An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

Same as → energy cascade

Named after L. F. Richardson (1922), Weather Prediction by Numerical Process (Cambridge Univ. Press); → cascade.

A condition for the onset of → instability in multilayer fluids which compares the balance between the restoring force of → buoyancy and the destabilizing effect of the → shear.

Named after the British meteorologist Lewis Fry Richardson (1881-1953), who first arrived in 1920 to the dimensionless ratio now called → Richardson number. The first formal proof of the criterion, however, came four decades later for → incompressible flows (Miles, J. W. 1961, J. Fluid Mech., 10, 496; Howard, L. N., 1961, J. Fluid Mech., 10, 509). Its extension to → compressible flows was demonstrated subsequently (Chimonas 1970, J. Fluid Mech., 43, 833); → criterion.

A dimensionless number which is used according to the → Richardson criterion to describe the condition for the → stability of a flow in the presence of vertical density stratification. If the → shear flow is characterized by linear variation of velocity and density, with velocities and densities ranging from U₁ to U₂ and ρ₁ to ρ₂ (ρ₂>ρ₁), respectively, over a depth H, then the Richardson number is expressed as: Ri = (ρ₂ - ρ₁) gH / ρ₀ (U₁ - U₂)². If Ri < 0.25, somewhere in the flow turbulence is likely to occur. For Ri > 0.25 the flow is stable.

→ Richardson criterion; → number.

The property of being very abundant.

→ rich; → -ness.

A classification of → galaxy clusters into six groups (0 to 5), as in the → Abell catalog. It depends on the number of galaxies in a given cluster that lie within a → magnitude range m₃ to m₃₊₂, where m₃ is the magnitude of the 3rd brightest member of the cluster. The first group contains 30-49 galaxies and the last group more than 299 galaxies.

→ richness; → group.

1) A question or statement so framed as to exercise one's ingenuity in answering it or discovering its meaning; conundrum.
2) A puzzling question, problem, or matter (Dictionary.com).

M.E. redel, redels, from O.E. rædels "riddle; counsel; conjecture; imagination;" cf. O.Fr. riedsal "riddle," O.Sax. radisli, M.Du. raetsel, Du. raadsel, O.H.G. radisle, Ger. Rätsel "riddle."

Kervas "riddle, puzzle" [Dehxodâ], Kurd. karvâs "riddle," of unknown origin.

A long, narrow elevation of the Earth's surface, generally sharp crested with steep sides, either independently or as part of a larger mountain or hill. See also: → submarine ridge, → wrinkle ridge, → mid-Atlantic ridge.

M.E. rigge; O.E. hrycg "spine, back of a man or beast" (cf. O.Fris. hregg, Du. rug, O.H.G. hrukki, Ger. Rücken "the back").

Ruk, from dialectal Tabari ruk "mountain, ridge;" cf. (Dehxodâ) raš "hill."

A 4th → rank tensor that characterizes the deviation of the geometry of space from the Euclidean type. The curvature tensor R^λ_μνκ is defined through the → Christoffel symbols Γ^λ_μν as follows: R^λ_μνκ = (∂Γ^λ_μκ)/(∂x^ν) - (∂Γ^λ_μν)/(∂x^κ) + Γ^η_μκΓ^λ_ην - Γ^η_μνΓ^λ_ηκ.

→ Riemannian geometry; → curvature; → tensor.

The combination of a → partial differential equation and a → piecewise constant → initial condition. The Riemann problem is a basic tool in a number of numerical methods for wave propagation problems. The canonical form of the Riemann problem is: ∂u/∂t + ∂f(u)/∂x = 0, x ∈ R, t > 0, u(x,0) = u_l if x < 0, and u(x,0) = u_r if x > 0 .

→ Riemann's geometry; → problem.

Same as → Riemannian geometry.

→ Riemannian; → geometry.

Of or pertaining to Georg Friedrich Bernhard Riemann (1826-1866) or his mathematics findings. → Riemannian geometry, → Riemannian manifold, → Riemannian metric, → Riemann problem, → Riemann curvature tensor.

After the German mathematician Georg Friedrich Bernhard Riemann (1826-1866), the inventor of the elliptic form of → non-Euclidean geometry, who made important contributions to analysis and differential geometry, some of them paving the way for the later development of → general relativity.

