Stated by the turbulence's own statistics — a dissipation, a scale, a spectrum

• A cascade that arrives as stripes — eps = 1 · turbulent-limit
• A cloud grows out of its bursts and keeps their shape — inertial range below the integral scale L; direction memory 0.7, amplitude memory 3; three seeds · wander · hero
• A cloud grows out of its bursts and keeps their shape — inertial range below the integral scale L; μ as measured, 0.2 to 0.3 · wander
• A cloud grows out of its bursts and keeps their shape — inertial range below the integral scale L; direction memory 0.7, amplitude memory 3; three seeds · wander
• A cloud grows out of its bursts and keeps their shape — inertial range below the integral scale L; direction memory 0.7, amplitude memory 3; three seeds · wander
• A cloud grows out of its bursts and keeps their shape — inertial range below the integral scale L; direction memory 0.7, amplitude memory 3; three seeds · wander
• A cloud grows out of its bursts and keeps their shape — inertial range below the integral scale L; direction memory 0.7, amplitude memory 3; three seeds · wander
• A cloud grows out of its bursts and keeps their shape — inertial range below the integral scale L; direction memory 0.7, amplitude memory 3; three seeds · wander
• A cloud grows out of its bursts and keeps their shape — inertial range below the integral scale L; direction memory 0.7, amplitude memory 3; three seeds · wander
• A dissipation correlated across every scale — log-normal cascade — a model spectrum · what-turbulence-forgets
• A dissipation correlated across every scale — four decades of inertial range, mu = 0.25 — a model spectrum · what-turbulence-forgets
• A dissipation correlated across every scale — log-normal cascade — a model spectrum · what-turbulence-forgets
• A dissipation correlated across every scale — log-normal cascade with mu = 0.25 — a model spectrum · what-turbulence-forgets
• A dissipation correlated across every scale — four decades of inertial range — a model spectrum · what-turbulence-forgets
• A dissipation correlated across every scale — D = 2.8 for the beta-model, mu = 0.25 for the log-normal · turbulent-limit
• A dissipation that lags its production — four decades of inertial range, mu = 0.25 — a model spectrum · what-turbulence-forgets
• A pair's memory shapes the cloud it spreads into — inertial range, decades of separation wide; k₀ = ε = 1, released at r₀ = 0.01, seeded · wander · hero
• A pair's memory shapes the cloud it spreads into — inertial range, decades of separation wide; k₀ = ε = 1, released at r₀ = 0.01, seeded · wander
• A pair's memory shapes the cloud it spreads into — inertial range, decades of separation wide; k₀ = ε = 1, released at r₀ = 0.01, seeded · wander
• A pair's memory shapes the cloud it spreads into — inertial range, decades of separation wide; k₀ = ε = 1, released at r₀ = 0.01, seeded · wander
• A pair's memory shapes the cloud it spreads into — inertial range, decades of separation wide; k₀ = ε = 1, released at r₀ = 0.01, seeded · wander
• A pair's memory shapes the cloud it spreads into — inertial range, decades of separation wide; k₀ = ε = 1, released at r₀ = 0.01, seeded · wander
• A relation with no turbulence in it — Pope's model spectrum with its two shape constants solved from the energy and the dissipation · field-statistics · hero
• A relation with no turbulence in it — Pope's model spectrum with its two shape constants solved from the energy and the dissipation · field-statistics
• A relation with no turbulence in it — Reλ = 1,000 · field-statistics
• A relation with no turbulence in it — Reλ = 1,000; cL = 1.9511, cη = 0.4018 · field-statistics
• A relation with no turbulence in it — Pope's model spectrum at three Reynolds numbers · field-statistics
• A relation with no turbulence in it — Pope's model spectrum, five Reynolds numbers · field-statistics
• A relation with no turbulence in it — Reλ = 1,000 · field-statistics
• A relation with no turbulence in it — Pope's model spectrum; three Reynolds numbers · field-statistics
• A relation with no turbulence in it — Pope's model spectrum, fitted at each Reynolds number · field-statistics
• A snapshot counts areas, and a flow counts its edge — stationary; integral scale one in all three fields, five samples to it · field-statistics · hero
• A snapshot counts areas, and a flow counts its edge — stationary; integral scale one in all three fields, five samples to it · field-statistics
