Matches in SemOpenAlex for { <https://semopenalex.org/work/W2145046971> ?p ?o ?g. }
Showing items 1 to 66 of
66
with 100 items per page.
- W2145046971 endingPage "49" @default.
- W2145046971 startingPage "31" @default.
- W2145046971 abstract "An analysis is constructed in order to estimate the dispersion relation for internal waves trapped in a layer and propagating linearly in a fluid of infinite depth with a rigid surface. The main interest is in predicting the structure of internal wave wakes, but the results are applicable to any internal waves. It is demonstrated that, in general 1/ c p = 1/ C p O + k /ω max + ∈( k ) where c p is the wave phase speed for a particular mode, C p O is the phase speed at k = 0, ω max is the maximum possible wave angular frequency and ω max ≤ N max where N max is the maximum buoyancy frequency. Also, ∈(0) = 0, ∈( k ) = o ( k ) for k large, and is bounded for finite k. In particular, when ∈( k ) can be neglected, the dispersion relation for a lowest mode wave is approximately 1/ c p ≈ (∫ ∞ 0 N 2 (y)ydy) -½ + k /ω max . The eigenvalue problem is analysed for a class of buoyancy frequency squared functions N 2 ( x ) which is taken to be a class of realvalued functions of a real variable x where O ≤ x ∞ such that N 2 ( x ) = O (e -β x ) as x → ∞ and 1/β is an arbitrary length scale. It is demonstrated that N 2 ( x ) can be represented by a power series in e -β x . The eigenfunction equation is constructed for such a function and it is shown that there are two cases of the equation which have solutions in terms of known functions (Bessel functions and confluent hypergeometric functions). For these two cases it is shown that ∈( k ) can be neglected and that, in addition, ω max = N max . More generally, it is demonstrated that when k → ∞ it is possible to approximate the equation uniformly in such a way that it can be compared with the confluent hypergeometric equation. The eigenvalues are then, approximately, zeros of the Whittaker functions. The main result which follows from this approach is that if N 2 ( x ) is O (e -β x ) as x → ∞ and has a maximum value N 2 max then a sufficient condition for 1/ c p ∼ k / N max to hold for large k for the lowest mode is that N 2 ( t )/ t is convex for O ≤ t ≤ 1 where t = e -β x ." @default.
- W2145046971 created "2016-06-24" @default.
- W2145046971 creator A5043345617 @default.
- W2145046971 date "1993-07-01" @default.
- W2145046971 modified "2023-09-27" @default.
- W2145046971 title "On the dispersion relation for trapped internal waves" @default.
- W2145046971 cites W4237082351 @default.
- W2145046971 doi "https://doi.org/10.1017/s0022112093003659" @default.
- W2145046971 hasPublicationYear "1993" @default.
- W2145046971 type Work @default.
- W2145046971 sameAs 2145046971 @default.
- W2145046971 citedByCount "14" @default.
- W2145046971 countsByYear W21450469712021 @default.
- W2145046971 countsByYear W21450469712023 @default.
- W2145046971 crossrefType "journal-article" @default.
- W2145046971 hasAuthorship W2145046971A5043345617 @default.
- W2145046971 hasConcept C107706756 @default.
- W2145046971 hasConcept C120665830 @default.
- W2145046971 hasConcept C121130766 @default.
- W2145046971 hasConcept C121332964 @default.
- W2145046971 hasConcept C128803854 @default.
- W2145046971 hasConcept C134306372 @default.
- W2145046971 hasConcept C146864707 @default.
- W2145046971 hasConcept C158693339 @default.
- W2145046971 hasConcept C197320386 @default.
- W2145046971 hasConcept C202579712 @default.
- W2145046971 hasConcept C26682833 @default.
- W2145046971 hasConcept C33923547 @default.
- W2145046971 hasConcept C34388435 @default.
- W2145046971 hasConcept C538625479 @default.
- W2145046971 hasConcept C62520636 @default.
- W2145046971 hasConceptScore W2145046971C107706756 @default.
- W2145046971 hasConceptScore W2145046971C120665830 @default.
- W2145046971 hasConceptScore W2145046971C121130766 @default.
- W2145046971 hasConceptScore W2145046971C121332964 @default.
- W2145046971 hasConceptScore W2145046971C128803854 @default.
- W2145046971 hasConceptScore W2145046971C134306372 @default.
- W2145046971 hasConceptScore W2145046971C146864707 @default.
- W2145046971 hasConceptScore W2145046971C158693339 @default.
- W2145046971 hasConceptScore W2145046971C197320386 @default.
- W2145046971 hasConceptScore W2145046971C202579712 @default.
- W2145046971 hasConceptScore W2145046971C26682833 @default.
- W2145046971 hasConceptScore W2145046971C33923547 @default.
- W2145046971 hasConceptScore W2145046971C34388435 @default.
- W2145046971 hasConceptScore W2145046971C538625479 @default.
- W2145046971 hasConceptScore W2145046971C62520636 @default.
- W2145046971 hasLocation W21450469711 @default.
- W2145046971 hasOpenAccess W2145046971 @default.
- W2145046971 hasPrimaryLocation W21450469711 @default.
- W2145046971 hasRelatedWork W1593596111 @default.
- W2145046971 hasRelatedWork W1977659907 @default.
- W2145046971 hasRelatedWork W1990842824 @default.
- W2145046971 hasRelatedWork W2006122712 @default.
- W2145046971 hasRelatedWork W2119836309 @default.
- W2145046971 hasRelatedWork W2145046971 @default.
- W2145046971 hasRelatedWork W2182692072 @default.
- W2145046971 hasRelatedWork W2383846213 @default.
- W2145046971 hasRelatedWork W128178425 @default.
- W2145046971 hasRelatedWork W2523039933 @default.
- W2145046971 hasVolume "252" @default.
- W2145046971 isParatext "false" @default.
- W2145046971 isRetracted "false" @default.
- W2145046971 magId "2145046971" @default.
- W2145046971 workType "article" @default.