Barotropic

Blackadar, A. K., and Teimekes, H. (1968). Asymptotic similarity in neutral barotropic planetary boundary layers. J. Atmos. Sci. 25, 1015-1020. 

Note 2 Analogous changes can also occur on varying the pressure at constant temperature in which case the mesophase may be termed barotropic mesophase. 

Effect of Pressure on Micelles. While temperature studies of the phase transitions of bilayers and micelles have been performed for some time now, the utilization of pressure as a variable is a more recent development. Variation in temperature of a colloidal aggregate such as a bilayer causes simultaneous changes in thermal energy and volume, whereas isothermal variation in pressure (up to 50 kbar) yields spectroscopic changes due only to volume effects. A review of high pressure vibrational spectroscopy of phospholipid bilayers has recently appeared (74). in which the surprisingly rich barotropic phase behavior of these compounds is explored in detail. 

Vertical transport and gravitational circulation in estuaries are influenced by both stratification and turbulent mixing, which result from the destabilizing forces of tides and/or wind processes. Under highly stratified conditions, two-layered flow is largely determined by the interaction of baroclinic and barotropic forcing. 

Barotropic a condition in a water mass whereby the surfaces of constant pressure are parallel to the surfaces of constant density in a state of barotropic stratification, no potential energy is available for conversion into kinetic energy. 

The various oxidation-reduction reactions in the Black Sea occur in narrow layers of water of similar density and form features that are characteristic of the hydrochemical structure (e.g., maxima and minima, onset points). The position of these features in the density field is very stable [17-20] and it is possible to name this feature chemotropic [21] the connection between the water density and properties of the chemical structure (by analogy with barotropic—the connection between density and pressure). In Table 1 we summarize the correspondence of the key features of the chemical structure with the density values. These values have served as a benchmark for subsequent cruises to evaluate the stability of the characteristic features. 

It is a precondition for both operations that the density of the liquid pumped onto the top of the column is higher than the density of the supercritical gas. The difference should be large enough in order to give a proper phase separation. If, at very high pressures, the gas density surpasses the liquid density a so-called barotropic phase inversion can be observed at which the liquid swims on the dense gas. 

The barotropic flow in a channel of small width W and shallow depth H is treated as propagation of long waves in several text books of fluid dynamics, for example. Gill (1982). The pressure is assumed to satisfy the hydrostatic equation... 

The measured barotropic velocity projected onto the channel axis at the Darss Sill MARNET station reveals a rather Gaussian distribution, while the distributions of both the sea level difference between Viken and Skanoer and the transport derived according to Equation 2.14 differ significantly from the Gaussian distribution. However, the minimum of the wave-controlled and the frictional-controlled transports depicts a quite reasonable Gaussian distribution. 

FIGURE 2.4 Probability distributions of the barotropic current component at the Darss Sill toward 68 T (upper left panel) of the sea level difference between the Kattegat (Viken) and the northwestern par t of the Arkona Basin (Skanoer) (upper right panel), the frictional controlled transport proportional to the square root of the sea level difference (lower left panel), and the minimum of the wave and the frictional controlled transport. 

Quantifying the Stochastic Salt Exchange Associated with the Barotropic Water Exchange... 

Since the details of the advection of saltwater and brackish water due to the oscillating barotropic flow in the Belt Sea are hard to describe analytically and are strongly nonlinear, we consider the advection of salt by the barotropic flow as a stochastic salt flow igeit, which is proportional to the difference between the surface salinity at the Kattegat front and the salinity of the brackish surface water of the Arkona Basin Sb... 

From the above equation it follows that the surface salinity of the Baltic Sea is controlled by the ratio between the freshwater surplus and the sum of the stochastic salt fluxes normalized by the salinity difference between the Kattegat and the Arkona Sea surface water, see Fig. 2.6. The turbulent salt diffusivity k is a function of the geometry of the Belt Sea in terms of the length of the channel and the sill depth as well as of the spectrum of wind fluctuations determining the sea level difference between the Kattegat and the Arkona Sea and subsequently the barotropic current fluctuations in the Belt Sea. 

Seiches are transient motions that may constitute the transition to or from the dynamic balance between the barotropic pressure gradient and vertical friction in the water column denoted as wind stau... 

The arbitrary longshore shape of the wave described by G x — ci) remains unchanged while propagating along the coast and can be of a localized or a sinusoidal pattern. The Kelvin wave is trapped in a coastal wave guide along the coast and is not felt offshore of this guide with the width determined by the Rossby radius. Barotropic Kelvin waves have a wide Rossby radius of the order of = 0(100 km) and baroclinic waves a Rossby radius of the order of R = 0(5 km) in the Baltic Sea. 

Moreover, the Kelvin wave can control the water exchange between two basins connected by a channel. The basic physics of this process can be reduced to the Rossby adjustment process in a channel of uniform depth and uniform width. This problem was considered theoretically by Gill (1976) as an initial problem with a steplike sea level distribution in the channel. The results are similar for abarotropic and a baroclinic two-layer flow however, the sea level elevation must be replaced by the elevation of the interface and the barotropic long wave phase velocity by the baroclinic phase velocity, which is much smaller than the barotropic velocity. This implies that the baroclinic Rossby radius is more than one order of magnitude smaller than the barotropic radius. 

When the shelf scale is comparable with the internal Rossby radius, wave motions normal to the shelf induce vertical motions due to the inclined bottom that generate internal pressure gradients. Therefore, a separation between barotropic and baroclinic modes is not possible anymore and these modes are denoted as mixed or hybrid modes that have been called coastally trapped waves. To evaluate their dispersion relations with respect to frequency and longshore wave number and their modal structure in the vertical plain normal to the coast, a two-dimensional eigenvalue problem must be solved numerically (Brink, 1991). The nodal lines of the velocity modes of these hybrid modes are inclined with respect to the sea surface in contrast to the baroclinic modes in case of a flat-bottomed ocean. 

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