• A snapshot counts areas, and a flow counts its edge — stationary; integral scale one in all three fields, five samples to it · field-statistics
• A snapshot counts areas, and a flow counts its edge — stationary; integral scale one in all three fields, five samples to it · field-statistics
• A snapshot counts areas, and a flow counts its edge — stationary; integral scale one in all three fields, five samples to it · field-statistics
• A snapshot counts areas, and a flow counts its edge — stationary; a window 12.8 integral scales wide, sampled 1 to 20 times per integral scale · field-statistics
• A snapshot counts areas, and a flow counts its edge — stationary; integral scale one in all three fields, five samples to it · field-statistics
• A wing averages a gust through its own loading — linear, attached; span b in integral scales L, chord b/9; quasi-steady across the span · gust-average · hero
• A wing averages a gust through its own loading — linear, attached; span b in integral scales L, chord b/9; quasi-steady across the span · gust-average
• A wing averages a gust through its own loading — linear, attached; span b in integral scales L, chord b/9; quasi-steady across the span · gust-average
• A wing averages a gust through its own loading — linear, attached; span b in integral scales L, chord b/9; quasi-steady across the span; b = 0.1 L · gust-average
• A wing averages a gust through its own loading — linear, attached; span b in integral scales L, chord b/9; quasi-steady across the span · gust-average
• A wing averages a gust through its own loading — linear, attached; span b in integral scales L, chord b/9; quasi-steady across the span · gust-average
• A wing averages a gust through its own loading — linear, attached; span b in integral scales L, chord b/9; quasi-steady across the span; b = 0.1 L; Gaussian load · gust-average
• A wing averages a gust through its own loading — linear, attached; span b in integral scales L, chord b/9; quasi-steady across the span · gust-average
• An equilibrium a three-dimensional flow cannot have — eps = 1 · turbulent-limit
• At higher orders the bottleneck hides intermittency — Pope's model spectrum, Reλ 200 to 10,000; read where the second-order ratio is flattest · field-statistics
• Bursts and memory pull a cloud both ways — inertial range, decades of separation wide; diffusivity as separation to the 4/3; three seeds of 6,000 pairs · wander · hero
• Bursts and memory pull a cloud both ways — inertial range, decades of separation wide; diffusivity as separation to the 4/3; three seeds of 6,000 pairs · wander
• Bursts and memory pull a cloud both ways — inertial range, decades of separation wide; diffusivity as separation to the 4/3; three seeds of 6,000 pairs · wander
• Bursts and memory pull a cloud both ways — inertial range, decades of separation wide; diffusivity as separation to the 4/3; three seeds of 6,000 pairs · wander
• Bursts and memory pull a cloud both ways — inertial range, decades of separation wide; diffusivity as separation to the 4/3; three seeds of 6,000 pairs · wander
• Bursts and memory pull a cloud both ways — inertial range, decades of separation wide; 1500 pairs a cloud, twelve clouds · wander
• Bursts and memory pull a cloud both ways — inertial range, decades of separation wide; diffusivity as separation to the 4/3; three seeds of 6,000 pairs · wander
• Forcing at the integral scale leaves the cascade alone — Reλ = 200, band 0.5 wide in ln k; Kármán–Howarth on one model spectrum for every source; isotropic · turbulent-limit · hero
• Forcing at the integral scale leaves the cascade alone — Reλ = 200, band 0.5 wide in ln k; Kármán–Howarth on one model spectrum for every source; isotropic · turbulent-limit
• Forcing at the integral scale leaves the cascade alone — Reλ = 200; Kármán–Howarth on one model spectrum for every source; isotropic · turbulent-limit
• Forcing at the integral scale leaves the cascade alone — Kármán–Howarth on one model spectrum for every source; isotropic · turbulent-limit
• Forcing at the integral scale leaves the cascade alone — Kármán–Howarth on one model spectrum for every source; isotropic · turbulent-limit
• Forcing at the integral scale leaves the cascade alone — Reλ = 200; Kármán–Howarth on one model spectrum for every source; isotropic · turbulent-limit
• Forcing at the integral scale leaves the cascade alone — Kármán–Howarth on one model spectrum for every source; isotropic · turbulent-limit
