| Section S | S index | 81-89 of 1376 terms |
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scalar product(Also called dot product, direct product, inner product.) A scalar equal to the product of the magnitudes of any two vectors and the cosine of the angle θ between their positive directions. For two vectors A and B, the scalar product is most commonly written A · B, read “A dot B,” and occasionally as (AB). If the vectors A and B have the components Ax, Bx, Ay, By, and Az, Bz along rectangular Cartesian x, y, and z axes, respectively, then  If a scalar product is zero, one of the vectors is zero or else the two are perpendicular. See vector product.
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scalarAny physical quantity with a field that can be described by a single numerical value at each point in space. A scalar quantity is distinguished from a vector quantity by the fact that a scalar quantity possesses only magnitude, whereas a vector quantity possesses both magnitude and direction. Thus, pressure is a scalar quantity and velocity is a vector quantity.
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scale analysisAn analysis method usually using the nondimensional equations to determine which terms are dominant for a particular phenomenon or situation so that the smaller terms can be neglected, resulting in a simplified set of equations. For example, the quasigeostrophic equations were derived by a scale analysis.
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scale factor(Also called map scale, map factor.) The ratio between the distance separating two points on a map of the earth's surface at a standard latitude (or latitudes) and the distance between the corresponding points on the earth's surface itself. For most map projections, this factor is a slowly varying function of latitude, and for synoptic- chart base maps it is usually of the order of 10−6 to 10−7. The scale factor is sometimes defined as the reciprocal of the above ratio. Compare conformal map.
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scale1. Regular markings on an instrument used to allow the reading of the measured quantity or setting. 2. A factor that relates the indication of the measuring instrument to the value of the quantity. 3. An order of magnitude aid in estimating meteorological parameters (e.g., mesoscale).
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