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Analysis of the frozen flow assumption using GeMS telemetry data Angela Cortés 1, Alexander Rudy 2, Benoit Neichel 3, Lisa Poyneer 4, Mark Ammons 4, Andres Guesalaga 1 (1) Pontificia Universidad Católica de Chile, Santiago, Chile (2) University of California Santa Cruz (3) Gemini Observatory Southern Operations Center, La Serena, Chile (4) Lawrence Livermore National Laboratory

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Goal: Use telemetry data from the GeMS to study the validity of the frozen flow hypothesis using two types of algorithms: Spatio-temporal cross-correlations of 5 GeMS laser guidestars WFS The Fourier Wind Identification (FWI) Results: Number of layers present and their associated velocities. Estimation of their altitude and strength (turbulence profiler) Rate of de-correlation (how frozen is the flow?) Analysis of the frozen flow assumption using GeMS telemetry data

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← 60 arcseconds → ← 84.9 arcseconds → ← 42.4 arcsec → 16x16 grid Shack-Hartmann 204 active subapertures (total: 1020) sampling rate= < 800 Hz 5 WFSs 3 DMs 917 actuators in total 684 valid actuators (seen by the WFSs) 233 extrapolated actuators 0 km 4.5 km 9 km Gemini-South MCAO System (GeMS)

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Problems with SLODAR due to dome seeing Solution: spatio- temporal correlations Turbulence profiling using GeMS telemetry data (Cortés et al, MNRAS 2012) Variance in subapertures, Y direction Poster - N: :Performance of two turbulence profilers for a MCAO system under strong dome seeing condition

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For T = 0 s, the turbulence profile in altitude is extracted from the baseline For T > 0, the layers present can be detected and their velocity estimated w = 8.8 m/s α w = 187.1° w = 17.7 m/s α w = 227.7° The “wind profiler” or spatio-temporal correlations

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Next, we analyze 4 cases of Frozen Flow: 1.Dome Turbulence 2.Ground Layer Turbulence 3.Mid Altitude Turbulence 4.High Altitude Turbulence

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1. Frozen flow for turbulence inside the dome Decay in correlation for dome turbulence Wind speed = 0.0 m/s Dome Ground layer By applying this method, an estimate of the dome seeing can be obtained at any time!

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2. Frozen flow for turbulence at the ground layer wind speed = 8.8 m/s wind direction = 187.1° Decay in correlation for ground layer turbulence

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3. Frozen flow for turbulence at mid-altitude (~ 4 Km) Wind speed = 10.0 m/s Wind direction = 172.9° Decay in correlation for mid-altitude turbulence

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4. Frozen flow for turbulence at high-altitude (~ 12 Km) Wind speed = 21.3 m/s Wind direction = 227.7° Wind speed=17.7 m/s Wind direction = 227.7° Decay in correlation for high-altitude turbulence

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Dependence of frozen flow to wind speed w = 10.0 m/s |m|= 1.66 s -1 w = 17.7 m/s |m|= 3.26 s -1 w = 0.0 m/s |m|= 0.32 s -1 w = 8.8 m/s |m|= 1.33 s -1 More data is required to verify this!! 1 ~ 6 m Linear or just a coincidence ? Decay in correlation Absolute rate of fading, |m| vs. wind speed

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Use Fourier Modes in Space and Time to find Frozen Flow Fourier Wind Identification Fourier Modes “Blow” in Wind by

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Transform Open-Loop Phase into Fourier Modes Fourier Wind Identification Pseudo-Open Loop Phase Spatial and Temporal Fourier Modes GeMS TelemetryFourier Modes (Same as Angela’s data)

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Then Fit Temporal Fourier Peaks to Frozen-Flow Layers Fourier Wind Identification Find Peaks in Temporal Space Match Found Peaks to Layer Templates

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FWI Finds Frozen Flow Layers in GeMS Pseudo Open Loop Data Fourier Wind Identification Single Layer Identified (plus a weak second layer) 2 Layers Identified

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Wind Vector Remains Constant when Examined over Longer Times Fourier Wind Identification Time

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Analysis of Longer Telemetry Intervals Improves Overall Signal Fourier Wind Identification

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Spatial-temporal correlation and Fourier Wind Identification agree Wind speed=17.7 m/s Wind direction = 227.7°

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Conclusions Both Methods Detect Frozen Flow Turbulence The short-timescale Spatial Temporal Correlation complements the long timescale Fourier Wind Identification Both methods makes no assumption of Kolmogorov Turbulence. Frozen flow exists and its melting rate is proportional to the wind speed. The method provides an estimate of the dome seeing. Tracking correlation peaks is a major problem. Spatial-Temporal Correlation Fourier Wind Identification Non-Frozen Flow Turbulence is automatically rejected. No suppression of static modes, DC terms are fit like any other turbulence.

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