• Forcing at the integral scale leaves the cascade alone — Kármán–Howarth on one model spectrum for every source; isotropic · turbulent-limit
• Frames that share their eddies count as one — stationary; window 12.8 integral scales square, five samples to each; frozen, 100 swept · field-statistics · hero
• Frames that share their eddies count as one — stationary; window 12.8 integral scales square, five samples to each; frozen, 100 swept · field-statistics
• Frames that share their eddies count as one — stationary; window 12.8 integral scales square, five samples to each; no mean flow · field-statistics
• Frames that share their eddies count as one — stationary; window 12.8 integral scales square, five samples to each; scalar, long run · field-statistics
• Frames that share their eddies count as one — stationary; window 12.8 integral scales square, five samples to each; a frame per half scale · field-statistics
• Frames that share their eddies count as one — integral scale 10 mm, field 128 mm, U = 10 m/s, T = 10 ms; plane cut through 3-D flow · field-statistics
• Frames that share their eddies count as one — integral scale five samples; 256² periodic lattice, 32-sample windows, eight frames · field-statistics
• Sweep slows a wing root's gust cycles and leaves their excess over the lift — linear, attached; elliptic wing; span 0.08 integral scales; lift (light), one root (heavy) · gust-average · hero
• Sweep slows a wing root's gust cycles and leaves their excess over the lift — linear, attached; elliptic wing; span 0.08 integral scales; lift (light), one root (heavy) · gust-average
• Sweep slows a wing root's gust cycles and leaves their excess over the lift — linear, attached; elliptic wing; span b in integral scales L, chord b/9 · gust-average
• Sweep slows a wing root's gust cycles and leaves their excess over the lift — linear, attached; elliptic wing; span 0.08 integral scales, chord b/9 · gust-average
• Sweep slows a wing root's gust cycles and leaves their excess over the lift — linear, attached; elliptic wing; span 0.08 integral scales, sweep 35°; lift (light), one root (heavy) · gust-average
• Sweep slows a wing root's gust cycles and leaves their excess over the lift — linear, attached; elliptic wing; span 60 m, integral scale 760 m, chord b/9 · gust-average
• Sweep slows a wing root's gust cycles and leaves their excess over the lift — linear, attached; elliptic wing; span 0.08 integral scales, chord b/9 · gust-average
• The best estimate of a scale assumes its shape — stationary; integral scale one in both processes · field-statistics · hero
• The best estimate of a scale assumes its shape — stationary; integral scale one in both processes · field-statistics
• The best estimate of a scale assumes its shape — stationary; integral scale one in both processes · field-statistics
• The best estimate of a scale assumes its shape — stationary; integral scale one in both processes · field-statistics
• The best estimate of a scale assumes its shape — stationary; integral scale one in both processes · field-statistics
• The best estimate of a scale assumes its shape — stationary; integral scale one in both processes · field-statistics
• The best estimate of a scale assumes its shape — stationary; integral scale one in both processes · field-statistics
• The best estimate of a scale assumes its shape — stationary; integral scale one in both processes · field-statistics
• The camera needs the window's memory, not the probe's — integral scale λ = 4 samples, window 64 samples; τ(k) ∝ k^−p above the field's own wavenumber; scalar · field-statistics · hero
• The camera needs the window's memory, not the probe's — integral scale λ = 4 samples, window 64 samples; τ(k) ∝ k^−p above the field's own wavenumber; scalar · field-statistics
• The camera needs the window's memory, not the probe's — integral scale λ = 4 samples, window 64 samples; τ(k) ∝ k^−p above the field's own wavenumber · field-statistics
• The camera needs the window's memory, not the probe's — integral scale λ = 4 samples, window 64 samples; τ(k) ∝ k^−p above the field's own wavenumber; scalar, long run · field-statistics
• The camera needs the window's memory, not the probe's — integral scale λ = 4 samples, window 64 samples; τ(k) ∝ k^−p above the field's own wavenumber; scalar, no sweep · field-statistics
• The camera needs the window's memory, not the probe's — integral scale 10 mm, field 128 mm, U = 10 m/s, T = 10 ms; plane cut through 3-D flow · field-statistics
