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We use a discretized approximation to simulate temporal fluctuations of stochastically excited en... more We use a discretized approximation to simulate temporal fluctuations of stochastically excited energy modes in channel flows. We focus on a broad band spectrum and apply two colored noise mechanisms with high and lowpass characteristics. This is a realistic model of uncertainty analysis for industrial applications of jet turbulence problems in many airplane constructions. The non-normality of the dynamical system yields transient growth. This was discovered first for not amplified flows and it was found to be a typical three-dimensional (3D) feature. In the presence of white noise the growth is higher and the significance of 3D characteristics prevails. We extend the theory to the more realistic issue of colored noise with a broad band spectrum. We find that the mean value of the amplified energy grows with an intensity that reaches up to the fourth power of the Reynolds number. We calculate the average energy and its maximum value in a wide regime of stream and spanwise wavenumbers and notice the dominance of streamwise roller structures. In the case of a high-pass spectrum we detect an approximate equivalence of maximal average energy and least damped stability modes. The latter are linked to the peak of the spectrum, and we may reconcile in part the concept of non-normal growth with notion of the classical theory of maximally amplified (or least damped) modes. This means that in a broad-banded system we arrive at a synthesis of the formerly contradicting theories that attain now a wider sense and a scope of their respective theory.
Books by Peter Plaschko
Papers by Peter Plaschko
Höhere mathematische Methoden für Ingenieure und Physiker, 1989
Höhere mathematische Methoden für Ingenieure und Physiker, 1989
Höhere mathematische Methoden für Ingenieure und Physiker, 1989
Höhere mathematische Methoden für Ingenieure und Physiker, 1989
Höhere mathematische Methoden für Ingenieure und Physiker, 1989
Nichtlineare Dynamik, Bifurkation und Chaotische Systeme, 1995
Nichtlineare Dynamik, Bifurkation und Chaotische Systeme, 1995
Nichtlineare Dynamik, Bifurkation und Chaotische Systeme, 1995
Höhere mathematische Methoden für Ingenieure und Physiker, 1989
Zeitschrift für angewandte Mathematik und Physik, 1998
ABSTRACT
Physics of Fluids, 1984
ABSTRACT
Physics of Fluids, 1978
The spatial stability of jets in homogeneous parallel magnetic fields in analyzed. It is shown th... more The spatial stability of jets in homogeneous parallel magnetic fields in analyzed. It is shown that the magnetic stabilization is about proportional to the inverse of the profile gradient and that three-dimensional modes may become more unstable than their two-dimensional counterparts.
Physics of Fluids, 1981
ABSTRACT
Physics of Fluids, 1983
ABSTRACT
Acta Mechanica, Feb 28, 1993
In this paper we study the stability and the bifurcation of the equilibrium solution of a control... more In this paper we study the stability and the bifurcation of the equilibrium solution of a controlled Burgers equation; an integral term, representing a non-local behavior, has been added to the normal form of the equation describing flow through porous media. We find that a supercritical bifurcation from the rest solution occurs if the viscosity is reduced below a critical value. This value is calculated as a function of the porosity coefficient and the corresponding bifurcation solution is derived using perturbation forms up to fourth order.
Http Dx Doi Org 10 1080 0892702031000152163, May 17, 2006
The process is characterized by three disparate lengths: the solidification length, the wave leng... more The process is characterized by three disparate lengths: the solidification length, the wave length and the depth of the slab. We use an asymptotic expansion based on shallow water equations for long waves. The leading order equations govern disturbances of a quasi-parallel flow. Two different types of distur-bances are found: a weakly damped stable mode that runs downstream and a strongly damped perturbation traveling upstream. The downstream moving mode is disturbance is strongly frequency-dependent. There is a regime of parameters where the perturbations of the displacement grow. The pre-dictions are in qualitative agreement with the experi-mental observation of the wave lengths found in the completely solidified material.
