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Redekopp, L. G.

Publications and source records attributed to Redekopp, L. G..

17 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

A numerical study of bifurcations in a barotropic shear flow

In the last few years, more and more evidence has emerged suggesting that transition to turbulence may be viewed as a succession of bifurcations to deterministic chaos. Most experimental and numerical observations have been restricted to Rayleigh-Benard convection and Taylor-Couette flow between concentric cylinders. An attempt is made to accurately describe the bifurcation sequence leading to chaos in a 2-D temporal free shear layer on the beta-plane. The beta-plane is a locally Cartesian reduction of the equations describing the dynamicss of a shallow layer of fluid on a rotating spherical planet. It is a valid model for large scale flows of interest in meteorology and oceanography.

Huerre, P.↗
NASA NTRS1982

Initial conditions and Korteweg-de Vries solitons

The effects of rectangular initial data on the evolution of solitons governed by the Korteweg-de Vries equation is studied. Both isolated and separated disturbances are considered, providing some general insight into how the nature of the initial condition influences the appearance of solitons in the asymptotic state. The analytic approach is based on the inverse scattering transform which relates the initial condition to Schroedinger's equation. The results are used to model the initial shallow-water disturbances, and the results can be summarized by stating that the number of evolved solitons depends on the strength of each rectangular disturbance, the relative amplitudes of the rectangular disturbances, and the relative proximity of the disturbances.

Weidman, P. D.↗
NASA NTRS1980

Possible fluid dynamical interpretation of some reported features in the Jovian atmosphere

A fluid dynamical interpretation is presented of the two major types of disturbance found in the southern hemisphere of Jupiter by the Voyager 1 imaging data. The observed features always occur together, and consist of a compact elliptically shaped formation having an anticyclonic flow which is poleward of a pair of more elongated cyclonic structures, as in the Great Red Spot and the white ovals. It is noted that the anticyclonic features at 41 deg S may be described by the cnoidal wave solutions to the appropriate nonlinear evolution equation, and that flow patterns derived in the vicinity of the Great Red Spot and white ovals are strikingly similar to those obtained for the flow around a solitary wave of the type than can exist in a zonal flow such as that found in the Jupiter atmosphere. Results of computations in terms of solitary wave theory of flow fields in the atmospheric structure and zonal velocity profiles determined from Voyager infrared spectroscopy and radiometry data are then presented which show that the pattern must be a singular solitary wave mode, the east-west structure of which is best described by the Korteweg-de-Vries equation

Maxworthy, T.↗
NASA NTRS1980

Similarity solutions of some two-space-dimensional nonlinear wave evolution equations

Similarity reductions of the two-space-dimensional versions of the Korteweg-de Vries, modified Korteweg-de Vries, Benjamin-Davis-Ono, and nonlinear Schroedinger equations are presented, and some solutions of the reduced equations are discussed. Exact dispersive solutions of the two-dimensional Korteweg-de Vries equation are obtained, and the similarity solution of this equation is shown to be reducible to the second Painleve transcendent.

Redekopp, L. G.↗
NASA NTRS1980

Long nonlinear waves in stratified shear flows

The propagation of finite-amplitude internal waves in a shear flow is considered for wavelengths that are long compared to the shear-layer thickness. Both singular and regular modes are investigated, and the equation governing the amplitude evolution is derived. The theory is generalized to allow for a radiation condition when the region outside the stratified shear layer is unbounded and weakly stratified. In this case, the evolution equation contains a damping term describing energy loss by radiation which can be used to estimate the persistence of solitary waves or nonlinear wave packets in realistic environments. A continuous three-layer model is studied in detail and closed-form expressions are obtained for the phase speed and the coefficients of the nonlinear and dispersive terms in the amplitude equation as a function of Richardson number.

Maslowe, S. A.↗
NASA NTRS1980

Radiation damping of long, finite-amplitude internal waves

Numerical solutions of a damped, nonlinear wave equation are presented. The equation describes the propagation of waves in a narrow thermocline or inversion which lose energy by exciting internal waves in the weakly stratified ambient environment. The results provide estimates for the persistence of finite-amplitude internal waves propagating in a thermoclinic waveguide.

Pereira, N. R.↗
NASA NTRS1980

Solitary Rossby waves in the presence of vertical shear

The effects of vertical shear on regular neutral mode Rossby solitons driven by a horizontal shear are investigated in light of the proposition that certain features in the Jupiter atmosphere may be explained by solitary Rossby waves. Consideration is given to a two-layer quasi-geostrophic model in which the motion in each layer consists of a different zonal shear flow, with vertical shear concentrated at the interface between the layers. In the case of a strong vertical shear, it is found that only a very restricted set of flows will admit Rossby neutral model solitons. For the more realistic case of a weak vertical shear, results indicate similar, but latitudinally shifted, wave patterns in each layer. It is noted that no such slant has yet been detected in the Great Red Spot.

Weidman, P. D.↗
NASA NTRS1979

Solitary waves in stratified shear flows

An analysis is described of long, finite-amplitude internal waves in a stratified shear flow. Both regular and singular modes are considered with a nonlinear critical layer employed in the latter case. A three-layer model is used to develop the theory and closed-form expressions are obtained relating the phase speed to the Richardson number, the latter quantity being taken as O(1). The amplitude evolution equation is found to be either the Korteweg-de Vries equation or the Benjamin-Davis-Ono equation depending upon the distance of the more remote boundary from the edge of the shear layer.