• The camera needs the window's memory, not the probe's — integral scale λ = 4 samples, window 64 samples; τ(k) ∝ k^−p above the field's own wavenumber · field-statistics
• The constant that makes a variance negative — plane strain, k = 1, eps = 1 · turbulent-limit · hero
• The constant that makes a variance negative — plane strain, k = 1, eps = 1 · turbulent-limit
• The constant that makes a variance negative — plane strain · turbulent-limit
• The constant that makes a variance negative — plane strain, k = 1, eps = 1 · turbulent-limit
• The constant that makes a variance negative — plane strain, k = 1, eps = 1 · turbulent-limit
• The constant that travels — self-similar decay, Saffman's invariant in both; nu = 10⁻³ · turbulent-limit · hero
• The constant that travels — self-similar decay, Saffman's invariant in both; nu = 10⁻³ · turbulent-limit
• The constant that travels — self-similar decay — the invariant K ℓᵖ held to 2·10⁻¹⁵ along each run · turbulent-limit
• The constant that travels — self-similar decay with a conserved large-scale integral · turbulent-limit
• The constant that travels — self-similar decay — windows centred at 10, 100 and 1,000 initial eddy times · turbulent-limit
• The constant that travels — self-similar decay — both invariants, both closures; nu = 10⁻³ · turbulent-limit
• The constant that travels — self-similar decay — a one-decade window centred at 100 initial eddy times · turbulent-limit
• The constant that travels — self-similar decay, Saffman's invariant in both · turbulent-limit
• The constant that travels — self-similar decay, Saffman's invariant; ℓ/λ = 20 in the non-equilibrium branch · turbulent-limit
• The decay inside the four-fifths law — n = 1.2; Kármán–Howarth with Pope's model spectrum decaying as K ∝ t^(−n) at fixed ν; isotropic, homogeneous · turbulent-limit · hero
• The decay inside the four-fifths law — Reλ = 200, n = 1.2; Kármán–Howarth with Pope's model spectrum decaying as K ∝ t^(−n) at fixed ν; isotropic, homogeneous · turbulent-limit
• The decay inside the four-fifths law — n = 1.2; Kármán–Howarth with Pope's model spectrum decaying as K ∝ t^(−n) at fixed ν; isotropic, homogeneous · turbulent-limit
• The decay inside the four-fifths law — n = 1.2; Kármán–Howarth with Pope's model spectrum decaying as K ∝ t^(−n) at fixed ν; isotropic, homogeneous · turbulent-limit
• The decay inside the four-fifths law — Reλ = 200; Kármán–Howarth with Pope's model spectrum decaying as K ∝ t^(−n) at fixed ν; isotropic, homogeneous · turbulent-limit
• The decay inside the four-fifths law — n = 1.2; Kármán–Howarth with Pope's model spectrum decaying as K ∝ t^(−n) at fixed ν; isotropic, homogeneous · turbulent-limit
• The decay inside the four-fifths law — Kármán–Howarth with Pope's model spectrum decaying as K ∝ t^(−n) at fixed ν; isotropic, homogeneous · turbulent-limit
• The exponents that stop being thirds — D = 2.8 for the beta-model, mu = 0.25 for the log-normal · turbulent-limit · hero
• The exponents that stop being thirds — D = 2.8 for the beta-model, mu = 0.25 for the log-normal · turbulent-limit
• The exponents that stop being thirds — the same constants · turbulent-limit
• The exponents that stop being thirds — the same constants · turbulent-limit
• The exponents that stop being thirds — D = 2.8 for the beta-model, mu = 0.25 for the log-normal · turbulent-limit
• The exponents that stop being thirds — the asymptotic line of each model · turbulent-limit
• The exponents that stop being thirds — the same constants · turbulent-limit
• The exponents that stop being thirds — 4 decades of separation · turbulent-limit
• The exponents that stop being thirds — 6 decades of separation · turbulent-limit
• The exponents that stop being thirds — D = 2.8, mu = 0.25 · turbulent-limit
• The fraction that is really four thirds — nu = 10⁻⁶ m²/s, eps = 1 W/kg · field-statistics
• The fraction that is really four thirds — nu = 10⁻⁶ m²/s, eps = 1 W/kg, an integral scale of one metre · field-statistics
• The further apart, the faster they part — the four-thirds law between η and the integral scale — continued as K ∝ r² below and constant above · wander · hero
• The further apart, the faster they part — the four-thirds law between η and the integral scale — continued as K ∝ r² below and constant above · wander
• The further apart, the faster they part — the four-thirds law alone — no Kolmogorov or integral scale in it · wander
