Linear and nonlinear sensor placement strategies for mean-flow reconstruction via data assimilation

Two new techniques for the study of the linear and nonlinear instability in growing boundary layers are presented. The first technique employs partial differential equations of parabolic type exploiting the slow change of the mean flow, disturbance velocity profiles, wavelengths, and growth rates in the streamwise direction. The second technique solves the Navier–Stokes equation for spatially evolving disturbances using buffer zones adjacent to the inflow and outflow boundaries. Results of both techniques are in excellent agreement. The linear and nonlinear development of Tollmien–Schlichting (TS) waves in the Blasius boundary layer is investigated with both techniques and with a local procedure based on a system of ordinary differential equations. The results are compared with previous work and the effects of non-parallelism and nonlinearly are clarified. The effect of nonparallelism is confirmed to be weak and, consequently, not responsible for the discrepancies between measurements and theoretical results for parallel flow. Experimental uncertainties, the adopted definition of the growth rate, and the transient initial evolution of the TS wave in vibrating-ribbon experiments probably cause the discrepancies. The effect of nonlinearity is consistent with previous weakly nonlinear theories. White nonlinear effects are small near branch I of the neutral curve, they are significant near branch II and delay or event prevent the decay of the wave.

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Mean and Unsteady Flow Reconstruction Using Data-Assimilation and Resolvent Analysis

AIAA Journal ◽

10.2514/1.j057889 ◽

2020 ◽

Vol 58 (2) ◽

pp. 575-588 ◽

Cited By ~ 1

Author(s):

Sean Symon ◽

Denis Sipp ◽

Peter J. Schmid ◽

Beverley J. McKeon

Keyword(s):

Data Assimilation ◽

Unsteady Flow ◽

Flow Reconstruction ◽

Using Data

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Optimal sensor placement for variational data assimilation of unsteady flows past a rotationally oscillating cylinder

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.313 ◽

2017 ◽

Vol 823 ◽

pp. 230-277 ◽

Cited By ~ 12

Author(s):

Vincent Mons ◽

Jean-Camille Chassaing ◽

Pierre Sagaut

Keyword(s):

Data Assimilation ◽

Sensor Placement ◽

Computational Cost ◽

Unsteady Flows ◽

Variational Data Assimilation ◽

Model Parameters ◽

Oscillating Cylinder ◽

Optimal Sensor Placement ◽

Initial Flow ◽

Placement Procedure

An optimal sensor placement procedure is proposed within the framework of variational data assimilation (DA) for unsteady flows, with the aim of maximizing the efficiency of the DA procedure. It is dedicated to the a priori design of a sensor network, and relies on a first-order adjoint approach. The proposed methodology first consists in identifying, via optimal control, the locations in the flow that have the greatest sensitivity with respect to a change in the initial condition, boundary conditions or model parameters. In a second step, sensors are placed at these locations for DA purposes. The use of this optimal sensor placement procedure does not require extra development in the case where a variational DA suite is available. The proposed methodology is applied to the reconstruction of unsteady bidimensional flows past a rotationally oscillating cylinder. More precisely, the possibilities of reconstructing the rotational speed of the cylinder and the initial flow, which here encompasses upstream conditions, from various types of observations are investigated via variational DA. Then, the observation optimization procedure is employed to identify optimal locations for placing velocity sensors downstream of the cylinder. Both reduction in the computational cost and improvement in the quality of the reconstructed flow are achieved through optimal sensor placement, encouraging the application of the proposed methodology to more complex and realistic flows.