Maslowe, S. A.↗
NASA NTRS1978

On the development of packets of surface gravity waves moving over an uneven bottom

The object of study is the evolution of packets of gravity waves moving over variable depth, in particular, the transformation of packets moving into a shelf of increased or decreased depth. The variable-coefficient nonlinear Schroedinger equation with inhomogeneous term is derived for gravity waves moving over an uneven bottom. A solution for an envelope-hole soliton moving over variable depth is obtained when the amplitude-length ratio of the soliton is small. For the shelf problem, it is shown that the first soliton on the shelf will be the one with smallest depression, and the last will have greatest depression. This is in contrast to Korteweg-de Vries soliton fission.

Djordjevic, V. D.↗
NASA NTRS1978

Solitary Rossby waves in zonal shear flows and their interactions

Interactions of long-wave solitons propagating in shear flows are described by a coupled pair of Korteweg-de Vries equations. The basic equation of motion for the analysis is the quasi-geostrophic forecast equation, and the interaction of two wave modes is studied. The solution for mode 1-mode 2 interaction of solitary waves in an asymmetric shear flow of a barotropic atmosphere with divergence is constructed. Streamline patterns for certain flows are obtained. An unsteady solitary wave solution for a modified Korteweg-de Vries equation is derived.

Redekopp, L. G.↗
NASA NTRS1978

On the production and interaction of planetary solitary waves - Applications to the Jovian atmosphere

Further evidence is presented that strengthens the case for the interpretation of many features in the Jovian atmosphere as solitary Rossby waves (solitons). These include: a mechanism whereby such waves can evolve from the instability of the basic shear flows; further interpretation of the interaction between observed features, and comparison with calculations of the interaction between planetary solitons of a restricted class; and calculations of soliton morphology for a type of shear flow other than the type considered originally by Maxworthy and Redekopp (1976).

Maxworthy, T.↗
NASA NTRS1977

On the theory of solitary Rossby waves

The evolution of long, finite amplitude Rossby waves in a horizontally sheared zonal current is studied. The wave evolution is described by the Korteweg-de Vries equation or the modified Korteweg-de Vries equation depending on the atmospheric stratification. In either case, the cross-stream modal structure of these waves is given by the long-wave limit of the neutral eigensolutions of the barotropic stability equation. Both non-singular and singular eigensolutions are considered and the appropriate analysis is developed to yield a uniformly valid description of the motion in the critical-layer region where the wave speed matches the flow velocity. The analysis demonstrates that coherent, propagating, eddy structures can exist in stable shear flows and that these eddies have peculiar interaction properties quite distinct from the traditional views of turbulent motion.

Redekopp, L. G.↗
NASA NTRS1977

On two-dimensional packets of capillary-gravity waves

The motion of a two-dimensional packet of capillary-gravity waves on water of finite depth is studied. The evolution of a packet is described by two partial differential equations: the nonlinear Schroedinger equation with a forcing term and a linear equation, which is of either elliptic or hyperbolic type depending on whether the group velocity of the capillary-gravity wave is less than or greater than the velocity of long gravity waves. These equations are used to examine the stability of the Stokes capillary-gravity wave train. The analysis reveals the existence of a resonant interaction between a capillary-gravity wave and a long gravity wave. The interaction requires that the liquid depth be small in comparison with the wavelength of the (long) gravity waves and the evolution equations describing the dynamics of this interaction are derived.

Djordjevic, V. D.↗
NASA NTRS1976

A solitary wave theory of the Great Red Spot and other observed features in the Jovian atmosphere

It is shown that solitary waves in a planetary zonal shear have a shape and flow field that are virtually identical to those observed around the Red Spot and numerous other features that have been seen in the Jovian atmosphere. It is suggested that the theoretically calculated interaction between solitary waves has many characteristics in common with the observed interactions between these same Jovian features, and available atmospheric models are shown to be consistent with the very restrictive requirements of the theory.

Maxworthy, T.↗
NASA NTRS1976

New theory of the Great Red Spot from solitary waves in the Jovian atmosphere

It is shown that many characteristics of the Great Red Spot (GRS) and numerous other features that have been observed on Jupiter can be explained by solitary waves on a horizontally sheared zonal flow in a rotating, stratified atmosphere. Streamline patterns for waves corresponding to combined depression-elevation solitary waves (D-E solitrons) show a strong resemblence to the flow around the GRS. The morphology and flow pattern of the South Tropical Disturbance indicate that it was a D solitron. Numerous spot-like features situated in regions between cloud bands where horizontal shear forces might be expected have the morphology of E solitrons. Restrictions placed on the atmospheric parameters by the model are consistent with available models and observations.

Maxworthy, T.↗
NASA NTRS1975

On upstream blocking in a viscous diffusive stratified flow

The effect of diffusion of specie upon the flow about a transverse flat plate moving horizontally in a viscous stratified medium is considered. Asymptotic expansions are used to define a parameter regime where a viscous-diffusive-buoyancy balance is dominant. The solution, expressed in terms of an inverse Fourier transform, is numerically integrated. The results show that, as in the non-diffusive problem, a region of closed streamlines exists ahead of the body. However, unlike the case where diffusion is neglected, the density field within this recirculating region is uniquely determined and found to be statically stable. It is also found that varying the relative amount of diffusion affects not only the density distribution, but the velocity profile as well, indicating a strong coupling between the vorticity and specie equation.

Koop, C. G.↗