Technology / Technical guide
Wind Turbulence Spectra, Time Scales & Spatial Scales
Two wind signals can have the same mean and variance while distributing their fluctuations across different frequencies. A turbulence spectrum describes that distribution. Spatial correlation adds another dimension: nearby points need not experience identical changes at identical times.
Describe more than one turbulence number.
The spectrum, correlation and mean advection describe different physical aspects of a changing flow. Their distinctions explain why the same turbulence intensity can produce different time histories without proving one actual turbine response.
01 / Fluctuations
Mean speed does not contain the complete signal.
For a chosen interval and component, write u(t) = U + u′(t), with the fluctuation defined to have zero mean over that interval.
For a chosen interval and component, write u(t) = U + u′(t), with the fluctuation defined to have zero mean over that interval. Its variance describes the mean-square fluctuation. A different interval can change both the mean and variance.
Longer coherent variations and rapid smaller changes can coexist. A single standard deviation collapses their timing into one number. It does not show whether much of the variation lies near a structure’s characteristic response frequency or at a substantially different time scale.
02 / Spectral meaning
A spectrum allocates fluctuation variance.
For a compatible one-sided velocity spectrum S(f), the variance is the integral of S(f) over positive frequency.
For a compatible one-sided velocity spectrum S(f), the variance is the integral of S(f) over positive frequency. Its units are (m/s)² per hertz. The TurbSim guide explicitly uses spectra to represent turbulence and relates their integration to standard deviation.
Consider two hypothetical spectra whose integrals are both 4 (m/s)². Each has a standard deviation of 2 m/s, but one can place more variance at low frequency and the other at high frequency. Equal variance does not make their time histories or structural effects equal.
03 / Time correlation
Persistence differs from fluctuation magnitude.
An autocorrelation describes how a fluctuation relates to the same component after a time lag.
An autocorrelation describes how a fluctuation relates to the same component after a time lag. A signal that remains similar over longer lags has a different temporal structure from one that changes rapidly, even at equal variance.
An integral time scale is associated with integrating a defined normalised correlation over a specified lag convention. Its treatment depends on stationarity and the correlation model. It should not be confused with one oscillation period or declared a universal duration for every gust.
04 / Spatial scale
A temporal record is not automatically a spatial map.
A frozen-flow approximation treats a pattern as translating at a specified mean speed without changing while it passes.
A frozen-flow approximation treats a pattern as translating at a specified mean speed without changing while it passes. Under those conditions, a time scale τ corresponds approximately to a distance Uτ. An advected frequency can likewise correspond to a scale of order U/f.
At an assumed U = 8 m/s, a one-second translation corresponds to 8 m. This is hypothetical kinematics, not a measured eddy diameter. Flow evolution, shear and nonuniform advection can prevent a point record from reconstructing an entire rotor-plane field.
05 / Coherence
Different positions can fluctuate together only partly.
Cross-point correlation describes shared variation between separated locations.
Cross-point correlation describes shared variation between separated locations. A broad spatially coherent change can affect much of a rotor at once, while a small-scale change may affect only part of it. The spatial-average guide explains how that distinction enters an aggregate.
A model’s component spectra and coherence assumptions are separate inputs. Specifying one spectrum does not uniquely specify a three-dimensional fluctuating field. Nor does choosing a named model establish that it represents a particular terrain, weather condition or actual operating record.
06 / Scope
Keep modelled flow apart from structural response.
A spectrum describes an input distribution, while structural motion also depends on the system’s dynamics and coupling.
A spectrum describes an input distribution, while structural motion also depends on the system’s dynamics and coupling. A spectral peak is therefore not automatically a blade-mode frequency or a measured resonance. Input and response require distinct definitions.
This page explains physical scales, not spectral-estimation software or a permissible turbulence threshold for MARSTON equipment. The signal-spectrum guide treats the different question of representing sampled records and their analysis conventions.
Related technical guides: Rotor Spatial Averaging: Point Wind, Area Mean & Equivalent Speed · Yawed Rotor Inflow: Velocity Components & Skewed Wake · Power Spectral Density: Units, Integration & RMS.
General background: NREL TurbSim guide: turbulence spectra and spatial model conditions. These references explain industry concepts; they are separate from the applicable MARSTON product and project documents.
Key concepts and conditions.
Read each quantity with its reference, units and stated conditions. A general relation does not establish a model-specific value.
| Concept / quantity | Meaning / relation | Conditions / limits |
|---|---|---|
| Variance | Mean-square fluctuation | Depends on component and averaging interval. |
| One-sided S(f) | (m/s)²/Hz | Its integral represents variance. |
| Time scale | Correlation over lag | Not a universal gust duration. |
| Advection scale | Uτ under frozen flow | Requires stated translation assumptions. |
| Spatial coherence | Shared fluctuation across locations | Different from one-point variance. |
Engineering questions.
Do equal means imply equal turbulence?
No. Fluctuation variance, spectrum and spatial relationships can differ.
Do equal spectral integrals imply equal spectra?
No. The same variance can be distributed differently across frequency.
Is every time lag an eddy diameter divided by wind speed?
No. That interpretation requires an applicable frozen-flow approximation.
Does a one-point spectrum define the whole rotor-plane flow?
No. Spatial relationships and component assumptions also matter.
Is an input spectral peak proof of resonance?
No. Structural response depends on its own dynamics and coupling.
Does this supply a permitted MARSTON turbulence limit?
No. It explains quantities and model assumptions only.
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