Calculation of average characteristics of water environment stratification
A.E. Pogrebnoy |
Marine Hydrophysical Institute, Russian Academy of Sciences, Sevastopol, Russian Federation |
E-mail: pogrebok57@mail.ru |
Abstract
Problems arising at applying traditional procedure for averaging hydrophysical characteristics’ vertical profiles are analyzed. The conclusion on necessity of taking into account vertical displacements of fluid elements is drawn. For this purpose, the Lagrangian invariants, (particularly, the averaged background distribution of the density field) are proposed to be applied. It permits to calculate the averaged depths of the vertical structure various elements. If the fluid is stratified the surfaces of constant density is called isopycnal. They nowhere intersect and divide the fluid into the layers. In the ideal fluid (when the processes of diffusion/exchange are absent), its elements never cross the isopycnal surfaces. Note that in real ocean the exchange processes are always present. As a result the fluid element density can change; thereupon it leaves its isopycnal level. Therefore the in situ density is not the true Lagrangian invariant. The average value for each element corresponding to the average depth of this element is used as an average vertical distribution of a sought parameter. The means for increasing reliability of the stratification elements’ identification and applicability of the proposed method are discussed. The present method developed based on the thermodynamics general principles can also be applied for averaging the atmosphere parameters and the laboratory experiments. Besides, use of density as the Lagrangian invariant is not obligatory. The basic advantage of such a choice is conditioned by its monotonous dependence on depth. As well as for the ocean, in case there are uniformities of the parameter vertical gradient which permits to identify the stratification elements, additional background averaging can be used. The averaging vertical scale has to exceed the characteristic scales of small heterogeneities (for example, high-gradient streaks), but it is to be smaller than the background heterogeneities’ scales (mixed layers’ thicknesses). In case the denoted gradient heterogeneities are absent additional averaging is not required.
Keywords
substantial derivative, Lagrangian invariant, stepped structure.
DOI: 10.22449/1573-160X-2015-3-72-77