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Study on linear and nonlinear bottom friction parameterizations for regional tidal models using data assimilation

Continental Shelf Research ◽

10.1016/j.csr.2010.12.011 ◽

2011 ◽

Vol 31 (6) ◽

pp. 555-573 ◽

Cited By ~ 25

Author(s):

Jicai Zhang ◽

Xianqing Lu ◽

Ping Wang ◽

Ya Ping Wang

Keyword(s):

Data Assimilation ◽

Bottom Friction ◽

Linear And Nonlinear ◽

Using Data

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Representation errors and retrievals in linear and nonlinear data assimilation

Quarterly Journal of the Royal Meteorological Society ◽

10.1002/qj.2464 ◽

2014 ◽

Vol 141 (690) ◽

pp. 1612-1623 ◽

Cited By ~ 26

Author(s):

Peter Jan van Leeuwen

Keyword(s):

Data Assimilation ◽

Linear And Nonlinear

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Assimilation of Nonlinear Observations with the Maximum Likelihood Ensemble Filter

10.5194/egusphere-egu21-10591 ◽

2021 ◽

Author(s):

Saori Nakashita ◽

Takeshi Enomoto

Keyword(s):

Maximum Likelihood ◽

Data Assimilation ◽

Cost Function ◽

Satellite Observations ◽

Observation Error ◽

Nonlinear Operators ◽

Linear And Nonlinear ◽

Nonlinear Observation ◽

The Cost ◽

Maximum Likelihood Ensemble Filter

Satellite observations have been a growing source for data assimilation in the operational numerical weather prediction. Remotely sensed observations require a nonlinear observation operator.&#160; Most ensemble-based data assimilation methods are formulated for tangent linear observation operators, which are often substituted by nonlinear observation operators. By contrast, the Maximum Likelihood Ensemble Filter (MLEF), which has features of both variational and ensemble approaches, is formulated for linear and nonlinear operators in an identical form and can use non-differentiable observation operators.&#160;In this study, we investigate the performance of MLEF and Ensemble Transform Kalman Filter (ETKF) with the tangent linear and nonlinear observation operators in assimilation experiments of nonlinear observations with a one-dimensional Burgers model.The ETKF analysis with the nonlinear operator diverges when the observation error is small due to unrealistically large increments associated with the high order observation terms. The filter divergence can be avoided by localization of the extent of observation influence, but the analysis error is still larger than that of MLEF. In contrast, MLEF is found to be more stable and accurate without localization owing to the minimization of the cost function. Notably, MLEF can make an accurate analysis solution even without covariance inflation, eliminating the labor of parameter adjustment.&#160;In addition, the smaller observation error is, or the stronger observation nonlinearity is, MLEF with the nonlinear operators can assimilate observations more effectively than MLEF with the tangent linear operators. This result indicates that MLEF can incorporate nonlinear effects and evaluate the observation term in the cost function appropriately. These encouraging results imply that MLEF is suitable for assimilation of satellite observations with high nonlinearity.

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Breakdown mechanisms and heat transfer overshoot in hypersonic zero pressure gradient boundary layers

Journal of Fluid Mechanics ◽

10.1017/jfm.2013.350 ◽

2013 ◽

Vol 730 ◽

pp. 491-532 ◽

Cited By ~ 44

Author(s):

Kenneth J. Franko ◽

Sanjiva K. Lele

Keyword(s):

Heat Transfer ◽

Turbulent Flow ◽

Plate Boundary ◽

Transitional Region ◽

Mean Flow ◽

Fundamental Resonance ◽

Nonlinear Development ◽

Second Mode ◽

Linear And Nonlinear ◽

Streamwise Streaks

AbstractA laminar Mach 6 flat plate boundary layer is perturbed using three different types of disturbances introduced through blowing and suction. The linear and nonlinear development and eventual breakdown to turbulence are investigated using direct numerical simulation. The three different transition mechanisms compared are first mode oblique breakdown, second mode oblique breakdown and second mode fundamental resonance. The focus of the present work is to compare the nonlinear development and breakdown to turbulence for the different transition mechanisms and explain the heat transfer overshoot observed in experiments. First mode oblique breakdown leads to the shortest transition length and a clear peak in wall heat transfer in the transitional region. For all three transition mechanisms, the development of streamwise streaks precedes the breakdown to fully turbulent flow. The modal linear and nonlinear development are analysed including the breakdown of the streaks. The effect of wall cooling is investigated for second mode fundamental resonance and no qualitative differences in the nonlinear processes are observed. Finally, the development towards fully turbulent flow including mean flow, turbulent spectra, and turbulent fluctuations is shown and the first mode oblique breakdown simulation shows the furthest development towards a fully turbulent flow.

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