arXiv subjects

Mark Schlutow

Publications and source records attributed to Mark Schlutow.

9 recordsLinked to original sources

arXiv2025

The Boundary Layer Dispersion and Footprint Model: A fast numerical solver of the Eulerian steady-state advection-diffusion equation

Understanding how greenhouse gases and pollutants move through the atmosphere is essential for predicting and mitigating their effects. We present a novel atmospheric dispersion and footprint model: the Boundary Layer Dispersion and Footprint Model (BLDFM), which solves the three-dimensional steady-state advection-diffusion equation in Eulerian form using a numerical approach based on the Fourier method, the linear shooting method and the exponential integrator method. The model is designed to be flexible and can be used for a wide range of applications, including climate impact studies, industrial emissions monitoring, agricultural planning and spatial flux attribution. We validate the model using an analytical test case. The numerical results show excellent agreement with the analytical solution. We also compare the model with the Kormann and Meixner (Boundary-Layer Meteorology, 2001) footprint model (FKM), and the results show overall good agreement but some differences in the fetch of the footprints, which are attributed to the neglect of streamwise turbulent mixing in the FKM model. Our results demonstrate the potential of the BLDFM model as a useful tool for atmospheric scientists, biogeochemists, ecologists, and engineers.

physics.flu-dyn↗

arXiv2023

Instability cascade of strongly nonlinear gravity waves in a vertically sheared atmosphere

Although internal gravity waves are generally recognized as an important mechanism to distribute energy through the atmosphere, their dynamics near the instability is only partially understood to date. Many types of instabilities, notably the classical modulational instability, a novel point spectrum modulational instability, the triadic resonant instability, the shear instability and the static instability have been studied mostly in idealized settings and mostly isolated from one another. Here, we identify the instability cascade of a quasi one-dimensional and stationary internal gravity wave modulated by a vertically sheared mean flow. We find indicators of various interdependent instability mechanisms which partly compete for dominance and partly follow one another. A key finding is that the particular dynamics of the local cascade depends on the sign of the background shear.

physics.flu-dyn↗

arXiv2023

An unstable mode of the stratified atmosphere under the non-traditional Coriolis acceleration

The traditional approximation neglects the cosine components of the Coriolis acceleration, and this approximation has been widely used in the study of geophysical phenomena. However, the justification of the traditional approximation is questionable under a few circumstances. In particular, dynamics with substantial vertical velocities or geophysical phenomena in the tropics have non-negligible cosine Coriolis terms. Such cases warrant investigations with the non-traditional setting, i.e., the full Coriolis acceleration. In this manuscript, we study the effect of the non-traditional setting on an isothermal, hydrostatic and compressible atmosphere assuming a meridionally homogeneous flow. Employing linear stability analysis, we show that, given appropriate boundary conditions, i.e., a bottom boundary condition that allows for a vertical energy flux and non-reflecting boundary at the top, the atmosphere at rest becomes prone to a novel unstable mode. The validity of assuming a meridionally homogeneous flow is investigated via scale analysis. Numerical experiments were conducted, and Rayleigh damping was used as a numerical approximation for the non-reflecting top boundary. Our three main results are as follows. 1) Experiments involving the full Coriolis terms exhibit an exponentially growing instability, yet experiments subjected to the traditional approximation remain stable. 2) The experimental instability growth rate is close to the theoretical value. 3) A perturbed version of the unstable mode arises even under sub-optimal bottom boundary conditions. Finally, we conclude our study by discussing the limitations, implications, and remaining open questions. Specifically, the influence on numerical deep-atmosphere models and possible physical interpretations of the unstable mode are discussed.

physics.flu-dyn↗

arXiv2021

Waves in the gas centrifuge: asymptotic theory and similarities with the atmosphere

We study the stratified gas in a rapidly rotating centrifuge as a model for the Earth's atmosphere. Based on methods of perturbation theory, it is shown that in certain regimes, internal waves in the gas centrifuge have the same dispersion relation to leading order as their atmospheric siblings. Assuming an air filled centrifuge with a radius of circa 50 cm, the optimal rotational frequency for realistic atmosphere-like waves is around 10 000 rounds per minute. Using gases of lower heat capacities at constant pressure, like xenon, the rotational frequencies can be even halved to obtain the same results. Similar to the atmosphere, it is feasible in the gas centrifuge to generate a clear scale separation of wave frequencies and therefore phase speeds between acoustic waves and internal waves. In addition to the centrifugal force, the Coriolis force acts in the same plane. However, its influence on axially homogeneous internal waves appears only as a higher-order correction. We conclude that the gas centrifuge provides an unprecedented opportunity to investigate atmospheric internal waves experimentally with a compressible working fluid.

physics.flu-dyn↗

arXiv2020

On strongly nonlinear gravity waves in a vertically sheared atmosphere, Part I: Spectral stability of the refracted wave

