Upload a CSV from any flow incident where your system alarmed. The τ(3) analysis will show you exactly how many seconds of advance warning you would have had — using your own real data, processed entirely in your browser.
timestamp,velocity_ms,pressure_kpa,temp_c
2026-01-15 09:00:00,2.14,410.2,18.4
2026-01-15 09:00:01,2.15,410.5,18.4
2026-01-15 09:00:02,2.18,411.1,18.5
...
[your alarm row],3.92,487.3,19.1
timestamp — any date/time format
velocity_ms — flow velocity (m/s)
from your flow meter
pressure_kpa — line pressure (kPa)
from your pressure tx
temp_c — fluid temperature (°C)
(optional — improves accuracy)
[alarm col] — optional: your system alarm
1=alarmed, 0=normal
Export from your SCADA historian, DCS, OSIsoft PI, or any data logging system.
Minimum 60 rows recommended. Incident should occur within the dataset.
Download sample incident file to see the format and test the analysis.
| System | Method | First Alert (row) | Alert Type | Lead Time |
|---|
Turbulent transition is preceded by a characteristic redistribution of kinetic energy across wavenumbers — the Kolmogorov energy cascade. This redistribution begins seconds to tens of seconds before the macroscopic consequences appear in pressure or velocity. The τ(3) index quantifies the spectral signature of this redistribution as it develops.
Every existing alarm system monitors Reynolds number, pressure, or flow velocity — all macroscopic quantities that change at or after transition. Re thresholds are also geometry-specific and empirically calibrated, meaning they only work where they were set up and provide no warning before the event they are measuring.
Because τ(3) is derived analytically from the Navier-Stokes equations rather than fitted empirically, the critical exponent is universal. The system requires one commissioning run to establish the system-specific Φ_critical constant. After that it operates without recalibration across the full operating range.
Oil, gas, and water transmission pipelines operating near transitional Reynolds numbers. Turbulent transition causes fatigue loading, erosion, and pressure surges. τ(3) monitoring enables flow rate adjustment before structural damage occurs — giving operators the intervention window their existing alarms cannot provide.
Oil & Gas · Water Infrastructure · Process PipelinesLaminar-to-turbulent transition on wing surfaces and engine nacelles causes drag increases of 30–50%. Real-time τ(3) monitoring of surface pressure arrays enables active flow control systems to maintain laminar conditions at higher angles of attack and across wider flight envelopes.
Aerospace · UAV · Engine Nacelles · PropulsionHeat exchanger efficiency is critically dependent on flow regime. Uncontrolled turbulent transition disrupts thermal boundary layers and causes vibration fatigue in tube bundles. τ(3) monitoring enables proactive flow control maintaining optimal thermal efficiency and extending equipment life.
Chemical Processing · Power Generation · RefiningTurbulent transition in cryogenic propellant feed lines can cause pressure oscillations leading to combustion instability. τ(3) provides the first predictive indicator compatible with the millisecond timescales of rocket engine and gas turbine control systems.
Defence · Space · Gas Turbines · Cryogenic SystemsIf the τ(3) analysis showed advance warning on your incident data, the t3flow team wants to hear about it. Send us your results and we will discuss what a pilot integration would look like on your specific system — pipeline, heat exchanger, aerospace, or propulsion.
τ(3) critical flux-spectrum law · Patent pending · Filed 2026 · United Kingdom