A → non-Euclidean geometry in which there are no → parallel lines, and the sum of the → angles of a → triangle is always greater than 180°. Riemannian figures can be thought of as figures constructed on a curved surface. The geometry is called elliptic because the section formed by a plane that cuts the curved surface is an ellipse.

→ Riemannian; → geometry.

A → manifold on which there is a defined → Riemannian metric (Douglas N. Clark, 2000, Dictionary of Analysis, Calculus, and Differential Equations).

→ Riemannian; → metric.

A positive-definite inner product, (.,.)_x, on T_x(M), the tangent space to a manifold M at x, for each x  ∈ M, which varies continually with x (Douglas N. Clark, Dictionary of Analysis, Calculus, and Differential Equations).

→ Riemannian; → metric.

1) General: a gap or break made by splitting, cleaving, etc.; fissure; cleft.
2) Geology: A narrow cleft, fissure, or other opening in rock, made by cracking or splitting.
3) Geology: An elongated trough in the Earth's crust bounded by → faults.

M.E., from a Scandinavian source; cf. Dan., Norw. rift "a cleft."

1) Câk "fissure, rupture, cleft, crack," related to caqidan "to drive a nail, strike together, fix a spike;" caxidan "to quarrel, strive;" diatectal Shughni cuγ, Roshani coγ "breaking, tearing, ripping up;" Malâyeri ceqidan "cracking of a cold porcelain bowl when receiving hot water;" Yazghulami cok-, coxt "to pound, to stamp;" Wakhi cuk-, cukt "to strike;" Ossetic cædyn "to shake, strike iron;" Lori cok "a mark fixed to separate two grounds;" Sogd. cax "to battel, fight;" Mid.Pers. (prefixed) pacên "copy" (see also Cheung 2007). Gosal-darré, from gosal, → fault, + darré, → valley.

A long, narrow valley formed by the lowering of land between two → faults. Also called → graben.

→ rift; → valley.

The brightest star in the constellation → Orion (visual magnitude 0.18). A → blue supergiant of type B8 Iab with an initial mass of 17 solar masses, Rigel is 773 light-years away, and actually shines with the light of 40,000 Suns. It is accompanied by a fairly bright, seventh magnitude companion nine seconds of arc apart. The companion is itself double, the components much fainter and much less massive → main sequence stars of type B.

Rigel "foot," short for Ar. rijl al-jauza' (رجل‌الجوزاء) "the foot of jauza'." The latter word means "the manifest one," initially "black sheep with white middle." The Gk. figure was translated as such because of its conspicuousness among other constellations.

Rejl, from Ar., as above.

Same as the star → Alpha Centauri.

From Ar. Rijl al-Qanturis "foot of Centaurus," from rijl "foot," + Qanturis Arabicized → Centaurus.

Pâ-ye Kantawros, "foot of Centaurus," from pâ, → foot, + Kentawros, → Centaurus.

1a) Straight, free from curves, angles, or irregularities. → right ascension.
1b) Opposite of → left. → right-hand rule, → right-hand screw rule.
2) In accordance with fact, reason, or truth; correct or true.
3) Something that a person is or should be morally or legally allowed to have, get, or do (Merriam-Webster).

M.E.; O.E. reht, riht; cf. O.H.G. reht, Ger. recht, O.N. rettr, Goth. raihts; P.Gmc. *rekhtaz, cognate with Pers. râst, as below.

1) Râst "right, true; just, upright, straight;" Mid.Pers. râst "true, straight, direct;" Soghdian rəšt "right;" O.Pers. rāsta- "straight, true," rās- "to be right, straight, true;" Av. rāz- "to direct, put in line, set," razan- "order;" related to Mid.Pers. rây-, râyênitan "to arrange;" Mod.Pers. raj "line, row," variants raž, rak, râk, rezg (Lori), radé, râdé "line, rule, row," rasté, râsté "row, a market with regular ranges of shops;" ris, risé "straight;" cf. Skt. raj- "to direct, stretch," rjuyant- "walking straight;" Gk. orektos "stretched out;" L. regere "to lead straight, guide, rule," p.p. rectus "right, straight;" PIE base *reg- "move in a straight line," hence, "to direct, rule;"
2) Dorost "correct, whole, complete, healthy," → integral.
3) Râšan, related to râst, as above; cf. Mid.Pers. Rašn "Justice deity; calendar 18th day;" Av. rašnu- "the Zoroastrian Justice deity, orientation."

An angle of 90°.

→ right; → angle.