We use a discretized approximation to simulate temporal fluctuations of stochastically excited en... more We use a discretized approximation to simulate temporal fluctuations of stochastically excited energy modes in channel flows. We focus on a broad band spectrum and apply two colored noise mechanisms with high and lowpass characteristics. This is a realistic model of uncertainty analysis for industrial applications of jet turbulence problems in many airplane constructions. The non-normality of the dynamical system yields transient growth. This was discovered first for not amplified flows and it was found to be a typical three-dimensional (3D) feature. In the presence of white noise the growth is higher and the significance of 3D characteristics prevails. We extend the theory to the more realistic issue of colored noise with a broad band spectrum. We find that the mean value of the amplified energy grows with an intensity that reaches up to the fourth power of the Reynolds number. We calculate the average energy and its maximum value in a wide regime of stream and spanwise wavenumbers and notice the dominance of streamwise roller structures. In the case of a high-pass spectrum we detect an approximate equivalence of maximal average energy and least damped stability modes. The latter are linked to the peak of the spectrum, and we may reconcile in part the concept of non-normal growth with notion of the classical theory of maximally amplified (or least damped) modes. This means that in a broad-banded system we arrive at a synthesis of the formerly contradicting theories that attain now a wider sense and a scope of their respective theory.
Höhere mathematische Methoden für Ingenieure und Physiker, 1989
Höhere mathematische Methoden für Ingenieure und Physiker, 1989
Höhere mathematische Methoden für Ingenieure und Physiker, 1989
Höhere mathematische Methoden für Ingenieure und Physiker, 1989
Höhere mathematische Methoden für Ingenieure und Physiker, 1989
Nichtlineare Dynamik, Bifurkation und Chaotische Systeme, 1995
Nichtlineare Dynamik, Bifurkation und Chaotische Systeme, 1995
Nichtlineare Dynamik, Bifurkation und Chaotische Systeme, 1995
Höhere mathematische Methoden für Ingenieure und Physiker, 1989
Zeitschrift für angewandte Mathematik und Physik, 1998
ABSTRACT
Physics of Fluids, 1984
ABSTRACT
Physics of Fluids, 1978
The spatial stability of jets in homogeneous parallel magnetic fields in analyzed. It is shown th... more The spatial stability of jets in homogeneous parallel magnetic fields in analyzed. It is shown that the magnetic stabilization is about proportional to the inverse of the profile gradient and that three-dimensional modes may become more unstable than their two-dimensional counterparts.
Physics of Fluids, 1981
ABSTRACT
Physics of Fluids, 1983
ABSTRACT
Acta Mechanica, Feb 28, 1993
In this paper we study the stability and the bifurcation of the equilibrium solution of a control... more In this paper we study the stability and the bifurcation of the equilibrium solution of a controlled Burgers equation; an integral term, representing a non-local behavior, has been added to the normal form of the equation describing flow through porous media. We find that a supercritical bifurcation from the rest solution occurs if the viscosity is reduced below a critical value. This value is calculated as a function of the porosity coefficient and the corresponding bifurcation solution is derived using perturbation forms up to fourth order.
Http Dx Doi Org 10 1080 0892702031000152163, May 17, 2006
The process is characterized by three disparate lengths: the solidification length, the wave leng... more The process is characterized by three disparate lengths: the solidification length, the wave length and the depth of the slab. We use an asymptotic expansion based on shallow water equations for long waves. The leading order equations govern disturbances of a quasi-parallel flow. Two different types of distur-bances are found: a weakly damped stable mode that runs downstream and a strongly damped perturbation traveling upstream. The downstream moving mode is disturbance is strongly frequency-dependent. There is a regime of parameters where the perturbations of the displacement grow. The pre-dictions are in qualitative agreement with the experi-mental observation of the wave lengths found in the completely solidified material.
Archive of Applied Mechanics, Oct 1, 2000
ABSTRACT