We investigate strongly nonlinear stationary gravity waves which experience refraction due to a thin vertical shear layer of horizontal background wind. The velocity amplitude of the waves is of the same order of magnitude as the background flow and hence the self-induced mean flow alters the modulation properties to leading order. In this theoretical study, we show that the stability of such a refracted wave depends on the classical modulation stability criterion for each individual layer, above and below the shearing. Additionally, the stability is conditioned by novel instability criteria providing bounds on the mean-flow horizontal wind and the amplitude of the wave. A necessary condition for instability is that the mean-flow horizontal wind in the upper layer is stronger than the wind in the lower layer.

physics.flu-dyn↗

arXiv2020

Generalized modulation theory for strongly nonlinear gravity waves in a compressible atmosphere

This study investigates nonlinear gravity waves in the compressible atmosphere from the Earth's surface to the deep atmosphere. These waves are effectively described by Grimshaw's dissipative modulation equations which provide the basis for finding stationary solutions such as mountain lee waves and testing their stability in an analytic fashion. Assuming energetically consistent boundary and far-field conditions, that is no energy flux through the surface, free-slip boundary, and finite total energy, general wave solutions are derived and illustrated in terms of realistic background fields. These assumptions also imply that the wave-Reynolds number must become less than unity above a certain height. The modulational stability of admissible, both non-hydrostatic and hydrostatic, waves is examined. It turns out that, when accounting for the self-induced mean flow, the wave-Froude number has a resonance condition. If it becomes $1/\sqrt{2}$, then the wave destabilizes due to perturbations from the essential spectrum of the linearized modulation equations. However, if the horizontal wavelength is large enough, waves overturn before they can reach the modulational stability condition.

physics.ao-ph↗

arXiv2019

Modulational stability of nonlinear saturated gravity waves

Stationary gravity waves, such as mountain lee waves, are effectively described by Grimshaw's dissipative modulation equations even in high altitudes where they become nonlinear due to their large amplitudes. In this theoretical study, a wave-Reynolds number is introduced to characterize general solutions to these modulation equations. This non-dimensional number relates the vertical linear group velocity with wavenumber, pressure scale height and kinematic molecular/eddy viscosity. It is demonstrated by analytic and numerical methods that Lindzen-type waves in the saturation region, i.e. where the wave-Reynolds number is of order unity, destabilize by transient perturbations. It is proposed that this mechanism may be a generator for secondary waves due to direct wave-mean-flow interaction. By assumption the primary waves are exactly such that altitudinal amplitude growth and viscous damping are balanced and by that the amplitude is maximized. Implications of these results on the relation between mean-flow acceleration and wave breaking heights are discussed.

physics.ao-ph↗

arXiv2018

Reflection and transmission of gravity waves at non-uniform stratification layers

The present study focuses on the interaction of gravity waves in the atmosphere with the tropopause. As the vertical extent of the latter is small compared to the density scale height, wave propagation is described by the Taylor-Goldstein equation as derived from the linearised Boussinesq approximation. Of particular interest in the construction of gravity wave parameterisations for the upper atmosphere are the transmission and reflection properties of the tropopause as these determine the upward fluxes of energy and momentum carried by internal waves. A method is presented that decomposes internal waves explicitly into upward and downward propagating contributions, thus giving direct access to transmission and reflection coefficients of finite regions of non-uniform stratification in a stationary atmosphere. The scheme utilizes a piecewise constant approximation for the background stratification and matches up- and downward propagating plane wave solutions in each layer through physically meaningful coupling conditions. As a result, transmission and reflection coefficients follow immediately.

physics.ao-ph↗

arXiv2018

Spectral stability of nonlinear gravity waves in the atmosphere

We apply spectral stability theory to investigate nonlinear gravity waves in the atmosphere. These waves are determined by modulation equations that result from Wentzel-Kramers-Brillouin theory. First, we establish that plane waves, which represent exact solutions to the inviscid Boussinesq equations, are spectrally stable with respect to their nonlinear modulation equations under the same conditions as what is known as modulational stability from weakly nonlinear theory. In contrast to Boussinesq, the pseudo-incompressible regime does account for the altitudinal varying background density. Second, we show for the first time that upward-traveling wave fronts solving the inviscid modulation equations, that compare to pseudo-incompressible theory, are unconditionally unstable. Both inviscid regimes turn out to be ill-posed as the spectra allow for arbitrarily large instability growth rates. Third, a regularization is found by including dissipative effects. The corresponding traveling wave solutions have localized amplitude and blow up unconditionally by embedded eigenvalue instabilities but the instability growth rate is bounded from above. Additionally, all three types of nonlinear modulation equations are solved numerically to further investigate and illustrate the nature of the analytic stability results.

physics.flu-dyn↗