What question did this study set out to answer?

Develop a fully analytic calculator for homogeneous isotropic turbulence to compute various flow quantities.

April 25, 2026Open Access

CASCADE: Analytic Turbulence Spectrum

Key Points

Develop a fully analytic calculator for homogeneous isotropic turbulence to compute various flow quantities.
Utilizes turbulent rms velocity, integral scale, and kinematic viscosity as inputs.
Computes complete energy spectrum, structure functions, and cascade scales.
Validates predictions against direct numerical simulations across a range of Reynolds numbers.
Accurate prediction of the energy spectrum including the dissipation range with validation across Re_λ = 240 to 1201.
Achieves a closed-form analytic result for the Kolmogorov constant C_K ≈ 1.5874.
Allows for direct comparison with measured or simulated spectra through CSV uploads.

Abstract

CASCADE is a fully analytic turbulence calculator for homogeneous isotropic turbulence. Given three physical inputs: turbulent rms velocity u′, integral scale L, kinematic viscosity ν), it computes: the complete energy spectrum E (k), second- and third-order structure functions S₂ and S₃, cascade scales (η, kL, k_η), flow quantities (ε, Re, Re_λ) The Kolmogorov constant CK = 2^ (2/3) ≈ 1. 5874 is a closed-form analytic result. No empirical closures and no fitted parameters are used. The prediction is validated against direct numerical simulations spanning Re_λ = 240 to 1201 across four independent DNS groups. The full spectrum including the dissipation range is a falsifiable prediction; the tool accepts CSV upload of measured or simulated spectra for direct overlay and comparison. CASCADE is freely accessible at arcadialab. fr (no account required, no ads).

CASCADE: Analytic Turbulence Spectrum

Key Points

Abstract

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