persistence of the fossil patches increases with the parameter γ o /N, which is the rate of strain of turbulence at the time of fossilization compared to the Brunt-Vaisala frequency. Information about the original turbulence, such as γ o and the size and location of the turbulent region, is preserved in the fossil turbulence structure.

Effects of temperature and humidity fluctuations on the optical refractive index in the marine boundary layer

The variance and power spectrum of atmospheric optical refractive-index fluctuations are shown to be composed of three terms: the variance and power spectra of the temperature and humidity fluctuations and the correlation and cospectrum of the temperature and humidity fluctuations, respectively. Humidity fluctuations are found to be significant because of the correlation term. The signs of the temperature–humidity correlation and cospectrum can be positive or negative, and therefore can add to or subtract from refractive-index fluctuations caused by only temperature fluctuations. The results of two atmospheric boundary-layer experiments are reported, which show the large effect of the temperature–humidity correlation term. For cold air blowing over warm ocean water, the correlation term was positive and accounted for 17% of the total refractive-index variance. For dry hot desert air blowing over the cold Salton Sea, the correlation was −268% of the total, effectively cancelling the contribution due to temperature variance.

Fine Structure of Scalar Fields Mixed by Turbulence. II. Spectral Theory

Universal similarity hypotheses are proposed based on the local straining mechanisms, Kolmogoroffs local isotropy theory, and the mixing theories of Obukhov, Corrsin, and Batchelor. Three sets of similarity coordinates follow from the hypotheses depending on five fundamental parameters of turbulent mixing: e, the turbulence dissipation rate; χ, the scalar variance dissipation rate; γ, the local strain rate; ν, the kinematic viscosity; and D, the molecular diffusivity of the scalar. Transformations between coordinate systems are shown to depend only on Pr ≡ ν/D as a mapping parameter. A unified spectral array with convergence properties required by the hypotheses is produced when the similarity hypotheses are used to predict the scalar spectrum function Γ. The inertial subrange (Γ ∼ k−5/3, k is the wavenumber) of Obukhov and Corrsin and the large Pr value viscous‐convective (Γ ∼ k−1) subrange of Batchelor are reproduced. However, for small Pr values, a new inertial‐diffusive subrange arises with Γ ∼ k−3 a...