• The further apart, the faster they part — the four-thirds law between η and the integral scale — continued as K ∝ r² below and constant above · wander
• The further apart, the faster they part — the four-thirds law between η and the integral scale — continued as K ∝ r² below and constant above · wander
• The further apart, the faster they part — the four-thirds law between η and the integral scale — continued as K ∝ r² below and constant above · wander
• The further apart, the faster they part — the four-thirds law between η and the integral scale — continued as K ∝ r² below and constant above · wander
• The range a real Reynolds number does not have — L = 1, K = 1, Reλ 60 to 3,200 · turbulent-limit · hero
• The range a real Reynolds number does not have — L = 1, K = 1, Reλ 60 to 3,200 · turbulent-limit
• The range a real Reynolds number does not have — tolerance 0.05 on the local slope · turbulent-limit
• The range a real Reynolds number does not have — Reλ 100 to 1,600 · turbulent-limit
• The range a real Reynolds number does not have — the band centred on 1/sqrt(L eta) · turbulent-limit
• The range a real Reynolds number does not have — Reλ 30 to 3,200 · turbulent-limit
• The range a real Reynolds number does not have — Reλ 100 to 1,600 · turbulent-limit
• The range a real Reynolds number does not have — L = 1, K = 1, Reλ 60 to 3,200 · turbulent-limit
• The range a real Reynolds number does not have — L = 1, K = 1 · turbulent-limit
• The scalar has its own cascade — Sc = 2,000, eps = 1 W/kg, nu = 10⁻⁶ m²/s · structure-and-mixture · hero
• The scalar has its own cascade — Sc = 2,000, eps = 1 W/kg, nu = 10⁻⁶ m²/s · structure-and-mixture
• The scalar has its own cascade — Sc = 2,000 · structure-and-mixture
• The scalar has its own cascade — eps = 1 W/kg, nu = 10⁻⁶ m²/s · structure-and-mixture
• The scalar has its own cascade — eps = 1 W/kg, nu = 10⁻⁶ m²/s, Sc = 2,000 · structure-and-mixture
• The scalar has its own cascade — Sc = 2,000 · structure-and-mixture
• The scalar has its own cascade — Sc = 2,000 · structure-and-mixture
• The scalar has its own cascade — eps = 1 W/kg, nu = 10⁻⁶ m²/s · structure-and-mixture
• The three that never converge — 2 to 64 octaves above the forcing wavenumber · regime-exact
• Universal, and one of five — self-similar decay in the final period — the nonlinear term is absent rather than small · turbulent-limit · hero
• Universal, and one of five — self-similar decay in the final period — the nonlinear term is absent rather than small · turbulent-limit
• Universal, and one of five — self-similar decay; nu = 10⁻³ in units of the initial scale and energy · turbulent-limit
• Universal, and one of five — the final period — nu = 10⁻³, from 10⁵ to 10⁸ eddy times · turbulent-limit
• Universal, and one of five — self-similar decay; the initial Reℓ is 5000 · turbulent-limit
• Universal, and one of five — self-similar decay; the final period taken to begin at Reℓ of 1 · turbulent-limit
• Universal, and one of five — self-similar decay, k⁴ at the origin in all three; nu = 10⁻³ · turbulent-limit
• Universal, and one of five — self-similar decay in the final period; nu = 10⁻³ · turbulent-limit
• What decay never forgets — K = 1 and l = 1 at t = 1 · turbulent-limit · hero
• What decay never forgets — K = 1 and l = 1 at t = 1 · turbulent-limit
• What decay never forgets — identical initial energy and integral scale · turbulent-limit
• What decay never forgets — identical initial energy and integral scale · turbulent-limit
• What decay never forgets — K = 1 and l = 1 at t = 1 · turbulent-limit
• What decay never forgets — self-similar decay at p = 3 and p = 5 · turbulent-limit
• What decay never forgets — K = 1 and l = 1 at t = 1 · turbulent-limit
• Where the inverse cascade stops — eps = 1 · turbulent-limit · hero
• Where the inverse cascade stops — eps = 1 · turbulent-limit
• Where the inverse cascade stops — ten octaves from the forcing scale to the box · turbulent-limit
• Where the inverse cascade stops — eps = 1, box of size 1 · turbulent-limit
• Where the inverse cascade stops — eps = 1 · turbulent-limit
• Where the inverse cascade stops — octaves above the forcing scale · turbulent-limit
• Where the inverse cascade stops — Kraichnan's logarithmic correction · turbulent-limit
• Where the inverse cascade stops — octaves above the forcing scale · turbulent-limit
• Where the inverse cascade stops — eps = 1, box of size 1 · turbulent-limit

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